Carlos Forsythe; Xiaodong Zhou; Takashi Taniguchi; Kenji Watanabe; Abhay Pasupathy; Pilkyung Moon; Mikito Koshino; Philip Kim; Cory R. Dean arXiv:1710.01365 , undefined (2017) [Link]
The ability to manipulate two-dimensional (2D) electrons with external electric fields provides a route to synthetic band engineering. By imposing artificially designed and spatially periodic superlattice (SL) potentials, 2D electronic properties can be further engineered beyond the constraints of naturally occurring atomic crystals. Here we report a new approach to fabricate high mobility SL devices by integrating surface dielectric patterning with atomically thin van der Waals materials. By separating the device assembly and SL fabrication processes, we address the intractable tradeoff between device processing and mobility degradation that constrains SL engineering in conventional systems. The improved electrostatics of atomically thin materials moreover allows smaller wavelength SL patterns than previously achieved. Replica Dirac cones in ballistic graphene devices with sub 40nm wavelength SLs are demonstrated, while under large magnetic fields we report the fractal Hofstadter spectra from SLs with designed lattice symmetries vastly different from that of the host crystal. Our results establish a robust and versatile technique for band structure engineering of graphene and related van der Waals materials with dynamic tunability.
Matthew Yankowitz, Jeil Jung, Evan Laksono, Nicolas Leconte, Bheema L. Chittari, K. Watanabe, T. Taniguchi, Shaffique Adam, David Graf, Cory R. Dean arXiv:1707.09054 , undefined (2017) [Link]
Heterostructures of atomically-thin materials have attracted significant interest owing to their ability to host novel electronic properties fundamentally distinct from their constituent layers. In the case of graphene on boron nitride, the closely-matched lattices yield a moir\'e superlattice that modifies the graphene electron dispersion and opens gaps both at the primary Dirac point (DP) and the moir\'e-induced secondary Dirac point in the valence band. While significant effort has focused on controlling the superlattice period via the rotational stacking order, the role played by the magnitude of the interlayer coupling has received comparatively little attention. Here, we modify the interaction between graphene and boron nitride by tuning their separation with hydrostatic pressure. We observe a dramatic enhancement of the primary DP gap with increasing pressure, but little change in the secondary DP gap. Our surprising results identify the critical role played by atomic-scale structural deformations of the graphene lattice and reveal new opportunities for band structure engineering in van der Waals heterostructures.
Martin V. Gustafsson, Matthew Yankowitz, Carlos Forsythe, Daniel Rhodes, Kenji Watanabe, Takashi Taniguchi, James Hone, Xiaoyang Zhu, Cory R. Dean arXiv:1707.08083 , (2017) [Link]
Monolayer transition metal dichalcogenides offer a unique platform to study the behavior of electrons with coupled spin and valley degrees of freedom. However, intrinsic material defects and difficulties in making ohmic contact at low temperature complicate magnetotransport measurements of semiconducting TMDs, thus signatures of their intricate spin phenomena have largely remained elusive. Here, we report measurements of the Landau level dispersion in monolayer WSe2 for both electrons and holes as a function of doping and magnetic field. We achieve this by probing local variations in the chemical potential and electronic compressibility of the material using single-electron transistors. The gaps between Landau levels follow an unusual sequence, where the Zeeman energy in the valence band is several times higher than the cyclotron energy. The Zeeman effect is far stronger than predicted by a single-particle model and tunes significantly with doping, suggesting exceptionally strong exchange-driven many-body interactions.
J.I.A.Li, C. Tan, S. Chen, Y. Zeng, T. Taniguchi, K. Watanabe, J. Hone, C.R. Dean science 358, 648-652 (2017) [DOI: 10.1126/science.aao2521]
The unique Landau level spectrum of bilayer graphene (BLG) is predicted to support a non-Abelian even-denominator fractional quantum Hall state (FQHE) similar to the Embedded Image state first identified in GaAs. However, the nature of this state has remained difficult to characterize. Here we report transport measurements of a robust sequence of even denominator FQHE in dual gated BLG devices. Parallel field measurement confirms the spin-polarized nature of the ground state, consistent with the Pfaffian/anti-Pfaffian description. The sensitivity of the even denominator states to both filling fraction and transverse displacement field, provides new opportunities for tunability. Our results suggest that BLG is a platform where topological ground states with possible non-Abelian excitations can be manipulated and controlled.
B.M. Hunt, J.I.A. Li, A.A. Zibrov, L. Wang, T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean, M. Zaletel, R.C. Ashoori, A.F. Young Nature Comm. 8, 948 (2017) [10.1038/s41467-017-00824-w]
The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.
Xiaomeng Liu, Lei Wang, Kin Chung Fong, Yuanda Gao, Patrick Maher, Kenji Watanabe, Takashi Taniguchi, James Hone, Cory Dean, Philip Kim Phys. Rev. Lett. 119, 056802 (2017) [10.1103/PhysRevLett.119.056802] [Link]
Coulomb interaction between two closely spaced parallel layers of electron system can generate the frictional drag effect by interlayer Coulomb scattering. Employing graphene double layers separated by few layer hexagonal boron nitride (hBN), we investigate density tunable magneto- and Hall-drag under strong magnetic fields. The observed large magneto-drag and Hall-drag signals can be related with Laudau level (LL) filling status of the drive and drag layers. We find that the sign and magnitude of the magneto- and Hall-drag resistivity tensor can be quantitatively correlated to the variation of magneto-resistivity tensors in the drive and drag layers, confirming a theoretical formula for magneto-drag in the quantum Hall regime. The observed weak temperature dependence and ∼B2 dependence of the magneto-drag are qualitatively explained by Coulomb scattering phase-space argument.
Xu Cui; En-Min Shih; Luis A. Jauregui; Sang Hoon Chae; Young Duck Kim; Baichang Li; Dongjea Seo; Kateryna Pistunova; Jun Yin; Ji-Hoon Park; Heon-Jin Choi; Young Hee Lee; Kenji Watanabe; Takashi Taniguchi; Philip Kim; Cory R. Dean; and James C. Hone Nano Lett. 17, (2017) [10.1021/acs.nanolett.7b01536] [Link]
Monolayer MoS2, among many other transition metal dichalcogenides, holds great promise for future applications in nanoelectronics and optoelectronics due to its ultrathin nature, flexibility, sizable band gap, and unique spin-valley coupled physics. However, careful study of these properties at low temperature has been hindered by an inability to achieve low-temperature Ohmic contacts to monolayer MoS2, particularly at low carrier densities. In this work, we report a new contact scheme that utilizes cobalt (Co) with a monolayer of hexagonal boron nitride (h-BN) that has the following two functions: modifies the work function of Co and acts as a tunneling barrier. We measure a flat-band Schottky barrier of 16 meV, which makes thin tunnel barriers upon doping the channels, and thus achieve low-T contact resistance of 3 kΩ.μm at a carrier density of 5.3 × 1012/cm2. This further allows us to observe Shubnikov–de Haas oscillations in monolayer MoS2 at much lower carrier densities compared to previous work.
J.I.A. Li, T. Taniguchi, K. Watanabe, J. Hone, C.R. Dean Nat. Phys. 22, 274 (2017) [doi:10.1038/nphys4140]
A spatially indirect exciton is created when an electron and a hole, confined to separate layers of a double quantum well system, bind to form a composite boson1, 2. Such excitons are long-lived, and in the limit of strong interactions are predicted to undergo a Bose–Einstein condensate-like phase transition into a superfluid ground state1, 2, 3. Here, we report evidence of an exciton condensate in the quantum Hall effect regime of double-layer structures of bilayer graphene. Interlayer correlation is identified by quantized Hall drag at matched layer densities, and the dissipationless nature of the phase is confirmed in the counterflow geometry4, 5. A selection rule for the condensate phase is observed involving both the orbital and valley indices of bilayer graphene. Our results establish double bilayer graphene as an ideal system for studying the rich phase diagram of strongly interacting bosonic particles in the solid state.
Annette S. Plaut, Ulrich Wurstbauer, Sheng Wang, Antonio L. Levy, Lara Fernandes dos Santos, Lei Wang, Loren N. Pfeiffer, Kenji Watanabe, Takashi Taniguchi, Cory R. Dean, James Hone, Aron Pinczuk, Jorge M. Garcia Carbon 114, (2017) [10.1016/j.carbon.2016.12.031]
We demonstrate growth of single-layer graphene (SLG) on hexagonal boron nitride (h-BN) by molecular beam epitaxy (MBE), only limited in area by the finite size of the h-BN flakes. Using atomic force microscopy and micro-Raman spectroscopy, we show that for growth over a wide range of temperatures (500 °C – 1000 °C) the deposited carbon atoms spill off the edge of the h-BN flakes. We attribute this spillage to the very high mobility of the carbon atoms on the BN basal plane, consistent with van der Waals MBE. The h-BN flakes vary in size from 30 μm to 100 μm, thus demonstrating that the migration length of carbon atoms on h-BN is greater than 100 μm. When sufficient carbon is supplied to compensate for this loss, which is largely due to this fast migration of the carbon atoms to and off the edges of the h-BN flake, we find that the best growth temperature for MBE SLG on h-BN is ∼950 °C. Self-limiting graphene growth appears to be facilitated by topographic h-BN surface features: We have thereby grown MBE self-limited SLG on an h-BN ridge. This opens up future avenues for precisely tailored fabrication of nano- and hetero-structures on pre-patterned h-BN surfaces for device applications.
Johannes Jobst; Alexander J. H. van der Torren; Eugene E. Krasovskii; Jesse Balgley; Cory R. Dean; Rudolf M. Tromp; Sense Jan van der Molen Nature Comm. 7, 13621 (2016) [10.1038/ncomms13621]
High electron mobility is one of graphene’s key properties, exploited for applications and fundamental research alike. Highest mobility values are found in heterostructures of graphene and hexagonal boron nitride, which consequently are widely used. However, surprisingly little is known about the interaction between the electronic states of these layered systems. Rather pragmatically, it is assumed that these do not couple significantly. Here we study the unoccupied band structure of graphite, boron nitride and their heterostructures using angle-resolved reflected-electron spectroscopy. We demonstrate that graphene and boron nitride bands do not interact over a wide energy range, despite their very similar dispersions. The method we use can be generally applied to study interactions in van der Waals systems, that is, artificial stacks of layered materials. With this we can quantitatively understand the ‘chemistry of layers’ by which novel materials are created via electronic coupling between the layers they are composed of.
Yong-Tao Cui, Bo Wen, Eric Y. Ma, Georgi Diankov, Zheng Han, Francois Amet, Takashi Taniguchi, Kenji Watanabe, David Goldhaber-Gordon, Cory R. Dean, Zhi-Xun Shen Phys. Rev. Lett. 117, undefined (2016) [10.1103/PhysRevLett.117.186601] [Link]
We report simultaneous transport and scanning microwave impedance microscopy to examine the
correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime
in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized
transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still
conductive. This result points to a revised understanding of transport quantization when carriers are
accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in
graphene and related topological states in other two-dimensional electron systems.
Shaowen Chen, Zheng Han, Mirza M. Elahi, K. M. Masum Habib, Lei Wang, Bo Wen, Yuanda Gao, Takashi Taniguchi, Kenji Watanabe, James Hone, Avik W. Ghosh, Cory R. Dean Science 353, 1522-1525 (2016) [10.1126/science.aaf5481]
Electrons transmitted across a ballistic semiconductor junction undergo refraction, analogous to light rays across an optical boundary. A pn junction theoretically provides the equivalent of a negative index medium, enabling novel electron optics such as negative refraction and perfect (Veselago) lensing. In graphene, the linear dispersion and zero-gap bandstructure admit highly transparent pn junctions by simple electrostatic gating, which cannot be achieved in conventional semiconductors. Moreover ballistic transport over micron length scales at ambient temperature has been realized, providing an ideal platform to realize a new generation of device based on electron lensing. Robust demonstration of these effects, however, has not been forthcoming. Here we employ transverse magnetic focusing to probe propagation across an electrostatically defined graphene junction. We find perfect agreement with the predicted Snells law for electrons, including observation of both positive and negative refraction. Resonant transmission across the pn junction provides a direct measurement of the angle dependent transmission coefficient, and we demonstrate good agreement with theory. Comparing experimental data with simulation reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing novel electron optics based on graphene pn junctions.
J.I.A. Li; T. Taniguchi; K. Watanabe; J. Hone; A. Levchenko; C.R. Dean Phys. Rev. Lett. 117, 46802 undefined (2016) [10.1103/PhysRevLett.117.046802]
Coulomb drag between parallel quantum wells provides a uniquely sensitive measurement of electron correlations since the drag response depends on interactions only. Recently it has been demonstrated that a new regime of strong interactions can be accessed for devices consisting of two monlolayer graphene (MLG) crystals, separated by few layer hexagonal boron-nitride. Here we report measurement of Coulomb drag in a double bilayer graphene (BLG) stucture, where the interaction potential is anticipated to be yet further enhanced compared to MLG. At low temperatures and intermediate densities a new drag response with inverse sign is observed, distinct from the momentum and energy drag mechanisms previously reported in double MLG. We demonstrate that by varying the device aspect ratio the negative drag component can be suppressed and a response showing excellent agreement with the density and temperature dependance predicted for momentum drag in double BLG is found. Our results pave the way for pursuit of emergent phases in strongly interacting bilayers, such as the exciton condensate.
Tarun Chari; Rebeca Ribeiro-Palau; Cory R. Dean; Kenneth L. Shepard Nano Letters , undefined (2016) [doi:10.1021/acs.nanolett.6b01657]
Robust electrical contact of bulk conductors to two-dimensional (2D) material, such as graphene, is critical to the use of these 2D materials in practical electronic devices. Typical metallic contacts to graphene, whether edge or areal, yield a resistivity of no better than 100 Ω-µm but are typically > 10 kΩ-µm. In this Letter, we employ single crystal graphite for the bulk contact to graphene instead of conventional metals. The graphite contacts exhibit a transfer length up to four times longer than in conventional metallic contacts. Furthermore, we are able to drive the contact resistivity to as little as 6.6 Ω-µm2 by tuning the relative orientation of the graphite and graphene crystals. We find that the contact resistivity exhibits a 60° periodicity corresponding to crystal symmetry with additional sharp decreases around 22° and 39°, which are among the commensurate angles of twisted bi-layer graphene.
Sanfeng Wu; Lei Wang; You Lai; Wen-Yu Shan; Grant Aivazian; Xian Zhang; Takashi Taniguchi; Kenji Watanabe; Di Xiao; Cory Dean; James Hone; Zhiqiang Li; Xiaodong Xu Sci. Adv. 2, 5 undefined (2016) [doi:10.1126/sciadv.1600002]
In conventional light-harvesting devices, the absorption of a single photon only excites one electron, which sets the standard limit of power-conversion efficiency, such as the Shockley-Queisser limit. In principle, generating and harnessing multiple carriers per absorbed photon can improve efficiency and possibly overcome this limit. We report the observation of multiple hot-carrier collection in graphene/boron-nitride Moiré superlattice structures. A record-high zero-bias photoresponsivity of 0.3 A/W (equivalently, an external quantum efficiency exceeding 50%) is achieved using graphene’s photo-Nernst effect, which demonstrates a collection of at least five carriers per absorbed photon. We reveal that this effect arises from the enhanced Nernst coefficient through Lifshtiz transition at low-energy Van Hove singularities, which is an emergent phenomenon due to the formation of Moiré minibands. Our observation points to a new means for extremely efficient and flexible optoelectronics based on van der Waals heterostructures.
A. W. Tsen, B. Hunt, Y. D. Kim, Z. J. Yuan, S. Jia, R. J. Cava, J. Hone, P. Kim, C. R. Dean, A. N. Pasupathy Nature Physics , (2015) [doi:10.1038/nphys3579] [Link]
Two-dimensional (2D) materials are not expected to be metals at low temperature due to electron localization. Consistent with this, pioneering studies on thin films reported only superconducting and insulating ground states, with a direct transition between the two as a function of disorder or magnetic field. However, more recent works have revealed the presence of an intermediate metallic state occupying a substantial region of the phase diagram whose nature is intensely debated. Here, we observe such a state in the disorder-free limit of a crystalline 2D superconductor, produced by mechanical co-lamination of NbSe2 in inert atmosphere. Under a small perpendicular magnetic field, we induce a transition from superconductor to the intermediate metallic state. We find a new power law scaling with field in this phase, which is consistent with the Bose metal model where metallic behavior arises from strong phase fluctuations caused by the magnetic field.
D. K. Efetov, L. Wang, C. Handschin, K. B. Efetov, J. Shuang, R. Cava, T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean, P. Kim Nature Physics , (2015) [doi:10.1038/nphys3583] [Link]
Electrons incident from a normal metal onto a superconductor are reflected back as holes - a process called Andreev reflection. In a normal metal where the Fermi energy is much larger than a typical superconducting gap, the reflected hole retraces the path taken by the incident electron. In graphene with ultra low disorder, however, the Fermi energy can be tuned to be smaller than the superconducting gap. In this unusual limit, the holes are expected to be reflected specularly at the superconductor-graphene interface due to the onset of interband Andreev processes, where the effective mass of the reflected holes change sign. Here we present measurements of gate modulated Andreev reflections across the low disorder van der Waals interface formed between graphene and the superconducting NbSe2. We find that the conductance across the graphene-superconductor interface exhibits a characteristic suppression when the Fermi energy is tuned to values smaller than the superconducting gap, a hallmark for the transition between intraband retro- and interband specular- Andreev reflections.
Lei Wang, Yuanda Gao, Bo Wen, Zheng Han, Takashi Taniguchi, Kenji Watanabe, Mikito Koshino, James Hone, Cory R. Dean Science 350, 6365 1231-1234 (2015) [10.1126/science.aad2102] [Link]
The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to the trivial case of low Bloch band filling where only the Landau level index plays a significant role. Here we report measurement of high mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observe coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, a new series of states appear at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point towards a new type of many-body state.
Tarun Chari, Inanc Meric, Cory Dean, and Kenneth Shepard IEEE 12, (2015) [10.1109/TED.2015.2482823]
We present the characterization of ballistic
graphene field-effect transistors (GFETs) with an effective oxide
thickness of 3.5 nm. Graphene channels are fully encapsulated
within hexagonal boron nitride, and self-aligned contacts are
formed to the edge of the single-layer graphene. Devices of
channel lengths (LG) down to 67 nm are fabricated, and a
virtual-source transport model is used to model the resulting
current–voltage characteristics. The mobility and sourceinjection
velocity as a function of LG yields a mean-free-path,
ballistic velocity, and effective mobility of 850 nm, 9.3×107 cm/s,
and 13 700 cm2/Vs, respectively, which are among the highest
velocities and mobilities reported for GFETs. Despite these bestin-class
attributes, these devices achieve transconductance (gm)
and output conductance (gds) of only 600 and 300 µS/µm,
respectively, due to the fundamental limitations of graphene’s
quantum capacitance and zero-bandgap. gm values, which are
less than those of comparable ballistic silicon devices, benefit from
the high ballistic velocity in graphene but are degraded by an
effective gate capacitance reduced by the quantum capacitance.
The gds values, which limit the effective power gain achievable
in these devices, are significantly worse than comparable silicon
devices due to the properties of the zero-bandgap graphene
Patrick Maher; Lei Wang; Yuanda Gao; Carlos Forsythe; Takashi Taniguchi; Kenji Watanabe; Dmitry Abanin; Zlatko Papić; Paul Cadden-Zimansky; James Hone; Philip Kim; Cory R. Dean Science 334, 6192 (2014) [10.1126/science.1252875]
Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse electric field. This result provides a model platform to study the role of symmetry breaking in emergent states with distinct topological order.
Chen, Zheyuan; Darancet, Pierre; Wang, Lei; Crowther, Andrew; Gao, Yuanda; Dean, Cory; Taniguchi, Takashi; Watanabe, Kenji; Hone, James; Marianetti, Chris; Brus, Louis. ACS Nano 8, 3 (2014) [10.1021/nn500265f]
We present a detailed study of gaseous Br2 adsorption and charge transfer on graphene, combining in situ Raman spectroscopy and density functional theory (DFT). When graphene is encapsulated by hexagonal boron nitride (h-BN) layers on both sides, in a h-BN/graphene/h-BN sandwich structure, it is protected from doping by strongly oxidizing Br2. Graphene supported on only one side by h-BN shows strong hole doping by adsorbed Br2. Using Raman spectroscopy, we determine the graphene charge density as a function of pressure. DFT calculations reveal the variation in charge transfer per adsorbed molecule as a function of coverage. The molecular adsorption isotherm (coverage versus pressure) is obtained by combining Raman spectra with DFT calculations. The Fowler–Guggenheim isotherm fits better than the Langmuir isotherm. The fitting yields the adsorption equilibrium constant (0.31 Torr–1) and repulsive lateral interaction (20 meV) between adsorbed Br2 molecules. The Br2 molecule binding energy is 0.35 eV. We estimate that at monolayer coverage each Br2 molecule accepts 0.09 e– from single-layer graphene. If graphene is supported on SiO2 instead of h-BN, a threshold pressure is observed for diffusion of Br2 along the (somewhat rough) SiO2/graphene interface. At high pressure, graphene supported on SiO2 is doped by adsorbed Br2 on both sides.
Lei Wang; Inanc Meric; Pinshane Y. Huang; Qun Gao; Yuanda Gao; Helen Tran; Takashi Taniguchi; Kenji Watanabe; Luis M. Campos; David A. Muller; Jun Guo,; Philip Kim; James Hone; Kenneth L. Shepard; Cory R. Dean Science 342, 614-617 (2013) [10.1126/science.1244358]
Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal boron nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality electrical contact. Here, we report a contact geometry in which we metalize only the 1D edge of a 2D graphene layer. In addition to outperforming conventional surface contacts, the edge-contact geometry allows a complete separation of the layer assembly and contact metallization processes. In graphene heterostructures, this enables high electronic performance, including low-temperature ballistic transport over distances longer than 15 micrometers, and room-temperature mobility comparable to the theoretical phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2D materials.
Li, Yilei; Rao, Yi; Mak, Kin; You, Yumeng; Wang, Shuyuan; Dean, Cory; Heinz, Tony F; Nano letters 13, 7 3329–3333 (2013) [10.1021/nl401561r]
We have measured optical second-harmonic generation (SHG) from atomically thin samples of MoS2 and h-BN with one to five layers. We observe strong SHG from materials with odd layer thickness, for which a noncentrosymmetric structure is expected, while the centrosymmetric materials with even layer thickness do not yield appreciable SHG. SHG for materials with odd layer thickness was measured as a function of crystal orientation. This dependence reveals the rotational symmetry of the lattice and is shown to provide a purely optical method of determining the orientation of crystallographic axes. We report values for the nonlinearity of monolayers and odd-layers of MoS2 and h-BN and compare the variation as a function of layer thickness with a model that accounts for wave propagation effects.
Dean, CR; Wang, L; Maher, P; Forsythe, C; Ghahari, F; Gao, Y; Katoch, J; Ishigami, M; Moon, P; Koshino, M; Nature 497, 7451 598-602 (2013) [10.1038/nature12186]
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. In 1976 Douglas Hofstadter theoretically considered the intersection of these two problems and discovered that 2D electrons subjected to both a magnetic field and a periodic electrostatic potential exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from a delicate interplay between the characteristic lengths associated with the two quantizing fields, and represents one of the first quantum fractals discovered in physics. In the decades since, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical crystalline systems (<1 nm periodicity) require impossibly large magnetic fields to reach the commensurability condition, while in artificially engineered structures (>100 nm), the corresponding fields are too small to completely overcome disorder. Here we demonstrate that moire superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a nearly ideal-sized periodic modulation, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall effect features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of Hofstadter's spectrum in graphene provides the further opportunity to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.
Inanc Meric; Cory R Dean; Nicholas Petrone ; Lei Wang; James Hone; Philip Kim; Kenneth L Shepard; Proceedings of the IEEE 101, 7 (2013) [10.1109/JPROC.2013.2257634]
Two-dimensional atomic sheets of graphene represent a new class of nanoscale materials with potential applications in electronics. However, exploiting the intrinsic characteristics of graphene devices has been problematic due to impurities and disorder in the surrounding dielectric and graphene/dielectric interfaces. Recent advancements in fabricating graphene heterostructures by alternately layering graphene with crystalline hexagonal boron nitride (hBN), its insulating isomorph, have led to an order of magnitude improvement in graphene device quality. Here, recent developments in graphene devices utilizing boron-nitride dielectrics are reviewed. Field-effect transistor (FET) characteristics of these systems at high bias are examined. Additionally, existing challenges in material synthesis and fabrication and the potential of graphene/BN heterostructures for novel electronic applications are discussed.
Maher, P; Dean, CR; Young, AF; Taniguchi, T; Watanabe, K; Shepard, KL; Hone, J; Kim, P; Nature Physics (2013) [10.1038/nphys2528]
The quantum spin Hall effect is characterized by spin-polarized counter-propagating edge states 1, 2, 3. It has been predicted that this edge state configuration could occur in graphene when spin-split electron-and hole-like Landau levels are forced to cross at the edge of the sample 4, 5, 6. In particular, a quantum-spin-Hall analogue has been predicted in bilayer graphene with a Landau level filling factor ν= 0 if the ground state is a spin ferromagnet 7. Previous studies have demonstrated that the bilayer ν= 0 state is an ...
Burson, Kristen M; Cullen, William G; Shaffique, Adam; Dean, Cory; Watanabe, Kenji; Taniguchi, Takashi; Kim, Philip; Fuhrer, Michael S; Nano letters (2013) [10.1021/nl4012529]
Kelvin probe microscopy in ultrahigh vacuum is used to image the local electrostatic potential fluctuations above hexagonal boron nitride (h-BN) and SiO2, common substrates for graphene. Results are compared to a model of randomly distributed charges in a two-dimensional (2D) plane. For SiO2, the results are well modeled by 2D charge densities ranging from 0.24 to 2.7× 1011 cm–2, while h-BN displays potential fluctuations 1–2 orders of magnitude lower than SiO2, consistent with the improvement in charge carrier mobility ...
Wang, Lei; Chen, Zheyuan; Dean, Cory; Taniguchi, Takashi; Watanabe, Kenji; Brus, Louis; Hone, James; ACS nano (2012) [10.1021/nn304004s]
Using Raman spectroscopy, we study the environmental sensitivity of mechanically exfoliated and electrically floating single-layer graphene transferred onto a hexagonal boron nitride (h-BN) substrate, in comparison with graphene deposited on a SiO2 substrate. In order to understand and isolate the substrate effect on graphene electrical properties, we model and correct for Raman optical interference in the substrates. As-deposited and unannealed graphene shows a large I2D/IG ratio on both substrates, indicating extremely high quality, close to that of graphene suspended in vacuum. Thermal annealing strongly activates subsequent environmental sensitivity on the SiO2 substrate; such activation is reduced but not eliminated on the h-BN substrate. In contrast, in a h-BN/graphene/h-BN sandwich structure, with graphene protected on both sides, graphene remains pristine despite thermal processing. Raman data provide a deeper understanding of the previously observed improved graphene electrical conductivity on h-BN substrates. In the sandwich structure, the graphene 2D Raman feature has a higher frequency and narrower line width than in pristine suspended graphene, implying that the local h-BN environment modestly yet measurably changes graphene electron and phonon dispersions.
Chae, Jungseok; Jung, Suyong; Young, Andrea F; Dean, Cory R; Wang, Lei; Gao, Yuanda; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L; Physical Review Letters 109, 11 116802 (2012) [10.1103/PhysRevLett.109.116802]
In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200 meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.
Young, AF; Dean, CR; Meric, I; Sorgenfrei, S; Ren, H; Watanabe, K; Taniguchi, T; Hone, J; Shepard, KL; Kim, P; Physical Review-Section B-Condensed Matter 85, 23 235458 (2012) [10.1103/PhysRevB.85.235458] [Link]
We report on a capacitance study of dual gated bilayer graphene. The measured capacitance allows us to probe the electronic compressibility as a function of carrier density, temperature, and applied perpendicular electrical displacement D̅ . As a band gap is induced with increasing D̅ , the compressibility minimum at charge neutrality becomes deeper but remains finite, suggesting the presence of localized states within the energy gap. Temperature dependent capacitance measurements show that compressibility is sensitive to the intrinsic band gap. For large displacements, an additional peak appears in the compressibility as a function of density, corresponding to the presence of a one-dimensional van Hove singularity (vHs) at the band edge arising from the quartic bilayer graphene band structure. For D̅ >0, the additional peak is observed only for electrons, while for D̅ <0 the peak appears only for holes. This asymmetry can be understood in terms of the finite interlayer separation and may be useful as a direct probe of the layer polarization.
Garcia, Jorge M; Wurstbauer, Ulrich; Levy, Antonio; Pfeiffer, Loren N; Pinczuk, Aron; Plaut, Annette S; Wang, Lei; Dean, Cory R; Buizza, Roberto; Van Der Zande, Arend; Solid State Communications 152, 12 975–978 (2012) [10.1016/j.ssc.2012.04.005]
The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms.
Petrone, Nicholas; Dean, Cory R; Meric, Inanc; van der Zande, Arend M; Huang, Pinshane Y; Wang, Lei; Muller, David; Shepard, Kenneth L; Hone, James; Nano letters 12, 6 2751-2756 (2012) [10.1021/nl204481s] [Link]
While chemical vapor deposition (CVD) promises a scalable method to produce large-area graphene, CVD-grown graphene has heretofore exhibited inferior electronic properties in comparison with exfoliated samples. Here we test the electrical transport properties of CVD-grown graphene in which two important sources of disorder, namely grain boundaries and processing-induced contamination, are substantially reduced. We grow CVD graphene with grain sizes up to 250 μm to abate grain boundaries, and we transfer graphene utilizing a novel, dry-transfer method to minimize chemical contamination. We fabricate devices on both silicon dioxide and hexagonal boron nitride (h-BN) dielectrics to probe the effects of substrate-induced disorder. On both substrate types, the large-grain CVD graphene samples are comparable in quality to the best reported exfoliated samples, as determined by low-temperature electrical transport and magnetotransport measurements. Small-grain samples exhibit much greater variation in quality and inferior performance by multiple measures, even in samples exhibiting high field-effect mobility. These results confirm the possibility of achieving high-performance graphene devices based on a scalable synthesis process.
Dean, C; Young, AF; Wang, L; Meric, I; Lee, G-H; Watanabe, K; Taniguchi, T; Shepard, K; Kim, P; Hone, J; Solid State Communications 152, 15 1275–1282 (2012) [10.1016/j.ssc.2012.04.021] [Link]
The two dimensional charge carriers in monolayer and bilayer graphene are described by massless and massive chiral Dirac Hamiltonians, respectively. These two-dimensional materials are predicted to exhibit a wide range of behavior, etc. However, graphene devices on a typical three-dimensional insulating substrates such as SiO2 are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene. We have developed a novel technique for substrate engineering of graphene devices using layered dielectric materials to build graphene based vertical heterostructures. We employ hBN, an insulating isomorph of graphite, as a substrate and gate dielectric for graphene electronics. In this review, we describe the fabrication and characterization of high-quality exfoliated mono- and bilayer graphene devices on single-crystal hBN substrates, using a mechanical transfer process. Graphene devices on hBN substrates have mobilities and carrier inhomogeneities that are almost an order of magnitude better than devices on SiO2. We use the enhanced mobility of electrons in hBN supported graphene to investigate the effects of electronic interactions. We find that interactions drive spontaneous breaking of the emergent SU(4) symmetry of the graphene Landau levels, leading to a variety of non-trivial integer and fractional quantum Hall states. The ability to assemble crystalline layered materials in a controlled way permits the fabrication of graphene devices on other promising dielectrics and allows for the realization of more complex graphene heterostructures.
Young, Andrea F; Dean, Cory R; Wang, Lei; Ren, Hechen; Cadden-Zimansky, Paul; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L; Kim, Philip; Nature Physics 8 550–556 (2012) [10.1038/nphys2307] [Link]
Electronic systems with multiple degenerate degrees of freedom can support a rich variety of broken symmetry states. In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin–valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can break this symmetry, manifesting as further Hall plateaus outside the normal integer sequence. Here we report the observation of a number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using tilted field magnetotransport. The large activation gaps confirm the Coulomb origin of all the broken symmetry states, but the order depends strongly on LL index. In the high-energy LLs the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets hosting skyrmionic excitations at half filling, whereas in the ‘relativistic’ zero LL lattice scale interactions drive the system to a spin unpolarized state.
Lee, Gwan-Hyoung; Yu, Young-Jun; Lee, Changgu; Dean, Cory; Shepard, Kenneth L; Kim, Philip; Hone, James; Applied Physics Letters 99, 24 243114-243114-3 (2011) [10.1063/1.3662043] [Link]
Electron tunneling through atomically flat and ultrathin hexagonal boron nitride (h-BN) on gold-coated mica was investigated using conductive atomic force microscopy. Low-bias direct tunneling was observed in mono-, bi-, and tri-layer h-BN. For all thicknesses, Fowler-Nordheim tunneling (FNT) occurred at high bias, showing an increase of breakdown voltage with thickness. Based on the FNT model, the barrier height for tunneling (3.07 eV) and dielectric strength (7.94 MV/cm) of h-BN are obtained; these values are comparable to those of SiO2.
Meric, Inanc; Dean, Cory R; Han, Shu-Jen; Wang, Lei; Jenkins, Keith A; Hone, James; Shepard, KL; Electron Devices Meeting (IEDM), 2011 IEEE International 2.1. 1-2.1. 4 (2011) [10.1109/IEDM.2011.6131472] [Link]
High-frequency performance of graphene field-effect transistors (GFETs) with boron- nitride gate dielectrics is investigated. Devices show saturating IV characteristics and f max values as high as 34 GHz at 600-nm channel length. Bias dependence of f T and f max and the effect of the ambipolar channel on transconductance and output resistance are also examined.
Dean, CR; Young, AF; Cadden-Zimansky, P; Wang, L; Ren, H; Watanabe, K; Taniguchi, T; Kim, P; Hone, J; Shepard, KL; Nature Physics 7, 9 693-696 (2011) [10.1038/nphys2007] [Link]
The fractional quantum Hall effect1, 2, 3, 4 (FQHE) in an electron gas with multiple internal degrees of freedom provides a model system to study the interplay between symmetry breaking and emergent topological order5. In graphene, the structure of the honeycomb lattice endows the electron wavefunctions with an additional quantum number, termed valley isospin, which, combined with the usual electron spin, yields four-fold degenerate Landau levels (LLs; refs 6, 7). This additional symmetry modifies the FQHE and is conjectured to produce new incompressible ground states in graphene8, 9, 10, 11, 12, 13, 14, 15, 16, 17. Here we report multiterminal measurements of the FQHE in high-mobility graphene devices fabricated on hexagonal boron nitride substrates18. The measured energy gaps are large, particularly in the second Landau level, where they are up to 10 times larger than those reported in the cleanest conventional systems. In the lowest Landau level the hierarchy of FQH states reflects the additional valley degeneracy.
Meric, Inanc; Dean, Cory R; Young, Andrea F; Baklitskaya, Natalia; Tremblay, Noah J; Nuckolls, Colin; Kim, Philip; Shepard, Kenneth L; Nano letters 11, 3 1093–1097 (2011) [10.1021/nl103993z] [Link]
We investigate current saturation at short channel lengths in graphene field-effect transistors (GFETs). Saturation is necessary to achieve low-output conductance required for device power gain. Dual-channel pulsed current−voltage measurements are performed to eliminate the significant effects of trapped charge in the gate dielectric, a problem common to all oxide-based dielectric films on graphene. With pulsed measurements, graphene transistors with channel lengths as small as 130 nm achieve output conductance as low as 0.3 mS/μm in saturation. The transconductance of the devices is independent of channel length, consistent with a velocity saturation model of high-field transport. Saturation velocities have a density dependence consistent with diffusive transport limited by optical phonon emission.
Meric, Inanc; Dean, Cory; Young, Andrea; Hone, Jim; Kim, Philip; Shepard, Kenneth L; Electron Devices Meeting (IEDM), 2010 IEEE International 23.2. 1-23.2. 4 (2010) [10.1109/IEDM.2010.5703419] [Link]
Graphene field-effect transistors are fabricated utilizing single-crystal hexagonal boron nitride (h-BN), an insulating isomorph of graphene, as the gate dielectric. The devices exhibit mobility values exceeding 10,000 cm 2/V-sec and current saturation down to 500 nm channel lengths with intrinsic transconductance values above 400 mS/mm. The work demonstrates the favorable properties of using h-BNas a gate di-electric for graphene FETs.
Dean, CR; Young, AF; Meric, I; Lee, C; Wang, L; Sorgenfrei, S; Watanabe, K; Taniguchi, T; Kim, P; Shepard, KL; Nature nanotechnology 5, 10 722-726 (2010) [10.1038/nnano.2010.172]
Graphene devices on standard SiO 2 substrates are highly disordered, exhibiting characteristics that are far inferior to the expected intrinsic properties of graphene 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Although suspending the graphene above the substrate leads to a substantial improvement in device quality 13, 14, this geometry imposes severe limitations on device architecture and functionality. There is a growing need, therefore, to identify dielectrics that allow a substrate-supported geometry while retaining the quality achieved ...
Dean, CR; Piot, BA; Gervais, G; Pfeiffer, LN; West, KW; Phys. Rev. B 80, 15 (2009) [10.1103/PhysRevB.80.153301] [Link]
Electrically detected nuclear magnetic resonance was studied in detail in a two-dimensional electron gas as a function of current bias and temperature. We show that applying a relatively modest dc-current bias Idc≃0.5 μA can induce an enhanced nuclear-spin signal compared with the signal obtained under similar thermal equilibrium conditions at zero current bias. Our observations suggest that dynamic nuclear-spin polarization by small current flow is possible in a two-dimensional electron gas, allowing for easy manipulation of the nuclear spin by simple switching of a dc current.
Piot, BA; Jiang, Z; Dean, CR; Engel, LW; Gervais, G; Pfeiffer, LN; West, KW; Nature Physics 4, 12 936-939 (2008) [10.1038/nphys1094] [Link]
When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x–y), highly correlated states emerge as a result of the interplay between electron–electron interactions, confinement and disorder. These so-called fractional quantum Hall liquids1 form a series of states that ultimately give way to a periodic electron solid that crystallizes at high magnetic fields. This quantum phase of electrons has been identified previously as a disorder-pinned two-dimensional Wigner crystal with broken translational symmetry in the x–y plane. Here, we report our discovery of a new insulating quantum phase of electrons when, in addition to a perpendicular field, a very high magnetic field is applied in a geometry parallel (y direction) to the two-dimensional electron sheet. Our data point towards this new quantum phase being an electron solid in a 'quasi-three-dimensional' configuration induced by orbital coupling with the parallel field.
Dean, CR; Piot, BA; Hayden, P; Sarma, S Das; Gervais, G; Pfeiffer, LN; West, KW; Phys. Rev. Lett. 101, 18 (2008) [ 10.1103/PhysRevLett.101.186806] [Link]
Using a tilted-field geometry, the effect of an in-plane magnetic field on the even denominator ν=5/2 fractional quantum Hall state is studied. The energy gap of the ν=5/2 state is found to collapse linearly with the in-plane magnetic field above ∼0.5 T. In contrast, a strong enhancement of the gap is observed for the ν=7/3 state. The radically distinct tilted-field behavior between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wave function for the 5/2 fractional quantum Hall effect.
Dean, CR; Piot, BA; Hayden, P; Das Sarma, S; Gervais, G; Pfeiffer, LN; West, KW; Physical review letters 100, 14 146803 (2008) [10.1103/PhysRevLett.100.146803] [Link]
The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The ν=5/2 excitation gap at 2.63 T is measured to be 262±15 mK, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the 5/2 state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a 5/2 state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.
Buset, JM; Mack, AH; Laroche, D; Dean, CR; Lilly, MP; Reno, JL; Gervais, G; Physica E: Low-dimensional Systems and Nanostructures 40, 5 1252-1254 (2008) [10.1016/j.physe.2007.08.128]
We present an investigation into the manipulation of nuclear spins near the ν=1 quantum Hall state of GaAs/AlGaAs using optical pumping methods. For this, we have built a custom-designed polarization controller which allows for arbitrary polarizations of near-infrared laser light to be transmitted through fiber optics onto the sample. Using resistive readout, it is demonstrated that different polarizations of light induce specific changes in the transport properties in the first Landau level of the GaAs/AlGaAs quantum well.
Dean, CR; Piot, BA; Pfeiffer, LN; West, KW; Gervais, G; Physica E: Low-dimensional Systems and Nanostructures 40, 5 990-994 (2008) [10.1016/j.physe.2007.08.101] [Link]
A study of the resistively detected nuclear magnetic resonance (RDNMR) lineshape in the vicinity of ν=1 was performed on a high-mobility 2D electron gas formed in GaAs/AlGaAs. In higher Landau levels, application of an RF field at the nuclear magnetic resonance frequency coincides with an observed minimum in the longitudinal resistance, as predicted by the simple hyperfine interaction picture. Near ν=1 however, an anomalous dispersive lineshape is observed where a resistance peak follows the usual minimum. In an effort to understand the origin of this anomalous peak we have studied the resonance under various RF and sample conditions. Interestingly, we show that the lineshape can be completely inverted by simply applying a DC current. We interpret this as evidence that the minima and maxima in the lineshape originate from two distinct mechanisms.
Dean, Cory R; Robbie, Kevin; Madsen, Lynnette D; Journal of Materials Research 22, 9 2522-2530 (2007) [10.1557/jmr.2007.0312]
The effect of the substrate surface, structure, and chemistry on the interfacial interaction in Ni(thin film)/SiC was examined, with a focus on the recently discovered formation of a nickel intercalated graphite phase. Very thin Ni films (∼7 nm) were deposited onto heated 6H–SiC(0001) substrates prepared with: (i) an oxide layer, (ii) a surface reconstruction, and (iii) a pristine surface (no oxide and no reconstruction), followed by further annealing. Characterization using x-ray diffraction and atomic force microscopy revealed remarkable differences between the samples in terms of both surface morphology and crystallography. Nickel silicides were present in all samples; however, the phase composition differed depending on sample preparation. Furthermore, the pristine surface was the only one that clearly promoted the growth of the nickel graphite intercalation compound (Ni-GIC).
Mack, AH; Riordon, J; Dean, CR; Talbot, R; Gervais, G; Optics letters 32, 11 1378-1380 (2007) [10.1364/OL.32.001378]
A fiber-optic-based polarization control system that uses a backreflection measurement scheme at low temperatures has been developed. This provides a stringent test of the light polarization state at the output of the fiber, allowing for determination and control of the degree of circular polarization; i.e., it can generate linear, right, or left circular polarization with cryogenic fibers. This polarization controller is paving the way toward the control and manipulation of nuclear spins in semiconductors via the optical Overhauser effect and could be used, for example, for the purpose of quantum information processing with the large nuclear spins of GaAs .
Robbie, Kevin; Buzea, Cristina; Landry, Olivier; Dean, Cory; Journal of Laser Applications 18 81 (2006)
This article discusses the design and application of a simple eye-safe monitoring assembly of thin film deposition and its advantages over the existent eye protection filters. This assembly prevents users from being exposed to the radiation field caused by lasers or incandescent objects during thin film deposition. Its design is simple, the device being reliable and easy to operate.
Buzea, Cristina; Kaminska, Kate; Beydaghyan, Gisia; Brown, Tim; Elliott, Chelsea; Dean, Cory; Robbie, Kevin; Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 23, 6 2545 - 2552 (2005) [10.1116/1.2131079]
Thickness evaluation is a particular challenge encountered in the fabrication of nanosculptured thin films fabricated by glancing angle deposition (GLAD). In this article, we deduce equations which allow for accurate in situ thickness monitoring of GLAD thin films deposited onto substrates tilted with respect to the direction of incoming vapor. Universal equations are derived for the general case of Gaussian vapor flux distribution, off-axis sensors, variable substrate tilt, and nonunity sticking coefficient. The mathematical description leads to an incidence angle dependence of thickness and density, allowing for quantitative prediction of porosity in samples with different morphologies and thickness calibrations. In addition, variation of sticking probability with the incidence angle creates a nonmonotonic variation of the film thickness and porosity with the substrate tilt. We discuss the implications of the substrate type, sensor type, and source geometry in a precise quantitative determination of the thickness of thin films fabricated on tilted substrates. Our equations can be particularized for the case of films fabricated at normal incidence.
Effect of Silicon Carbide Surface Condition on the Growth of Nickel Intercalated Graphite Dean, Cory R; (2005) 
Robbie, Kevin; Beydaghyan, Gisia; Brown, Tim; Dean, Cory; Adams, Jonathan; Buzea, Cristina; Review of scientific instruments 75, 4 1089 (2004) [10.1063/1.1667254] [Link]
An ultrahigh vacuum apparatus for the deposition of thin films with controlled three-dimensional nanometer-scale structure is described. Our system allows an alternate, faster, cheaper way of obtaining nanoscale structured thin films when compared to traditional procedures of patterning and etching. It also allows creation of porous structures that are unattainable with known techniques. The unique feature of this system is the dynamic modification of the substrate tilt and azimuthal orientation with respect to the vapor source during deposition of a thin film. Atomic-scale geometrical shadowing creates a strong directional dependence in the aggregation of the film, conferring control over the resulting morphological structure on a scale of less than 10 nm. Motion can create pillars, helixes, zig–zags, etc. Significant features of the apparatus include variable substrate temperature, insertion and removal of specimens from atmospheric conditions without venting the deposition system, computer controlled process parameters, and in situ analysis capabilities. The deposition system was successfully employed for the fabrication of a variety of nanostructured thin films with a wide range of potential applications.
Piot, BA; Dean, CR; Gervais, G; Jiang, Z; Engel, LW; Pfeiffer, LN; West, KW; International Journal of Modern Physics B 23, 2713-2717 (2009)  [Link]