arXiv subjects

Randall M. Feenstra

Publications and source records attributed to Randall M. Feenstra.

At least 19 recordsLinked to original sources

arXiv2025

Path distributions for describing eigenstates of orbital angular momentum

The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of how paths contribute towards any given eigenstate. In the limit of long travel-time, these distributions turn out to be real-valued, non-negative functions of a momentum variable that describes classical travel between the endpoints of a path (with the paths explicitly including nonclassical ones, described in terms of elastica). The distributions are functions of both this characteristic momentum as well as a polar angle that provides a tilt, relative to the z-axis of the chosen coordinate system, of the geodesic that connects the endpoints. The resulting description provides a replacement for the well-known "vector model" for describing orbital angular momentum, and importantly, it includes treatment of the case when the quantum number $\ell$ is zero (i.e., s-states).

quant-ph↗

arXiv2025

Path distributions for describing eigenstates of the harmonic oscillator and other 1-dimensional problems

The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an integral expression is written that describes the wave function. This expression conventionally takes the form of an integral over initial locations of a particle, but it is re-expressed here in terms of a characteristic momentum associated with motion between the endpoints of a path. In this manner, the resulting expression can be analyzed using a generalization of stationary-phase analysis, leading to distributions of paths that exactly describe each eigenstate. These distributions are valid for all travel times, but when evaluated for long times they turn out to be real, non-negative functions of the characteristic momentum. For the harmonic oscillator in particular, a somewhat broad distribution is found, peaked at value of momentum that corresponds to a classical energy which in turn equals the energy eigenvalue for the state being described.

quant-ph↗

arXiv2020

Acquisition and Analysis of Scanning Tunneling Spectroscopy Data $-$ WSe$_2$ Monolayer

Acquisition and analysis is described for scanning tunneling spectroscopy data acquired from a monolayer of WSe$_2$ grown on epitaxial graphene on SiC. Curve fitting of the data is performed, in order to deduce band-edge energies. In addition to describing the details of the theoretical curves used for the fitting, the acquisition and analysis methods are also discussed within the larger context of the historical development of scanning tunneling spectroscopy techniques.

cond-mat.mes-hall↗

arXiv2020

Photo-physics and electronic structure of lateral graphene/MoS2 and metal/MoS2 junctions

Integration of semiconducting transition metal dichalcogenides (TMDs) into functional optoelectronic circuitries requires an understanding of the charge transfer across the interface between the TMD and the contacting material. Here, we use spatially resolved photocurrent microscopy to demonstrate electronic uniformity at the epitaxial graphene/molybdenum disulfide (EG/MoS2) interface. A 10x larger photocurrent is extracted at the EG/MoS2 interface when compared to metal (Ti/Au) /MoS2 interface. This is supported by semi-local density-functional theory (DFT), which predicts the Schottky barrier at the EG/MoS2 interface to be ~2x lower than Ti/MoS2. We provide a direct visualization of a 2D material Schottky barrier through combination of angle resolved photoemission spectroscopy with spatial resolution selected to be ~300 nm (nano-ARPES) and DFT calculations. A bending of ~500 meV over a length scale of ~2-3 micrometer in the valence band maximum of MoS2 is observed via nano-ARPES. We explicate a correlation between experimental demonstration and theoretical predictions of barriers at graphene/TMD interfaces. Spatially resolved photocurrent mapping allows for directly visualizing the uniformity of built-in electric fields at heterostructure interfaces, providing a guide for microscopic engineering of charge transport across heterointerfaces. This simple probe-based technique also speaks directly to the 2D synthesis community to elucidate electronic uniformity at domain boundaries alongside morphological uniformity over large areas.

physics.app-ph↗

arXiv2020

Flatbands and Mechanical Deformation Effects in the Moiré Superlattice of MoS$_2$-WSe$_2$ Heterobilayers

It has recently been shown that quantum-confined states can appear in epitaxially grown van der Waals material heterobilayers without a rotational misalignment ($θ=0^\circ$), associated with flat bands in the Brillouin zone of the moiré pattern formed due to the lattice mismatch of the two layers. Peaks in the local density of states and confinement in a MoS$_2$/WSe$_2$ system was qualitatively described only considering local stacking arrangements, which cause band edge energies to vary spatially. In this work, we report the presence of large in-plane strain variation across the moiré unit cell of a $θ=0^\circ$ MoS$_2$/WSe$_2$ heterobilayer, and show that inclusion of strain variation and out-of-plane displacement in density functional theory calculations greatly improves their agreement with the experimental data. We further explore the role of twist-angle by showing experimental data for a twisted MoS$_2$/WSe$_2$ heterobilayer structure with twist angle of $θ=15^\circ$, that exhibits a moiré pattern but no confinement.

cond-mat.mtrl-sci↗

arXiv2019

Formation of Graphene atop a Si adlayer on the C-face of SiC

The structure of the SiC(000-1) surface, the C-face of the {0001} SiC surfaces, is studied as a function of temperature and of pressure in a gaseous environment of disilane (Si2H6). Various surface reconstructions are observed, both with and without the presence of an overlying graphene layer (which spontaneously forms at sufficiently high temperatures). Based on cross-sectional scanning transmission electron microscopy measurements, the interface structure that forms in the presence of the graphene is found to contain 1.4 - 1.7 monolayers (ML) of Si, a somewhat counter-intuitive result since, when the graphene forms, the system is actually under C-rich conditions. Using ab initio thermodynamics, it is demonstrated that there exists a class of Si-rich surfaces containing about 1.3 ML of Si that are stable on the surface (even under C-rich conditions) at temperatures above about 400 K. The structures that thus form consist of Si adatoms atop a Si adlayer on the C-face of SiC, with or without the presence of overlying graphene.

cond-mat.mes-hall↗

arXiv2019

Proximity-induced superconducting gap in the quantum spin Hall edge state of monolayer WTe$_2$

The quantum spin Hall (QSH) state was recently demonstrated in monolayers of the transition metal dichalcogenide 1T'-WTe$_2$ and is characterized by a band gap in the two-dimensional (2D) interior and helical one-dimensional (1D) edge states. Inducing superconductivity in the helical edge states would result in a 1D topological superconductor, a highly sought-after state of matter. In the present study, we use a novel dry-transfer flip technique to place atomically-thin layers of WTe$_2$ on a van der Waals superconductor, NbSe$_2$. Using scanning tunneling microscopy and spectroscopy (STM/STS), we demonstrate atomically clean surfaces and interfaces and the presence of a proximity-induced superconducting gap in the WTe$_2$ for thicknesses from a monolayer up to 7 crystalline layers. At the edge of the WTe$_2$ monolayer, we show that the superconducting gap coexists with the characteristic spectroscopic signature of the QSH edge state. Taken together, these observations provide conclusive evidence for proximity-induced superconductivity in the QSH edge state in WTe$_2$, a crucial step towards realizing 1D topological superconductivity and Majorana bound states in this van der Waals material platform.

cond-mat.mes-hall↗

arXiv2018

Substitutional mechanism for growth of hexagonal boron nitride on epitaxial graphene

Monolayer-thick hexagonal boron nitride (h-BN) is grown on graphene on SiC(0001), by exposure of the graphene to borazine, (BH)3(NH)3, at 1100 C. The h-BN films form ~2-micrometer size grains with a preferred orientation of 30 degrees relative to the surface graphene. Low-energy electron microscopy is employed to provide definitive signatures of the number and composition of two-dimensional (2D) planes across the surface. These grains are found to form by substitution for the surface graphene, with the C atoms produced by this substitution then being incorporated below the h-BN (at the interface between the existing graphene and the SiC) to form a new graphene plane.

cond-mat.mes-hall↗

arXiv2018

Quantum-Confined Electronic States arising from Moiré Pattern of MoS2-WSe2 Hetero-bilayers

A two-dimensional (2D) hetero-bilayer system consisting of MoS2 on WSe2, deposited on epitaxial graphene, is studied by scanning tunneling microscopy and spectroscopy at temperatures of 5 and 80 K. A moiré pattern is observed, arising from lattice mismatch of 3.7% between the MoS2 and WSe2. Significant energy shifts are observed in tunneling spectra observed at the maxima of the moiré corrugation, as compared with spectra obtained at corrugation minima, consistent with prior work. Furthermore, at the minima of the moiré corrugation, sharp peaks in the spectra at energies near the band edges are observed, for spectra acquired at 5 K. The peaks correspond to discrete states that are confined within the moiré unit cells. Conductance mapping is employed to reveal the detailed structure of the wave functions of the states. For measurements at 80 K, the sharp peaks in the spectra are absent, and conductance maps of the band edges reveal little structure.

cond-mat.mes-hall↗

arXiv2018

Magnitude of the Current in Two-Dimensional Interlayer Tunneling Devices

Using the Bardeen tunneling method with first-principles wave functions, computations are made of the tunneling current in graphene / hexagonal-boron-nitride / graphene (G/h-BN/G) vertical structures. Detailed comparison with prior experimental results is made, focusing on the magnitude of the achievable tunnel current. With inclusion of the effects of translational and rotational misalignment of the graphene and the h-BN, predicted currents are found to be about 15x larger than experimental values. A reduction in this discrepancy, to a factor of 2.5x, is achieved by utilizing a realistic size for the band gap of the h-BN, hence affecting the exponential decay constant for the tunneling.

cond-mat.mes-hall↗

arXiv2016

Characteristics of Interlayer Tunneling Field Effect Transistors Computed by a "DFT-Bardeen" Method

Theoretical predictions are made for the current-voltage characteristics of two-dimensional heterojunction interlayer tunneling field-effect transistors (Thin-TFETs), focusing on the magnitude of the current that is achievable in such devices. A theory based on the Bardeen tunneling method is employed, using wavefunctions from first-principles density-functional theory. This method permits convenient incorporation of differing materials into the source and drain electrodes, i.e. with different crystal structures, lattice constants, and/or band structures. Large variations in the tunnel currents are found, depending on the particular two-dimensional materials used for the source and drain electrodes. Tunneling between states derived from the center (Gamma-point) of the Brillouin zone (BZ) is found, in general, to lead to larger current than for zone-edge (e.g. K-point) states. Differences, as large as an order of magnitude, between the present results and various prior predictions are discussed. Predicted values for the tunneling currents, including subthreshold swing, are compared with benchmark values for low-power digital applications. Contact resistance is considered and its effect on the tunneling currents is demonstrated.

cond-mat.mes-hall↗

arXiv2016

Epitaxial graphene homogeneity and quantum Hall effect in millimeter-scale devices

Quantized magnetotransport is observed in 5.6 x 5.6 mm^2 epitaxial graphene devices, grown using highly constrained sublimation on the Si-face of SiC(0001) at high temperature (1900 °C). The precise quantized Hall resistance of Rxy = h/2e^2 is maintained up to record level of critical current Ixx = 0.72 mA at T = 3.1 K and 9 T in a device where Raman microscopy reveals low and homogeneous strain. Adsorption-induced molecular doping in a second device reduced the carrier concentration close to the Dirac point(n ~ 1E10 (1/cm^2)), where mobility of 43700 cm^2/Vs is measured over an area of 10 mm^2. Atomic force, confocal optical, and Raman microscopies are used to characterize the large-scale devices, and reveal improved SiC terrace topography and the structure of the graphene layer. Our results show that the structural uniformity of epitaxial graphene produced by face-to-graphite processing contributes to millimeter-scale transport homogeneity, and will prove useful for scientific and commercial applications.

cond-mat.mtrl-sci↗

arXiv2016

Thickness characterization of atomically-thin WSe$_2$ on epitaxial graphene by low-energy electron reflectivity oscillations

In this work, low-energy electron microscopy is employed to probe structural as well as electronic information in few-layer WSe$_2$ on epitaxial graphene on SiC. The emergence of unoccupied states in the WSe$_2$--graphene heterostructures are studied using spectroscopic low-energy electron reflectivity. Reflectivity minima corresponding to specific WSe$_2$ states that are localized between the monolayers of each vertical heterostructure are shown to reveal the number of layers for each point on the surface. A theory for the origin of these states is developed and utilized to explain the experimentally observed featured in the WSe$_2$ electron reflectivity.

cond-mat.mes-hall↗

arXiv2016

Formation of hexagonal Boron Nitride on Graphene-covered Copper Surfaces

Graphene-covered copper surfaces have been exposed to borazine, (BH)3(NH)3, with the resulting surfaces characterized by low-energy electron microscopy. Although the intent of the experiment was to form hexagonal boron nitride (h-BN) on top of the graphene, such layers were not obtained. Rather, in isolated surface areas, h-BN is found to form micrometer-size islands that substitute for the graphene. Additionally, over nearly the entire surface, the properties of the layer that was originally graphene is observed to change in a manner that is consistent with the formation of a mixed h-BN/graphene alloy, i.e. h-BNC alloy. Furthermore, following the deposition of the borazine, a small fraction of the surface is found to consist of bare copper, indicating etching of the overlying graphene. The inability to form h-BN layers on top of graphene is discussed in terms of the catalytic behavior of the underlying copper surface and the decomposition of the borazine on top of the graphene.

cond-mat.mtrl-sci↗

arXiv2015

Topographic and electronic structure of cleaved SrTiO3(001) surfaces

The topographic and electronic structure of cleaved SrTiO3(001) surfaces were studied, employing samples that either had or had not been coated with Ti on their outer surfaces prior to fracture. In both cases, SrO- and TiO2-terminated terraces were present on the cleavage surface, enabling in situ studies on either termination. However, the samples coated with Ti prior to fracture were found to yield a rougher morphology on TiO2-terminated terraces as well as a higher density of oxygen vacancies during an annealing (outgassing) step following the coating. The higher density of oxygen vacancies in the bulk of the Ti-coated samples also provides higher conductivity which, in turn, improves a sensitivity of the spectroscopy and reduces the effect of tip-induced band bending. Nonetheless, similar spectral features, unique to each termination, were observed for samples both with and without the Ti coating. Notably, with moderate-temperature annealing following fracture, a strong discrete peak in the conductance spectra, arising from oxygen vacancies, was observed on the SrO-terminated terraces. This peak appears at slightly different voltages for coated and uncoated samples, signifying a possible effect of tip-induced band bending.

cond-mat.mtrl-sci↗

arXiv2015

Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer $SL-WSe_2$

Understanding quasiparticle band structures of transition metal dichalcogenides (TMDs) is critical for technological advances of these materials for atomic layer electronics and photonics. Although theoretical calculations to date have shown qualitatively similar features, there exist subtle differences which can lead to important consequences in the device characteristics. For example, most calculations have shown that all single layer (SL) TMDs have direct band gaps, while some have shown that $SL-WSe_2$ have an indirect gap. Moreover, there are large variations in the reported quasiparticle gaps, corresponding to large variations in exciton binding energies. By using a comprehensive form of scanning tunneling spectroscopy, we have revealed detailed quasiparticle electronic structures in TMDs, including the quasi-particle gaps, critical point energy locations and their origins in the Brillouin Zones (BZs). We show that $SL-WSe_2$ actually has an indirect quasi-particle gap with the conduction band minimum located at the Q point (instead of K), albeit the two states are nearly degenerate. Its implications on optical properties are discussed. We have further observed rich quasi-particle electronic structures of TMDs as a function of atomic structures and spin-orbital couplings.

cond-mat.mes-hall↗

arXiv2015

Theory of resonant tunneling in bilayer-graphene/hexagonal-boron-nitride heterostructures

A theory is developed for calculating vertical tunneling current between two sheets of bilayer graphene separated by a thin, insulating layer of hexagonal boron nitride, neglecting many-body effects. Results are presented using physical parameters that enable comparison of the theory with recently reported experimental results. Observed resonant tunneling and negative differential resistance in the current-voltage characteristics are explained in terms of the electrostatically-induced band gap, gate voltage modulation, density of states near the band edge, and resonances with the upper sub-band. These observations are compared to ones from similar heterostructures formed with monolayer graphene.

cond-mat.mes-hall↗

arXiv2015

Oxygen Vacancies on SrO-terminated SrTiO3(001) Surfaces studied by Scanning Tunneling Spectroscopy

The electronic structure of SrTiO3(001) surfaces was studied using scanning tunneling spectroscopy and density-functional theory. With high dynamic range measurements, an in-gap transition level was observed on SrO-terminated surfaces, at 2.7 eV above the valence band maximum. The density of centers responsible for this level was found to increase with surface segregation of oxygen vacancies and decrease with exposure to molecular oxygen. Based on these finding, the level is attributed to surface O vacancies. A level at a similar energy is predicted theoretically on SrO-terminated surfaces. For TiO2-terminated surfaces, no discrete in-gap state was observed, although one is predicted theoretically. This lack of signal is believed to be due to the nature of defect wavefunction involved, as well as the possible influence of transport limitations in the tunneling spectroscopy measurements.

cond-mat.mtrl-sci↗