arXiv subjects

Herbert A. Fertig

Publications and source records attributed to Herbert A. Fertig.

10 recordsLinked to original sources

arXiv2026

Umklapp-Enhanced Interlayer Valley Drag in Moiré Bilayers

Van der Waals materials may be combined to form moiré patterns that are effectively crystal lattices. These systems are unique in that their in-plane unit cell sizes may be orders of magnitude larger than interlayer separations, leading to unique behaviors emerging from interlayer interactions. In this work, we investigate interlayer valley drag in lattice-matched moiré bilayers, demonstrating a remarkable enhancement due to umklapp scattering. In contrast to drag phenomena in more conventional two-dimensional systems, interlayer valley drag appears at first order in the interlayer interaction, and remains non-vanishing in the low temperature limit even at this low order in the interlayer coupling. We propose an experimental geometry, feasible with current state-of-the-art fabrication techniques, to detect and characterize this effect in moiré bilayer systems.

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arXiv2021

Weyl Semimetal Path to Valley Filtering in Graphene

We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two-dimensional to three dimensional massless Dirac fermions. Due to the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs in the bulk of the graphene sheet, obviating the need for carefully shaped edges or dimensions.

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arXiv2020

Helical Edge States and Quantum Phase Transitions in Tetralayer Graphene

Helical conductors with spin-momentum locking are promising platforms for Majorana fermions. Here we report observation of two topologically distinct phases supporting helical edge states in charge neutral Bernal-stacked tetralayer graphene in Hall bar and Corbino geometries. As the magnetic field B and out-of-plane displacement field D are varied, we observe a phase diagram consisting of an insulating phase and two metallic phases, with 0, 1 and 2 helical edge states, respectively. These phases are accounted for by a theoretical model that relates their conductance to spin-polarization plateaus. Transitions between them arise from a competition among inter-layer hopping, electrostatic and exchange interaction energies. Our work highlights the complex competing symmetries and the rich quantum phases in few-layer graphene.

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arXiv2015

Emergence of a ZO Kohn anomaly in quasi-freestanding epitaxial graphene

In neutral graphene, two prominent cusps known as Kohn anomalies are found in the phonon dispersion of the highest optical phonon at $q=Γ$ (LO branch) and $q=K$ (TO branch), reflecting a significant electron-phonon coupling to undoped Dirac electrons. In this work, high-resolution electron energy loss spectroscopy is used to measure the phonon dispersion around the $Γ$ point in quasi-freestanding graphene epitaxially grown on Pt(111). The Kohn anomaly for the LO phonon is observed at finite momentum $q\sim2k_F$ from $Γ$, with a shape in excellent agreement with the theory and consistent with known values of the EPC and the Fermi level. More strikingly, we also observe a Kohn anomaly at the same momentum for the out-of-plane optical phonon (ZO) branch. This observation is the first direct evidence of the coupling of the ZO mode with Dirac electrons, which is forbidden for freestanding graphene but becomes allowed in the presence of a substrate. Moreover, we estimate the EPC to be even greater than that of the LO mode, making graphene on Pt(111) an optimal system to explore the effects of this new coupling in the electronic properties.

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arXiv2015

Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials

When the phonon spectrum of a material is measured in a scattering experiment, selection rules preclude the observation of phonons that are odd under reflection by the scattering plane. Understanding these rules is crucial to correctly interpret experiments and to detect broken symmetries. Taking graphene as a case study, in this work we derive the complete set of selection rules for the honeycomb lattice, showing that some of them have been missed or misinterpreted in the literature. Focusing on the technique of high-resolution electron energy loss spectroscopy (HREELS), we calculate the scattering intensity for a simple force constant model to illustrate these rules. In addition, we present HREELS measurements of the phonon dispersion for graphene on Ru(0001) and find excellent agreement with the theory. We also illustrate the effect of different symmetry breaking scenarios in the selection rules and discuss previous experiments in light of our results.

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arXiv2012

Power law Kohn anomalies and the excitonic transition in graphene

Dirac electrons in graphene in the presence of Coulomb interactions of strength $β$ have been shown to display power law behavior with $β$ dependent exponents in certain correlation functions, which we call the mass susceptibilities of the system. In this work, we first discuss how this phenomenon is intimately related to the excitonic insulator transition, showing the explicit relation between the gap equation and response function approaches to this problem. We then provide a general computation of these mass susceptibilities in the ladder approximation, and present an analytical computation of the static exponent within a simplified kernel model, obtaining $η_0 =\sqrt{1-β/β_c}$ . Finally we emphasize that the behavior of these susceptibilities provides new experimental signatures of interactions, such as power law Kohn anomalies in the dispersion of several phonons, which could potentially be used as a measurement of $β$.

cond-mat.str-el↗

arXiv2012

Power law Kohn anomaly in undoped graphene induced by Coulomb interactions

Phonon dispersions generically display non-analytic points, known as Kohn anomalies, due to electron-phonon interactions. We analyze this phenomenon for a zone boundary phonon in undoped graphene. When electron-electron interactions with coupling constant $β$ are taken into account, one observes behavior demonstrating that the electrons are in a critical phase: the phonon dispersion and lifetime develop power law behavior with $β$ dependent exponents. The observation of this signature would allow experimental access to the critical properties of the electron state, and would provide a measure of its proximity to an excitonic insulating phase.

cond-mat.str-el↗

arXiv2011

Quarter-Filled Honeycomb Lattice with a Quantized Hall Conductance

We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a state with a quantized Hall conductance generically arises in the presence of a Zeeman field of sufficient strength. We discuss the influence of Hubbard interactions and argue that spontaneous ferromagnetism (which breaks time-reversal) will occur, leading to a quantized anomalous Hall effect.

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arXiv2011

Edge States of Bilayer Graphene in the Quantum Hall Regime

We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear transformations to the spectra of quantum Hall edge--states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends BOTH on boundary conditions and the energies of the bulk states.

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arXiv2008

Theory of Activated Transport in Bilayer Quantum Hall Systems

We analyze the transport properties of bilayer quantum Hall systems at total filling factor $ν=1$ in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries, current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.

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