arXiv subjects

D. S. L. Abergel

Publications and source records attributed to D. S. L. Abergel.

At least 19 recordsLinked to original sources

arXiv2020

Interacting Dirac Materials

We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in Table~\ref{Summary}, we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.

cond-mat.str-el↗

arXiv2019

Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice

We study a tight-binding model on the honeycomb lattice of chiral $d$-wave superconductivity that breaks time-reversal symmetry. Due to its nontrivial sublattice structure, we show that it is possible to construct a gauge-invariant time-reversal-odd bilinear of the pairing potential. The existence of this bilinear reflects the sublattice polarization of the pairing state. We show that it generates persistent loop current correlations around each lattice site and opens a topological mass gap at the Dirac points, resembling Haldane's model of the anomalous quantum Hall effect. In addition to the usual chiral $d$-wave edge states, there also exist electron-like edge resonances due to the topological mass gap. We show that the presence of loop-current correlations directly leads to a nonzero intrinsic ac Hall conductivity, which produces the polar Kerr effect without an external magnetic field. Similar results also hold for the nearest-neighbor chiral $p$-wave pairing. We briefly discuss the relevance of our results to superconductivity in twisted bilayer graphene.

cond-mat.supr-con↗

arXiv2018

Electronic structure of graphene-nanoribbons on hexagonal boron nitride

Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just few atoms thick and its a very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi one dimensional (1D) systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a boron nitride substrate affects the electronic properties of graphene nanoribbons. We consider both armchair and zigzag nanoribbons. Our results show that for some stacking configurations the boron nitride can significantly affect the electronic structure of the ribbons. In particular, for zigzag nanoribbons, due to the lock between spin and sublattice degree of freedom at the edges, the hexagonal boron nitride can induce a very strong spin-splitting of the spin polarized, edge sates. We find that such spin-splitting can be as high as 40~meV.

cond-mat.mes-hall↗

arXiv2017

True exciton condensate of one-dimensional electrons through interwire tunneling

We theoretically predict that a true bilayer exciton condensate,characterised by off-diagonal long range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin--Wagner theorem. Electron--hole interactions then amplify this tendency towards off-diagonal long range order, enhancing the condensate properties by more than an order of magnitude over the noninteracting limit. We show that the temperatures below which a substantial condensate fraction would form could reach hundreds of Kelvin, a benefit of the weak screening in one-dimensional systems.

cond-mat.str-el↗

arXiv2016

First-order quantum phase transition in three-dimensional topological band insulators

Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a re-entrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2016

Robustness of topologically protected transport in graphene-boron nitride lateral heterostructures

Previously, graphene nanoribbons set in lateral heterostructures with hexagonal boron nitride were predicted to support topologically protected states at low energy. We investigate how robust the transport properties of these states are against lattice disorder. We find that forms of disorder that do not couple the two valleys of the zigzag graphene nanoribbon do not impact the transport properties at low bias, indicating that these lateral heterostructures are very promising candidates for chip-scale conducting interconnects. Forms of disorder that do couple the two valleys, such as vacancies in the graphene ribbon, or substantial inclusions of armchair edges at the graphene-hexagonal boron nitride interface will negatively affect the transport. However, these forms of disorder are not commonly seen in current experiments.

cond-mat.mes-hall↗

arXiv2016

A universal explanation of tunneling conductance in exotic superconductors

A longstanding mystery in understanding cuprate superconductors is the inconsistency between the experimental data measured by scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES). In particular, the gap between prominent side peaks observed in STS is much bigger than the superconducting gap observed by ARPES measurements. Here, we reconcile the two experimental techniques by generalising a theory which was previously applied to zero-dimensional mesoscopic Kondo systems to strongly correlated two-dimensional (2D) exotic superconductors. We show that the side peaks observed in tunneling conductance measurements in all these materials have a universal origin: They are formed by coherence-mediated tunneling under bias and do not directly reflect the underlying density of states (DOS) of the sample. We obtain theoretical predictions of the tunneling conductance and the density of states of the sample simultaneously and show that for cuprate and pnictide superconductors, the extracted sample DOS is consistent with the superconducting gap measured by ARPES.

cond-mat.mes-hall↗

arXiv2016

Two-Photon Absorption in Gapped Bilayer Graphene with a Tunable Chemical Potential

Despite the now vast body of two-dimensional materials under study, bilayer graphene remains unique in two ways: it hosts a simultaneously tunable band gap and electron density; and stems from simple fabrication methods. These two advantages underscore why bilayer graphene is critical as a material for optoelectronic applications. In the work that follows, we calculate the one- and two-photon absorption coefficients for degenerate interband absorption in a graphene bilayer hosting an asymmetry gap and adjustable chemical potential--all at finite temperature. Our analysis is comprehensive, characterizing one- and two-photon absorptive behavior over wide ranges of photon energy, gap, chemical potential, and thermal broadening. The two-photon absorption coefficient for bilayer graphene displays a rich structure as a function of photon energy and band gap due to the existence of multiple absorption pathways and the nontrivial dispersion of the low energy bands. This systematic work will prove integral to the design of bilayer-graphene-based nonlinear optical devices.

cond-mat.mes-hall↗

arXiv2015

Infrared absorption of closely-aligned heterostructures of monolayer and bilayer graphene with hexagonal boron nitride

We model optical absorption of monolayer and bilayer graphene on hexagonal boron nitride for the case of closely-aligned crystal lattices. We show that perturbations with different spatial symmetry can lead to similar absorption spectra. We suggest that a study of the absorption spectra as a function of the doping for almost completely full first miniband is necessary to extract meaningful information about the moire characteristics from optical absorption measurements and to distinguish between various theoretical proposals for the physically realistic interaction. Also, for bilayer graphene, the ability to compare spectra for the opposite signs of electric-field-induced interlayer asymmetry might provide additional information about the moire parameters.

cond-mat.mes-hall↗

arXiv2015

Excitonic condensation in spatially separated one-dimensional systems

We show theoretically that excitons can form from spatially separated one-dimensional ground state populations of electrons and holes, and that the resulting excitons can form a quasicondensate. We describe a mean-field Bardeen-Cooper-Schrieffer theory in the low carrier density regime and then focus on the core-shell nanowire giving estimates of the size of the excitonic gap for InAs/GaSb wires and as a function of all the experimentally relevant parameters. We find that optimal conditions for pairing include small overlap of the electron and hole bands, large effective mass of the carriers, and low dielectric constant of the surrounding media. Therefore, one-dimensional systems provide an attractive platform for the experimental detection of excitonic quasicondensation in zero magnetic field.

cond-mat.mes-hall↗

arXiv2015

Effects of a tilted magnetic field in a Dirac double layer

We calculate the energy spectrum of a Dirac double layer, where each layer has the Dirac electronic dispersion, in the presence of a tilted magnetic field and small interlayer tunneling. We show that the energy splitting between the Landau levels has an oscillatory dependence on the in-plane magnetic field and vanishes at a series of special tilt angles of the magnetic field. Using a semiclassical analysis, we show that these special tilt angles are determined by the Berry phase of the Dirac Hamiltonian. The interlayer tunneling conductance also exhibits an oscillatory dependence on the magnetic field tilt angle, known as the angular magnetoresistance oscillations (AMRO). Our results are applicable to graphene double layers and thin films of topological insulators.

cond-mat.mes-hall↗

arXiv2014

The role of spin-orbit coupling in topologically protected interface states in Dirac materials

We highlight the fact that two-dimensional materials with Dirac-like low energy band structures and spin-orbit coupling will produce linearly dispersing topologically protected Jackiw-Rebbi modes at interfaces where the Dirac mass changes sign. These modes may support persistent spin or valley currents parallel to the interface, and the exact arrangement of such topologically protected currents depends crucially on the details of the spin-orbit coupling in the material. As examples, we discuss buckled two-dimensional hexagonal lattices such as silicene or germanene, and transition metal dichalcogenides such as MoS$_2$.

cond-mat.mes-hall↗

arXiv2014

Weakly damped acoustic plasmon mode in transition metal dichalcogenides with Zeeman splitting

We analyze the effect of a strong Zeeman field on the spectrum of collective excitations of monolayer transition metal dichalcogenides. The combination of the Dresselhaus type spin orbit coupling and an external Zeeman field result in the lifting of the valley degeneracy in the valence band of these crystals. We show that this lifting of the valley degeneracy manifests in the appearance of an additional plasmon mode with linear in wavenumber dispersion along with the standard square root in wavenumber mode. Despite this novel mode being subject to the Landau damping, it corresponds to a well defined quasiparticle peak in the spectral function of the electron gas.

cond-mat.mes-hall↗

arXiv2013

Infrared absorption by graphene-hBN heterostructures

We propose a theory of optical absorption in monolayer graphene-hexagonal boron nitride (hBN) heterostructures. In highly oriented heterostructures, the hBN underlay produces a long-range moiré superlattice potential for the graphene electrons which modifies the selection rules for absorption of incoming photons in the infrared to visible frequency range. The details of the absorption spectrum modification depend on the relative strength of the various symmetry-allowed couplings between the graphene electrons and the hBN, and the resulting nature of the reconstructed band structure.

cond-mat.mes-hall↗

arXiv2013

Interlayer excitonic superfluidity in graphene

We discuss the conditions under which the predicted (but not yet observed) zero-field interlayer excitonic condensation in double layer graphene has a critical temperature high enough to allow detection. Crucially, disorder arising from charged impurities and corrugation in the lattice structure --- invariably present in all real samples --- affects the formation of the condensate via the induced charge inhomogeneity. In the former case, we use a numerical Thomas-Fermi-Dirac theory to describe the local fluctuations in the electronic density in double layer graphene devices and estimate the effect these realistic fluctuations have on the formation of the condensate. To make this estimate, we calculate the critical temperature for the interlayer excitonic superfluid transition within the mean-field BCS theory for both optimistic (unscreened) and conservative (statically screened) approximations for the screening of the interlayer Coulomb interaction. We also estimate the effect of allowing dynamic contributions to the interlayer screening. We then conduct similar calculations for double quadratic bilayer graphene, showing that the quadratic nature of the low-energy bands produces pairing with critical temperature of the same order of magnitude as the linear bands of double monolayer graphene.

cond-mat.mes-hall↗

arXiv2013

2D compressibility of surface states on 3D topological insulators

We develop a theory for the compressibility of the surface states of 3D topological insulators and propose that surface probes of the compressibility via scanning single electron transistor microscopy will be a straightforward way to access the topological states without interference from the bulk states. We describe the single-particle nature of the surface states taking into account an accurate Hamiltonian for the bands and then include the contribution from electron--electron interactions and discuss the implications of the ultra-violet cutoff, including the universality of the exchange contribution when expressed in dimensionless units. We also compare the theory with experimentally obtained dμ/dn as extracted from angle-resolved photoemission spectroscopy measurements. Finally, we point out that interaction-driven renormalization of the Fermi velocity may be discernible via this technique.

cond-mat.mes-hall↗

arXiv2012

Inhomogeneity and nonlinear screening in gapped bilayer graphene

We demonstrate that for gapped bilayer graphene, the nonlinear nature of the screening of an external disorder potential and the resulting inhomogeneity of the electron liquid are crucial for describing the electronic compressibility. In particular, traditional diagrammatic methods of many-body theory do not include this inhomogeneity and therefore fail to reproduce experimental data accurately, particularly at low carrier densities. In contrast, a direct calculation of the charge landscape via a numerical Thomas-Fermi energy functional method along with the appropriate bulk averaging procedure captures all the essential physics, including the interplay between the band gap and the inhomogeneity.

cond-mat.mes-hall↗

arXiv2012

The compressibility of graphene

We present a review of the electronic compressibility of monolayer and bilayer graphene. We focus on describing theoretical calculations of the effects of electron--electron interactions and various types of disorder, and also give a summary of current experiments and describe which aspects of theory they support. We also include a full analysis of all commonly-used contributions to the tight-binding Hamiltonian of bilayer graphene and their effects on the compressibility.

cond-mat.mes-hall↗