arXiv subjects

A. H. MacDonald

Publications and source records attributed to A. H. MacDonald.

At least 37 records · Page 2Linked to original sources

arXiv2020

WKB estimate of bilayer graphene's magic twist angles

Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck's constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wavefunctions. We find zero energy solutions at a discrete set of values of the dimensionless Planck's constant, which we obtain analytically. Our analytic flat band twist angles correspond closely to those determined numerically in previous work.

cond-mat.mes-hall↗

arXiv2020

Electrically Controlled Two-Dimensional Electron-Hole Fluids

We study the electronic properties of dual-gated electron-hole bilayers in which the two layers are separated by a perfectly opaque tunnel barrier. Combining an electrostatic and thermodynamic analysis with mean-field theory estimates of interacting system chemical potentials, we explain the dependence of the electron and hole densities on the two gate voltages. Because chemical potential jumps occur for both electrons and holes at neutrality, there is a finite area in gate voltage parameter space over which electron and hole densities are equal. In that regime the electron-hole pair density depends only on the sum of the two gate voltages. We are able to explain a recent experimental study of electrically controlled bilayers by allowing for interlayer tunneling and using a non-equilibrium steady-state transport picture.

cond-mat.mes-hall↗

arXiv2020

Topological Quantum Computing Using Nanowire Devices

The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana states by time-dependently tuning topologically non-trivial parameter regions. In this work, we simulate the exchange of four Majorana modes in T-shaped junctions made out of p-wave superconducting Rashba wires. We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Contrary to the widespread opinion, we show for the first time that in the adiabatic limit the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Further, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multi qubit setup, which allows for universal and in particular topologically protected quantum computing.

cond-mat.mes-hall↗

arXiv2019

Extremely imbalanced two-dimensional electron-hole-photon systems

We investigate the phases of two-dimensional electron-hole systems strongly coupled to a microcavity photon field in the limit of extreme charge imbalance. Using variational wave functions, we examine the competition between different electron-hole paired states for the specific cases of semiconducting III-V single quantum wells, electron-hole bilayers, and transition metal dichalcogenide monolayers embedded in a planar microcavity. We show how the Fermi sea of excess charges modifies both the electron-hole bound state (exciton) properties and the dielectric constant of the cavity active medium, which in turn affects the photon component of the many-body polariton ground state. On the one hand, long-range Coulomb interactions and Pauli blocking of the Fermi sea promote electron-hole pairing with finite center-of-mass momentum, corresponding to an excitonic roton minimum. On the other hand, the strong coupling to the ultra-low-mass cavity photon mode favors zero-momentum pairs. We discuss the prospect of observing different types of electron-hole pairing in the photon spectrum.

cond-mat.mes-hall↗

arXiv2019

Cavity QED of Strongly Correlated Electron Systems: A No-go Theorem for Photon Condensation

In spite of decades of work it has remained unclear whether or not superradiant quantum phases, referred to here as photon condensates, can occur in equilibrium. In this Letter, we first show that when a non-relativistic quantum many-body system is coupled to a cavity field, gauge invariance forbids photon condensation. We then present a microscopic theory of the cavity quantum electrodynamics of an extended Falicov-Kimball model, showing that, in agreement with the general theorem, its insulating ferroelectric and exciton condensate phases are not altered by the cavity and do not support photon condensation.

cond-mat.mes-hall↗

arXiv2019

Topological insulators in twisted transition metal dichalcogenide homobilayers

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe$_2$. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe$_2$ at $+K$ ($-K$) valley can be described using a two-band model with a layer-pseudospin magnetic field $\boldsymbolΔ(\boldsymbol{r})$ that has the moiré period. We show that $\boldsymbolΔ(\boldsymbol{r})$ has a topologically non-trivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell.

cond-mat.mes-hall↗

arXiv2018

Theory of phonon-mediated superconductivity in twisted bilayer graphene

We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moiré band electrons, we find that phonons generate attractive interactions in both $s$ and $d$ wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the $s$-wave channel is more favorable; however, on-site Coulomb repulsion can suppress $s$-wave pairing relative to $d$-wave. The pair amplitude varies spatially with the moiré period, and is identical in the two layers in the $s$-wave channel but phase shifted by $π$ in the $d$-wave channel. We discuss experiments that can distinguish the two pairing states.

cond-mat.supr-con↗

arXiv2018

Hubbard model physics in transition metal dichalcogenide moiré bands

Flexible long period moir\' e superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moir\' e bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moiré bands are partially filled, candidate many-body ground states at some special filling factors include spin-liquid states, quantum anomalous Hall insulators and chiral $d$-wave superconductors.

cond-mat.mes-hall↗

arXiv2018

Chiral transport and electronic correlations in surface states of HfNiSn single crystals

In most topological insulators, the valence and conduction band appear in reverse or inverted order compared to an equivalent insulator with isolated atoms. Here, we explore a different route towards topologically nontrivial states that may arise from metallic states present on the surface of bulk insulators without such band inversion. High-quality single crystals of HfNiSn show surface transport with weak anti-localization, consistent with a two-dimensional metallic state in the presence of strong spin-orbit coupling. Nonlinear I(V) curves indicate electronic correlations related to a chiral, nonlocal transport component that is qualitatively similar to a quantum Hall edge state, yet in the absence of external magnetic fields. The correlations themselves may play a decisive role in creating an apparent topologically nontrivial state on the HfNiSn surface.

cond-mat.mtrl-sci↗

arXiv2018

Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers

We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moiré pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moiré Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moiré potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moiré pattern to achieve scalable two-dimensional arrays of nearly identical quantum dots.

cond-mat.mes-hall↗

arXiv2017

Magneto-Coulomb Drag and Hall Drag in Double-Layer Dirac Systems

We develop a theory of Coulomb drag due to momentum transfer between graphene layers in a strong magnetic field. The theory is intended to apply in systems with disorder that is weak compared to Landau level separation, so that Landau level mixing is weak, but strong compared to correlation energies within a single Landau level, so that fractional quantum Hall physics is not relevant. We find that in contrast to the zero-field limit, the longitudinal magneto-Coulomb drag is finite, and in fact attains a maximum at the simultaneous charge neutrality point (CNP) of both layers. Our theory also predicts a sizable Hall drag resistivity at densities away from the CNP.

cond-mat.mes-hall↗

arXiv2017

Polariton Supercurrent Generation in Unipolar Electro-optic Devices

We describe a mechanism by which an electrical bias voltage applied across a unipolar semiconductor quantum well can drive an exciton or polariton supercurrent. The mechanism depends on the properties of electronic quasiparticles in quantum wells or two-dimensional materials that are dressed by interactions with the coherent exciton field of an exciton condensate or the coherent exciton and photon fields of a polariton condensate, and on approximate conservation laws. We propose experiments that can be performed to realize this new light-matter coupling effect, and discuss possible applications.

cond-mat.mes-hall↗

arXiv2017

Topological Exciton Bands in Moiré Heterojunctions

Moiré patterns are common in Van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valley Zeeman field.

cond-mat.mes-hall↗

arXiv2017

Theory of Two-Dimensional Spatially Indirect Equilibrium Exciton Condensates

We present a theory of bilayer two-dimensional electron systems that host a spatially indirect exciton condensate when in thermal equilibrium. Equilibrium bilayer exciton condensates (BXCs) are expected to form when two nearby semiconductor layers are electrically isolated, and when the conduction band of one layer is brought close to degeneracy with the valence band of a nearby layer by varying bias or gate voltages. BXCs are characterized by spontaneous inter-layer phase coherence and counterflow superfluidity. The bilayer system we consider is composed of two transition metal dichalcogenide monolayers separated and surrounded by hexagonal boron nitride. We use mean-field-theory and a bosonic weakly interacting exciton model to explore the BXC phase diagram, and time-dependent mean-field theory to address condensate collective mode spectra and quantum fluctuations. We find that a phase transition occurs between states containing one and two condensate components as the layer separation and the exciton density are varied, and derive simple approximate expressions for the exciton-exciton interaction strength which we show can be measured capacitively.

cond-mat.mes-hall↗

arXiv2016

Moiré Assisted Fractional Quantum Hall State Spectroscopy

Intra-Landau level excitations in the fractional quantum Hall regime are not accessible via optical absorption measurements. We point out that optical probes are enabled by the periodic potentials produced by a moiré pattern. Our observation is motivated by the recent observations of fractional quantum Hall incompressible states in moiré-patterned graphene on a hexagonal boron nitride substrate, and is theoretically based on $f-$sum rule considerations supplemented by a perturbative analysis of the influence of the moiré potential on many-body states.

cond-mat.mes-hall↗

arXiv2016

Stacking dependence of carrier-interactions in multilayer graphene systems

We identify qualitative trends in the stacking sequence dependence of carrier-carrier interaction phenomena in multilayer graphene. Our theory is based on a new approach which explicitly exhibits the important role in interaction phenomena of the momentum-direction dependent intersite phases determined by the stacking sequence. Using this method, we calculate and compare the self-energies, density--density response functions, collective modes, and ground-state energies of several different few layer graphene systems. The influence of electron--electron interactions on important electronic properties can be understood in terms of competition between intraband exchange, interband exchange and correlation contributions that vary systematically with stacking arrangement.

cond-mat.mes-hall↗

arXiv2016

Microscopic Theory of Equilibrium Polariton Condensates

We present a microscopic theory of the equilibrium polariton condensate state of a semiconductor quantum well in a planar optical cavity. The theory accounts for the adjustment of matter excitations to the presence of a coherent photon field, predicts effective polariton-polariton interaction strengths that are weaker and condensate exciton fractions that are smaller than in the commonly employed exciton-photon model, and yields effective Rabi coupling strengths that depend on the detuning of the cavity photon energy relative to the bare exciton energy. The dressed quasiparticle bands that appear naturally in the theory provide a mechanism for electrical manipulation of polariton condensates.

cond-mat.mes-hall↗

arXiv2016

Band offset and negative compressibility in graphene-MoS2 heterostructures

We use electron transport to characterize monolayer graphene - multilayer MoS2 heterostructures. Our samples show ambipolar characteristics and conductivity saturation on the electron branch which signals the onset of MoS2 conduction band population. Surprisingly, the carrier density in graphene decreases with gate bias once MoS2 is populated, demonstrating negative compressibility in MoS2. We are able to interpret our measurements quantitatively by accounting for disorder and using the random phase approximation (RPA) for the exchange and correlation energies of both Dirac and parabolic-band two-dimensional electron gases. This interpretation allows us to extract the energetic offset between the conduction band edge of MoS2 and the Dirac point of graphene.

cond-mat.mes-hall↗