arXiv subjects

A. H. MacDonald

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

At least 55 records · Page 3Linked to original sources

arXiv2016

Quantum Hall Edge States in Topological Insulator Nanoribbons

We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically-doped Bi$_2$Se$_3$-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. We use our theory to interpret recent transport experiments that exhibit non-zero longitudinal resistance in samples with accurately quantized Hall conductances.

cond-mat.mes-hall↗

arXiv2015

SU(3) Quantum Hall Ferromagnetism in SnTe

The (111) surface of SnTe hosts one isotropic $\barΓ$-centered and three degenerate anisotropic $\bar{M}$- centered Dirac surface states. We predict that a nematic phase with spontaneously broken $C_3$ symmetry will occur in the presence of an external magnetic field when the $N=0$ $\bar{M}$ Landau levels are $1/3$ or $2/3$ filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state, and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the three-fold $\bar{M}$ Landau level degeneracy, yielding a ground state energy with $2π/3$ periodicity as a function of Zeeman-field orientation angle.

cond-mat.mes-hall↗

arXiv2015

Thin films of a three-dimensional topological insulator in a strong magnetic field: a microscopic study

The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic field is investigated by performing magnetic bandstructure calculations for a realistic multi-band tight-binding model. Several crucial features of Landau quantization in a realistic three-dimensional topological insulator are revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement with experiment. In films with a crossover thickness of five quintuple layers, there is a signature of the $n=0$ level, whose overall trend as a function of magnetic field matches the established low-energy effective-model result. Importantly, we find a field-dependent splitting and a strong spin-polarization of the $n=0$ level which can be measured experimentally at reasonable field strengths. Our calculations show mixing between the surface and bulk Landau levels which causes the character of levels to evolve with magnetic field.

cond-mat.mes-hall↗

arXiv2015

Exciton band structure of monolayer MoS2

We address the properties of excitons in monolayer MoS$_2$ from a theoretical point of view, showing that low-energy excitonic states occur both at the Brillouin zone center and at the Brillouin-zone corners, that binding energies at the Brillouin-zone center deviate strongly from the $(n-1/2)^{-2}$ pattern of the two-dimensional hydrogenic model, and that the valley-degenerate exciton doublet at the Brillouin-zone center splits at finite momentum into an upper mode with non-analytic linear dispersion and a lower mode with quadratic dispersion. Although monolayer MoS$_2$ is a direct-gap semiconductor when classified by its quasiparticle band structure, it may well be an indirect gap material when classified by its excitation spectra.

cond-mat.mes-hall↗

arXiv2015

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of BiFeO3. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

cond-mat.mes-hall↗

arXiv2015

Topological Superconductivity induced by Ferromagnetic Metal Chains

Recent experiments have provided evidence that one-dimensional (1D) topological superconductivity can be realized experimentally by placing transition metal atoms that form a ferromagnetic chain on a superconducting substrate. We address some properties of this type of systems by using a Slater-Koster tight-binding model. We predict that topological superconductivity is nearly universal when ferromagnetic transition metal chains form straight lines on superconducting substrates and that it is possible for more complex chain structures. The proximity induced superconducting gap is $\sim ΔE_{so} / J$ where $Δ$ is the $s$-wave pair-potential on the chain, $E_{so}$ is the spin-orbit splitting energy induced in the normal chain state bands by hybridization with the superconducting substrate, and $J$ is the exchange-splitting of the ferromagnetic chain $d$-bands. Because of the topological character of the 1D superconducting state, Majorana end modes appear within the gaps of finite length chains. We find, in agreement with experiment, that when the chain and substrate orbitals are strongly hybridized, Majorana end modes are substantially reduced in amplitude when separated from the chain end by less than the coherence length defined by the $p$-wave superconducting gap. We conclude that Pb is a particularly favorable substrate material for ferromagnetic chain topological superconductivity because it provides both strong $s-$wave pairing and strong Rashba spin-orbit coupling, but that there is an opportunity to optimize properties by varying the atomic composition and structure of the chain. Finally, we note that in the absence of disorder a new chain magnetic symmetry, one that is also present in the crystalline topological insulators, can stabilize multiple Majorana modes at the end of a single chain.

cond-mat.mes-hall↗

arXiv2015

A novel platform for two-dimensional chiral topological superconductivity

We show that the surface of an $s$-wave superconductor decorated with a two-dimensional lattice of magnetic impurities can exhibit chiral topological superconductivity. If impurities order ferromagnetically and the superconducting surface supports a sufficiently strong Rashba-type spin-orbit coupling, Shiba sub-gap states at impurity locations can hybridize into Bogoliubov bands with non-vanishing, sometimes large, Chern number $C$. This topological superconductor supports $C$ chiral Majorana edge modes. We construct phase diagrams for model two-dimensional superconductors, accessing the dilute and dense magnetic impurity limits analytically and the intermediate regime numerically. To address potential experimental systems, we identify stable configurations of ferromagnetic iron atoms on the Pb (111) surface and conclude that ferromagnetic adatoms on Pb surfaces can provide a versatile platform for two-dimensional topological superconductivity.

cond-mat.mes-hall↗

arXiv2014

Electric manipulation of the Mn-acceptor binding energy and the Mn-Mn exchange interaction on the GaAs (110) surface by nearby As vacancies

We investigate theoretically the effect of nearby As (arsenic) vacancies on the magnetic properties of substitutional Mn (manganese) impurities on the GaAs (110) surface, using a microscopic tight-binding model which captures the salient features of the electronic structure of both types of defects in GaAs. The calculations show that the binding energy of the Mn-acceptor is essentially unaffected by the presence of a neutral As vacancy, even at the shortest possible ${\rm V}_{\rm As}$--Mn separation. On the other hand, in contrast to a simple tip-induced-band-bending theory and in agreement with experiment, for a positively charged As vacancy the Mn-acceptor binding energy is significantly reduced as the As vacancy is brought closer to the Mn impurity. For two Mn impurities aligned ferromagnetically, we find that nearby charged As vacancies enhance the energy level splitting of the associated coupled acceptor levels, leading to an increase of the effective exchange interaction. Neutral vacancies leave the exchange splitting unchanged. Since it is experimentally possible to switch reversibly between the two charge states of the vacancy, such a local electric manipulation of the magnetic dopants could result in an efficient real-time control of their exchange interaction.

cond-mat.mtrl-sci↗

arXiv2014

Theory of Transport Phenomena in Coherent Quantum Hall Bilayers

We argue that all anomalous transport properties of coherent quantum quantum Hall bilayers can be understood in terms of a mean-field transport theory in which the condensate phase is nearly uniform across the sample, and the strength of condensate coupling to interlayer tunneling processes is substantially reduced compared to the predictions of disorder-free microscopic mean-field theory. These ingredients provide a natural explanation for recently established I-V characteristics which feature a critical current above which the tunneling resistance abruptly increases and a non-local interaction between interlayer tunneling at the inner and outer edges of Corbino rings. We propose a microscopic picture in which disorder is the main agent responsible for the reduction of the effective interlayer tunneling strength.

cond-mat.mes-hall↗

arXiv2014

Impurity cyclotron resonance of anomalous Dirac electrons in graphene

We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of anomalous boundstates that have a sharp peak with a width $R$ in the probability density inside the potential and a broad peak of size magnetic length $\ell$ outside the potential. We investigate optical matrix elements of anomalous states, and find that they are unusually small and depend sensitively on magnetic field. The effect of many-body interactions on their optical conductivity is investigated using a self-consistent time-dependent Hartree-Fock approach (TDHFA). For a completely filled Landau level we find that an excited electron-hole pair, originating from the optical transition between two anomalous impurity states, is nearly uncorrelated with other electron-hole pairs, although it displays a substantial exchange self-energy effects. This absence of correlation is a consequence of a small vertex correction in comparison to the difference between renormalized transition energies computed within the one electron-hole pair approximation. However, an excited electron-hole pair originating from the optical transition between a normal and an anomalous impurity states can be substantially correlated with other electron-hole states with a significant optical strength.

cond-mat.mes-hall↗

arXiv2014

Spontaneous Layer-Pseudospin Domain Walls in Bilayer Graphene

Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structures related to order-induced topological characters. We use our results to estimate Ginzburg-Landau model parameters and transition temperatures for the ordered states of bilayer graphene.

cond-mat.mes-hall↗

arXiv2014

Distinct Competing Ordered ν=2 States in Bilayer Graphene

Because of its large density-of-states and the 2π Berry phase near its low-energy band-contact points, neutral bilayer graphene (BLG) at zero magnetic field (B) is susceptible to chiral-symmetry breaking, leading to a variety of gapped spontaneous quantum Hall states distinguished by valley and spin-dependent quantized Hall conductivities. Among these, the layer antiferromagnetic state, which has quantum valley Hall (QVH) effects of opposite sign for opposite spins, appears to be the thermodynamic ground state. Though other gapped states have not been observed experimentally at B=0, they can be explored by exploiting their adiabatic connection to quantum Hall states with the same total Hall conductivity σH. In this paper, by using a magnetic field to select filling factor ν=2 states with σH=2e^2/h, we demonstrate the presence of a quantum anomalous Hall (QAH) state for the majority spin, and a Kekulé state with spontaneous valley coherence and a quantum valley Hall state for the minority spin in BLG. By providing the first spectroscopic mapping of spontaneous Hall states at ν=2, our results shed further light on the rich set of competing ordered states in BLG.

cond-mat.mes-hall↗

arXiv2013

Anomalous Hall effect arising from noncollinear antiferromagnetism

In most conductors current flow perpendicular to electric field direction (Hall current) can be explained in terms of the Lorentz forces present when charged particles flow in an external magnetic field. However, as established in the very early work of Edwin Hall, ferromagnetic conductors such as Fe, Co, and Ni have an anomalous Hall conductivity contribution that cannot be attributed to Lorentz forces and therefore survives in the absence of a magnetic field. Although the anomalous Hall effect is experimentally strong, it has stood alone among metallic transport effects for much of the last century because it lacked a usefully predictive, generally accepted theory. Progress over the past decade has explained why. It is now clear that the anomalous Hall effect in ferromagnets has contributions from both extrinsic scattering mechanisms similar to those that determine most transport coefficients, and from an intrinsic mechanism that is independent of scattering. The anomalous Hall effect is also observed in paramagnets, which have nonzero magnetization induced by an external magnetic field. Although no explicit relationship has been established, the anomalous Hall effect in a particular material is usually assumed to be proportional to its magnetization. In this work we point out that it is possible to have an anomalous Hall effect in a noncollinear antiferromagnet with zero net magnetization provided that certain common symmetries are absent, and predict that Mn3Ir, a technologically important antiferromagnetic material with noncollinear order that survives to very high temperatures, has a surprisingly large anomalous Hall effect comparable in size to those of the elemental transition metal ferromagnets.

cond-mat.mtrl-sci↗

arXiv2013

Spintronics and Pseudospintronics in Graphene and Topological Insulators

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analog of giant magnetoresistance in bilayer graphene.

cond-mat.mes-hall↗

arXiv2013

Optical conductivity of the $t_{2g}$ two-dimensional electron gas

Motivated by recent interest in perovskite surfaces and heterostructures, we present an analysis of the Kubo conductivity of a two-dimensional electron gas (2DEG) formed in the $t_{2g}$ bands of an oxide with perovskite structure. We find that when the electric field is polarized in the plane of the 2DEG, the optical conductivity is dominated by nearly independent Drude contributions from two-dimensional subband Fermi surfaces, whereas for perpendicular-to-plane polarization it has strong intersubband features. Our analysis suggests that perpendicular-to-plane optical conductivity studies may help advance understanding of the interplay between lattice distortions and electron-electron interactions in complex oxide 2DEG quantum confinement physics.

cond-mat.mes-hall↗

arXiv2013

Landau Level Mixing and the Fractional Quantum Hall Effect

We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau level mixing by electron-electron interactions. To second order in the ratio of electron-electron interaction to cyclotron energy, Landau level mixing is accounted for by constructing effective interaction Hamiltonians that include two-body and three-body contributions characterized by Haldane pseudopotentials. Our study builds upon previous treatments, using as a stepping stone the observation that the effective Hamiltonian is fully determined by the few-body problem with N=2 and N=3 electrons in the partially filled Landau level. For the n=0 case we use a first quantization approach to provide a compact and transparent derivation of the effective Hamiltonian which captures a class of virtual processes omitted in earlier derivations of Landau-level-mixing corrected Haldane pseudopotentials.

cond-mat.str-el↗

arXiv2013

Transport studies of dual-gated ABC and ABA trilayer graphene: band gap opening and band structure tuning in very large perpendicular electric field

We report on the transport properties of ABC and ABA stacked trilayer graphene using dual, locally gated field effect devices. The high efficiency and large breakdown voltage of the HfO2 top and bottom gates enables independent tuning of the perpendicular electric field and the Fermi level over an unprecedentedly large range. We observe a resistance change of six orders of magnitude in the ABC trilayer, which demonstrates the opening of a band gap. Our data suggest that the gap saturates at a large displacement field of D ~ 3 V/nm, in agreement with self-consistent Hartree calculations. In contrast, the ABA trilayer remains metallic even under a large perpendicular electric field. Despite the absence of a band gap, the band structure of the ABA trilayer continues to evolve with increasing D. We observe signatures of two-band conduction at large D fields. Our self-consistent Hartree calculation reproduces many aspects of the experimental data, but also points to the need for more sophisticated theory.

cond-mat.mes-hall↗

arXiv2013

Valley Chern Numbers and Boundary Modes in Gapped Bilayer Graphene

Electronic states at domain walls in bilayer graphene are studied by analyzing their four and two band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures which occur in the bulk Hamiltonian parameter space. The important role played by intervalley coupling effects not directly captured by the continuum model is addressed using lattice calculations for specific domain wall structures.

cond-mat.mes-hall↗