It has been known for decades that a magnetic field can deflect phonons as they flow in response to a thermal gradient, producing a thermal Hall effect. Several recent experiments have revealed ratios of the phonon Hall conductivity to the phonon lon
gitudinal conductivity in oxide dielectrics that are larger than $10^{-3}$ when phonon mean-free-paths exceed phonon wavelengths. At the same time $kappa_{H}/kappa_{L}$ is not strongly temperature dependent. We argue that these two properties together imply a mechanism related to phonon scattering from defects that break time-reversal symmetry, and we show that Lorentz forces acting on charged defects produce substantial skew-scattering amplitudes, and related thermal Hall effects that are consistent with recent observations.
It has long been speculated that quasi-two-dimensional superconductivity can reappear above its semiclassical upper critical field due to Landau quantization, yet this reentrant property has never been observed. Here, we argue that twisted bilayer gr
aphene at a magic angle (MATBG) is an ideal system in which to search for this phenomenon because its Landau levels are doubly degenerate, and its superconductivity appears already at carrier densities small enough to allow the quantum limit to be reached at relatively modest magnetic fields. We study this problem theoretically by combining a simplified continuum model for the electronic structure of MATBG with a phenomenological attractive pairing interaction, and discuss obstacles to the observation of quantum Hall superconductivity presented by disorder, thermal fluctuations, and competing phases.
MnBi$_2$Te$_4$ (MBT) is a promising antiferromagnetic topological insulator whose films provide access to novel and technologically important topological phases, including quantum anomalous Hall states and axion insulators. MBT device behavior is exp
ected to be sensitive to the various collinear and non-collinear magnetic phases that are accessible in applied magnetic fields. Here, we use classical Monte Carlo simulations and electronic structure models to calculate the ground state magnetic phase diagram as well as topological and optical properties for few layer films with thicknesses up to six septuple layers. Using magnetic interaction parameters appropriate for MBT, we find that it is possible to prepare a variety of different magnetic stacking sequences, some of which have sufficient symmetry to disallow non-reciprocal optical response and Hall transport coefficients. Other stacking arrangements do yield large Faraday and Kerr signals, even when the ground state Chern number vanishes.
We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle
flat bands. When the system is insulating at moire band filling $ u=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moire Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU(8)$ degree of freedom in each moire unit cell that we identify as the direct product of spin, valley, and an orbital pseudospin. Apart from spin and valley-wave modes, the collective mode spectrum includes a low-energy intra-flavor exciton mode associated with transitions between flat valence and conduction band orbitals.
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 d
iagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Plancks 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 Plancks constant, which we obtain analytically. Our analytic flat band twist angles correspond closely to those determined numerically in previous work.
We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moire band electrons, we find that phonons generate attractive interactions in both $s$ and $d$ wa
ve 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 moire period, and is identical in the two layers in the $s$-wave channel but phase shifted by $pi$ in the $d$-wave channel. We discuss experiments that can distinguish the two pairing states.
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.
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively a
s J=1 and J=2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including assessing the role of disorder in current experimental results. Special attention is given to the interesting low magnetic field limit and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.
A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic inter-edge superexchange interaction. We present a theory based on asymptotic properties of the Dirac-model ribbon wavefunction which predicts $W^{-2
}$ and $W^{-1}$ ribbon-width dependencies for the superexchange interaction strength and the charge gap respectively. We find that, unlike the case of conventional atomic scale superexchange, opposite spin-orientations on opposite edges of the ribbon are favored by both kinetic and interaction energies.
We analyse the influence of current induced torques on the magnetization configuration of a ferromagnet in a circuit containing a compensated antiferromagnet. We argue that these torques are generically non-zero and support this conclusion with a mic
roscopic NEGF calculation for a circuit containing antiferromagnetic NiMn and ferromagnetic Co layers. Because of symmetry dictated differences in the form of the current-induced torque, the phase diagram which expresses the dependence of ferromagnet configuration on current and external magnetic field differs qualitatively from its ferromagnet-only counterpart.
