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Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes. Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator MnBi2Te4. We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment, Kerr and Faraday effects occur. Under perpendicular electric field, antiferromagnetic topological insulators (AFMTI) show sharp peaks at the interband transition threshold, whereas trivial insulators show small adjacent positive and negative peaks. Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators. We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr (Faraday) angles and vanishing ellipticity. Under external magnetic moment, AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity. For the qualitative behaviors, AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change. These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.

We systematically study the impact of various electron-acoustic-phonon coupling mechanisms on valley physics in two-dimensional materials. In the static strain limit, we find that Dirac cone tilt and deformation potential have analogous valley Hall response since they fall into the same universality class of pseudospin structure. However, such argument fails for the coupling mechanism with position-dependent Fermi velocity. For the isotropic case, a significant valley Hall effect occurs near charge neutrality similar to the bond-length change, whereas for the anisotropic case, the geometric valley transport is suppressed, akin to the deformation potential. Gap opening mechanism by nonuniform strain is found to totally inhibit the valley Hall transport, even if the dynamics of strains are introduced. By varying gate voltage, a tunable phonon-assisted valley Hall response can be realized, which paves a way toward rich phenomena and new functionalities of valley acoustoelectronics., Comment: 6 pages, 1 figure

We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the valley Hall effect in graphene systems represents a new paradigm for the anomalous Hall physics where gauge disorder plays an important role.

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the $\bm k$-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and highlights the importance of the Berry curvature in the effective mass approximation., 4.5 pages, 2 figures, reference updated and minor changes

In conventional light harvesting devices, the absorption of a single photon only excites one electron, which sets the standard limit of power-conversion efficiency, such as the Shockley-Queisser limit. In principle, generating and harnessing multiple carriers per absorbed photon can improve the efficiency and possibly overcome this limit. Here, we report the observation of multiple hot carrier collection in graphene-boron-nitride Moire superlattice structures. A record-high zero-bias photoresponsivity of 0.3 ampere per watt, equivalently, an external quantum efficiency exceeding 50 percent, is achieved utilizing graphene photo-Nernst effect, which demonstrates a collection of at least 5 carriers per absorbed photon. We reveal that this effect arises from the enhanced Nernst coefficient through Lifshtiz transition at low energy Van Hove singularities, which is an emergent phenomenon due to the formation of Moire minibands. Our observation points to a new means for extremely efficient and flexible optoelectronics based on van der Waals heterostructures., 16 pages + 4 figures + supplementary information

We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results provide an alternative scheme to engineer topological SMs and shed new light on the application of Dirac and Weyl SMs in spintronics., Comment: 11 pages including supplemental materials, 2 figures

We present a general description of topological insulators from the point of view of Dirac equations. The Z_{2} index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic B term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, the Z_{2} index is modified as 1 for mB>0 and 0 for mB, 9 pages, published version

Bi2Se3 is theoretically predicted1 2and experimentally observed2,3 to be a three dimensional topological insulator. For possible applications, it is important to understand the electronic structure of the planar device. In this work, thickness dependent band structure of molecular beam epitaxy grown ultrathin films of Bi2Se3 is investigated by in situ angle-resolved photoemission spectroscopy. An energy gap is observed for the first time in the topologically protected metallic surface states of bulk Bi2Se3 below the thickness of six quintuple layers, due to the coupling between the surface states from two opposite surfaces of the Bi2Se3 film. The gapped surface states exhibit sizable Rashba-type spin-orbit splitting, due to breaking of structural inversion symmetry induced by SiC substrate. The spin-splitting can be controlled by tuning the potential difference between the two surfaces., Comment: 17 pages, 3 figures,1 table

Strong Rashba spin-orbit coupling (SOC) of the two-dimensional electron gas (2DEG) at the oxide interface $\mathrm{LaAlO_{3}/SrTiO_{3}}$ underlies a variety of exotic physics, but its nature is still under debate. We derive an effective Hamiltonian for the 2DEG at the oxide interface $\mathrm{LaAlO_{3}/SrTiO_{3}}$ and find a different anisotropic Rashba SOC for the $d_{xz}$ and $d_{yz}$ orbitals. This anisotropic Rashba SOC leads to anisotropic static spin susceptibilities and also distinctive behavior of the spin Hall conductivity. These unique spin responses may be used to determine the nature of the Rashba SOC experimentally and shed light on the orbital origin of the 2DEG.

Bilayer graphene can host topological currents that are robust against defects and are associated with the electron valleys. It is now shown that electric fields can tune this topological valley transport over long distances at room temperature. Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands1, is a distinct feature of two-dimensional Dirac materials1,2,3,4,5. Similar to spin, the valley pseudospin is spanned by a time-reversal pair of states, although the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interest2,3,4,5. Bilayer graphene is a unique system whose intrinsic inversion symmetry can be controllably broken by a perpendicular electric field, offering a rare possibility for continuously tunable topological valley transport. We used a perpendicular gate electric field to break the inversion symmetry in bilayer graphene, and a giant nonlocal response was observed as a result of the topological transport of the valley pseudospin. We further showed that the valley transport is fully tunable by external gates, and that the nonlocal signal persists up to room temperature and over long distances. These observations challenge the current understanding of topological valley transport in a gapped system, and the robust topological transport may lead to future valleytronic applications.

We study both the intrinsic and extrinsic spin Hall effect in spin-valley coupled monolayers of transition metal dichalcogenides. We find that whereas the skew-scattering contribution is suppressed by the large band gap, the side-jump contribution is comparable to the intrinsic one with opposite sign in the presence of scalar and magnetic scattering. Intervalley scattering tends to suppress the side-jump contribution due to the loss of coherence. By tuning the ratio of intra- to intervalley scattering, the spin Hall conductivity shows a sign change in hole-doped samples. The multiband effect in other doping regimes is considered, and it is found that the sign change exists in the heavily hole-doped regime, but not in the electron-doped regime.

We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$ orbitals of $M$ atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all $MX_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $\pm K$ valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor $M$-$M$ hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of $M$ atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between Mo$X_{2}$ and W$X_{2}$. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states., Comment: 11 pages, 10 figures, 4 tables

Effect of spin-orbit scattering on quantum diffusive transport of two-dimensional massive Dirac fermions is studied by the diagrammatic technique. The quantum diffusion of massive Dirac fermions can be viewed as a singlet Cooperon in the massless limit and a triplet Cooperon in the large-mass limit. The spin-orbit scattering behaves like random magnetic fields only to the triplet Cooperon, and suppresses the weak localization of Dirac fermions in the large-mass regime. This behavior suggests an experiment to detect the weak localization of bulk subbands in topological insulator thin films, in which a narrowing of the cusp of the negative magnetoconductivity is expected after doping heavy-element impurities. Finally, a detailed comparison between the conventional two-dimensional electrons and Dirac fermions is presented for impurities of orthogonal, symplectic, and unitary symmetries., 5 pages, 3 figures, 2 tables. To be submitted, comments are welcome

We present an exact solution of a modified Dirac equation for topological insulator in the presence of a hole or vacancy to demonstrate that vacancies can induce bound states in the band gap of topological insulators. They arise due to the ${\mathbb{Z}}_{2}$ classification of time-reversal invariant insulators. Coexistence of the in-gap bound states and the edge or surface states in topological insulators suggests that imperfections may affect transport properties of topological insulators via additional bound states near the system boundary.

We study the topologically nontrivial semimetals by means of the six-band Kane model. Existence of surface states is explicitly demonstrated by calculating the local density of states (LDOS) on the material surface. In the strain-free condition, surface states are divided into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uniaxial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict the existence of helical edge states and spin Hall effect in the thin-film topological semimetals, which could be tested by future experiments. Disorder is found to significantly enhance the spin-Hall effect in the valence band of the thin films.

We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film., Comment: 7 pages, 5 figures

In-gap bound states induced by non-magnetic impurities in various dimensional topological insulators are investigated based on a modified Dirac model that considers quadratic corrections to the mass term. Their existence and features greatly rely on the potential form of the impurity as well as the dimensionality of the topological insulator. It is analytically proven that the impurity potential modeled by the delta function can induce the bound states in one dimension (1D), but not in two and three. For a single non-magnetic impurity with a general isotropic potential, formal solutions are obtained and further numerical calculations are performed. In particular, the in-gap bound states induced by a non-magnetic impurity with isotropic Gaussian potentials in two-dimensional (2D) and three-dimensional (3D) topological insulators are numerically investigated. Information on how many in-gap bound states can be trapped by a non-magnetic Gaussian impurity is presented for the parameters from a series of topologically non-trivial materials.

Two-dimensional effective continuous models are derived for the surface states and thin films of the three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on the first principles calculation [Zhang \emph{et al}, Nat. Phys. 5, 438 (2009)], we present solutions for both the surface states in a semi-infinite boundary condition and in the thin film with finite thickness. An effective continuous model was derived for surface states and the thin film 3DTI. The coupling between opposite topological surfaces and structure inversion asymmetry (SIA) give rise to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum. Besides, the SIA leads to asymmetric distributions of wavefunctions along the film growth direction, making some branches in the energy spectra much harder than others to be probed by light. These features agree well with the recent angle-resolved photoemission spectra of Bi$_{2}$Se $_{3}$ films grown on SiC substrate [Zhang et al, arXiv: 0911.3706]. More importantly, we use the effective model to fit the experimental data and determine the model parameters. The result indicates that the thin film Bi$_{2}$Se$_{3}$ lies in quantum spin Hall region based on the calculation of the Chern number and the $Z_{2}$ invariant. In addition, strong SIA always intends to destroy the quantum spin Hall state., Comment: 12 pages, 7 figures, references are updated