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Register a new userConnectivity of edge and surface states in topological insulators
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The edge states of a two-dimensional quantum spin Hall (QSH) insulator form a one-dimensional helical metal which is responsible for the transport property of the QSH insulator. Conceptually, such a one-dimensional helical metal can be attached to any scattering region as the usual metallic leads. We study the analytical property of the scattering matrix for such a conceptual multiterminal scattering problem in the presence of time reversal invariance. As a result, several theorems on the connectivity property of helical edge states in two-dimensional QSH systems as well as surface states of three-dimensional topological insulators are obtained. Without addressing real model details, these theorems, which are phenomenologically obtained, emphasize the general connectivity property of topological edge/surface states from the mere time reversal symmetry restriction.
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We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the 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 uni-axial 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 existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films.
We propose a surface-edge state theory for half quantized Hall conductance of surface states in topological insulators. The gap opening of a single Dirac cone for the surface states in a weak magnetic field is demonstrated. We find a new surface state resides on the surface edges and carries chiral edge current, resulting in a half-quantized Hall conductance in a four-terminal setup. We also give a physical interpretation of the half quantized conductance by showing that this state is the product of splitting of a boundary bound state of massive Dirac fermions which carries a conductance quantum.
We investigate the spin and charge densities of surface states of the three-dimensional topological insulator $Bi_2Se_3$, starting from the continuum description of the material [Zhang {em et al.}, Nat. Phys. 5, 438 (2009)]. The spin structure on surfaces other than the 111 surface has additional complexity because of a misalignment of the contributions coming from the two sublattices of the crystal. For these surfaces we expect new features to be seen in the spin-resolved ARPES experiments, caused by a non-helical spin-polarization of electrons at the individual sublattices as well as by the interference of the electron waves emitted coherently from two sublattices. We also show that the position of the Dirac crossing in spectrum of surface states depends on the orientation of the interface. This leads to contact potentials and surface charge redistribution at edges between different facets of the crystal.
We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show that these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-Hove singularities in their dispersion, which can serve as an experimental fingerprint. In addition, we study the response of the surface states to magnetic fields.
We theoretically study the effect of magnetic moire superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moire potentials generically gap out the moire surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Delta_1$ moire potential strengths are equal to each other, we find that energetically the first three bands of $Gamma$-valley moire surface electrons are non-degenerate and realize i) an $s$-orbital model on a honeycomb lattice, ii) a degenerate $p_x,p_y$-orbitals model on a honeycomb lattice, and iii) a hybridized $sd^2$-orbital model on a kagome lattice, where moire surface Dirac cones in these bands emerge. When $U_0 eqDelta_1$, the difference between the two moire potential serves as an effective spin-orbit coupling and opens a topological gap in the emergent moire surface Dirac cones.
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