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Register a new userExcitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators
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We study the effects of strong electron-electron interactions on the surface of cubic topological Kondo insulators (such as samarium hexaboride, SmB$_6$). Cubic topological Kondo insulators generally support three copies of massless Dirac nodes on the surface, but only two of them are energetically degenerate and exhibit an energy offset relative to the third one. With a tunable chemical potential, when the surface states host electron and hole pockets of comparable size, strong interactions may drive this system into rotational symmetry breaking nematic and translational symmetric breaking excitonic spin- or charge-density-wave phases, depending on the relative chirality of the Dirac cones. Taking a realistic surface band structure into account we analyze the associated Ginzburg-Landau theory and compute the mean field phase diagram for interacting surface states. Beyond mean field theory, this system can be described by a two-component isotropic Ashkin-Teller model at finite temperature, and we outline the phase diagram of this model. Our theory provides a possible explanation of recent measurements which detect a two-fold symmetric magnetoresistance and an upturn in surface resistivity with tunable gate voltage in SmB$_6$. Our discussion can also be germane to other cubic topological insulators, such as ytterbium hexaboride (YbB$_6$), plutonium hexaboride (PuB$_6$).
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The surface states of 3D topological insulators can exhibit Fermi surfaces of arbitrary area when the chemical potential is tuned away from the Dirac points. We focus on topological Kondo insulators and show that the surface states can acquire a finite Fermi surface even when the chemical potential is pinned to the Dirac point energy. We illustrate how this can occur when the crystal symmetry is lowered from cubic to tetragonal in a minimal two-orbital model. We label such surface modes as `shadow surface states. We also show that for certain bulk hybridization the Fermi surface of the shadow states can become comparable to the extremal area of the unhybridized bulk bands. The `large Fermi surface of the shadow states is expected to lead to large-frequency quantum oscillations in the presence of an applied magnetic field. Consequently, shadow surface states provide an alternative to mechanisms involving bulk Landau-quantized levels or surface Kondo breakdown for anomalous magnetic quantum oscillations in topological Kondo insulators with tetragonal crystal symmetry.
A fascinating type of symmetry-protected topological states of matter are topological Kondo insulators, where insulating behavior arises from Kondo screening of localized moments via conduction electrons, and non-trivial topology emerges from the structure of the hybridization between the local-moment and conduction bands. Here we study the physics of Kondo holes, i.e., missing local moments, in three-dimensional topological Kondo insulators, using a self-consistent real-space mean-field theory. Such Kondo holes quite generically induce in-gap states which, for Kondo holes at or near the surface, hybridize with the topological surface state. In particular, we study the surface-state quasiparticle interference (QPI) induced by a dilute concentration of surface Kondo holes and compare this to QPI from conventional potential scatterers. We treat both strong and weak topological-insulator phases and, for the latter, specifically discuss the contributions to QPI from inter-Dirac-cone scattering.
We investigate interaction effects in three dimensional weak topological insulators (TI) with an even number of Dirac cones on the surface. We find that the surface states can be gapped by a surface charge density wave (CDW) order without breaking the time-reversal symmetry. In this sense, time reversal symmetry alone can not robustly protect the weak TI state in the presence of interactions. If the translational symmetry is additionally imposed in the bulk, a topologically non-trivial weak TI state can be obtained with helical edge states on the CDW domain walls. In other words, a CDW domain wall on the surface is topologically equivalent to the edge of a two-dimensional quantum spin Hall insulator. Therefore, the surface state of a weak topological insulator with translation symmetry breaking on the surface has a half quantum spin Hall effect, in the same way that the surface state of a strong topological insulator with time-reversal symmetry breaking on the surface has a half quantum Hall effect. The on-site and nearest neighbor interactions are investigated in the mean field level and the phase diagram for the surface states of weak topological insulators is obtained.
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.
A prominent feature of topological insulators (TIs) is the surface states comprising of spin-nondegenerate massless Dirac fermions. Recent technical advances have made it possible to address the surface transport properties of TI thin films while tuning the Fermi levels of both top and bottom surfaces across the Dirac point by electrostatic gating. This opened the window for studying the spin-nondegenerate Dirac physics peculiar to TIs. Here we report our discovery of a novel planar Hall effect (PHE) from the TI surface, which results from a hitherto-unknown resistivity anisotropy induced by an in-plane magnetic field. This effect is observed in dual-gated devices of bulk-insulating Bi$_{2-x}$Sb$_{x}$Te$_{3}$ thin films, in which both top and bottom surfaces are gated. The origin of PHE is the peculiar time-reversal-breaking effect of an in-plane magnetic field, which anisotropically lifts the protection of surface Dirac fermions from back-scattering. The key signature of the field-induced anisotropy is a strong dependence on the gate voltage with a characteristic two-peak structure near the Dirac point which is explained theoretically using a self-consistent T-matrix approximation. The observed PHE provides a new tool to analyze and manipulate the topological protection of the TI surface in future experiments.
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