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Register a new userSurface theory of a second-order topological insulator beyond the Dirac approximation
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We study the surface states and chiral hinge states of a 3D second-order topological insulator in the presence of an external magnetic gauge field. Surfaces pierced by flux host Landau levels, while surfaces parallel to the applied field are not significantly affected. The chiral hinge modes mediate spectral flow between neighbouring surfaces. As the magnetic field strength is increased, the surface Landau quantization deviates from that of a massive Dirac cone. Quantitatively, the $n = 0$ Landau level falls inside the surface Dirac gap, and not at the gap edge. The $n e 0$ levels exhibit a further, qualitative discrepancy: while the massive Dirac cone is expected to produce pairs of levels ($pm n$) which are symmetric around zero energy, the $n$ and $-n$ levels become asymmetric in our lattice model -- one of the pair may even be absent from the spectrum, or hybridized with the continuum. In order to resolve the issue, we extend the standard 2D massive Dirac surface theory, by including additional Hamiltonian terms at $mathcal{O} (k^2)$. While these terms do not break particle-hole symmetry in the absence of magnetic field, they lead to the aforementioned Landau level asymmetry once the magnetic field is applied. We argue that similar $mathcal{O}(k^2)$ correction terms are generically expected in lattice models containing gapped Dirac fermions, using the BHZ model of a 2D topological insulator as an example.
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Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo insulator compound SmB6 are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The surface conductance, on the order of 100 e^2/h and electron-like, exhibits a field-effect mobility of 133 cm^2/V/s and a large carrier density of ~2x10^{14}/cm^2, in good agreement with recent photoemission results. With the ability to gate-modulate surface conduction by more than 25%, this approach provides promise for both fundamental and applied studies of gate-tuned devices structured on bulk crystal samples.
In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the [001] surface of a topological crystalline insulator (TCI) Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the topological stability of the step edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate the experimental signatures of the particle-hole symmetry breaking. We also reveal the effects of an external magnetic field on the 1D bound states. Our work suggests the possibility of similar topological step edge modes in other topological materials with a rocks-salt structure.
We uncover an edge geometric phase mechanism to realize the second-order topological insulators and topological superconductors (SCs), and predict realistic materials for the realization. The theory is built on a novel result shown here that the nontrivial pseudospin textures of edge states in a class of two-dimensional (2D) topological insulators give rise to the geometric phases defined on the edge, for which the effective edge mass domain walls are obtained across corners when external magnetic field or superconductivity is considered, and the Dirac or Majorana Kramers corner modes are resulted. Remarkably, with this mechanism we predict the Majorana Kramers corner modes by fabricating 2D topological insulator on only a uniform and conventional $s$-wave SC, in sharp contrast to the previous proposals which applies unconventional SC pairing or SC $pi$-junction. We find that Au/GaAs(111) can be a realistic material candidate for realizing such Majorana Kramers corner modes.
Three-dimensional (3D) topological insulators (TIs) are new forms of quantum matter that are characterized by their insulating bulk state and exotic metallic surface state, which hosts helical Dirac fermions1-2. Very recently, BiTeCl, one of the polar semiconductors, has been discovered by angle-resolved photoemission spectroscopy to be the first strong inversion asymmetric topological insulator (SIATI). In contrast to the previously discovered 3D TIs with inversion symmetry, the SIATI are expected to exhibit novel topological phenomena, including crystalline-surface-dependent topological surface states, intrinsic topological p-n junctions, and pyroelectric and topological magneto-electric effects3. Here, we report the first transport evidence for the robust topological surface state in the SIATI BiTeCl via observation of Shubnikov-de Haas (SdH) oscillations, which exhibit the 2D nature of the Fermi surface and pi Berry phase. The n = 1 Landau quantization of the topological surface state is observed at B . 12 T without gating, and the Fermi level is only 58.8 meV above the Dirac point, which gives rise to small effective mass, 0.055me, and quite large mobility, 4490 cm2s-1. Our findings will pave the way for future transport exploration of other new topological phenomena and potential applications for strong inversion asymmetric topological insulators.
The electrodynamics of topological insulators (TIs) is described by modified Maxwells equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of $e^2 / 2 h c $ per surface. Here, we report on the observation of this so-called topological magnetoelectric (TME) effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semi-transparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant $alpha = e^2 / hbar c$ when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
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