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Register a new userTwo-dimensional Dirac fermions in a topological insulator: transport in the quantum limit
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Pulsed magnetic fields of up to 55T are used to investigate the transport properties of the topological insulator Bi_2Se_3 in the extreme quantum limit. For samples with a bulk carrier density of n = 2.9times10^16cm^-3, the lowest Landau level of the bulk 3D Fermi surface is reached by a field of 4T. For fields well beyond this limit, Shubnikov-de Haas oscillations arising from quantization of the 2D surface state are observed, with the u =1 Landau level attained by a field of 35T. These measurements reveal the presence of additional oscillations which occur at fields corresponding to simple rational fractions of the integer Landau indices.
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The recent theoretical prediction and experimental realization of topological insulators (TI) has generated intense interest in this new state of quantum matter. The surface states of a three-dimensional (3D) TI such as Bi_2Te_3, Bi_2Se_3 and Sb_2Te_3 consist of a single massless Dirac cones. Crossing of the two surface state branches with opposite spins in the materials is fully protected by the time reversal (TR) symmetry at the Dirac points, which cannot be destroyed by any TR invariant perturbation. Recent advances in thin-film growth have permitted this unique two-dimensional electron system (2DES) to be probed by scanning tunneling microscopy (STM) and spectroscopy (STS). The intriguing TR symmetry protected topological states were revealed in STM experiments where the backscattering induced by non-magnetic impurities was forbidden. Here we report the Landau quantization of the topological surface states in Bi_2Se_3 in magnetic field by using STM/STS. The direct observation of the discrete Landau levels (LLs) strongly supports the 2D nature of the topological states and gives direct proof of the nondegenerate structure of LLs in TI. We demonstrate the linear dispersion of the massless Dirac fermions by the square-root dependence of LLs on magnetic field. The formation of LLs implies the high mobility of the 2DES, which has been predicted to lead to topological magneto-electric effect of the TI.
We experimentally investigate the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We find that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a non-monotonic differential resistance of narrow channels. We show that the observed initial increase in resistance can be attributed to electron-hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron-hole scattering in the transport properties of topological insulators.
We study nonlocal resistance in an H-shaped two-dimensional HgTe/CdTe quantum well consist of injector and detector, both of which can be tuned in the quantum spin Hall or metallic spin Hall regime. Because of strong spin-orbit interaction, there always exist spin Hall effect and the nonlocal resistance in HgTe/CdTe quantum well. We find that when both detector and injector are in the quantum spin Hall regime, the nonlocal resistance is quantized at $0.25frac{h}{e^2}$, which is robust against weak disorder scattering and small magnetic field. While beyond this regime, the nonlocal resistance decreases rapidly and will be strongly suppressed by disorder and magnetic field. In the presence of strong magnetic field, the quantum spin Hall regime will be switched into the quantum Hall regime and the nonlocal resistance will disappear. The nonlocal signal and its various manifestation in different hybrid regimes originate from the special band structure of HgTe/CdTe quantum well, and can be considered as the fingerprint of the helical quantum spin Hall edge states in two-dimensional topological insulator.
We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite honeycomb lattice with a zigzag boundary. It is revealed that, in a one-dimensional Brillouin zone, the edge states merge into the continuous bands of the bulk states through a bifurcation of the edge-state width. We discuss the implications of the results to the experiments in monolayer or thin films of topological insulators.
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a heavy Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can reduce the Fermi velocity of Dirac fermions. Due to the negligible linear term, interaction effects will be greatly enhanced and can drive heavy Dirac fermion states into the half quantum Hall state with non-zero Hall conductance.
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