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Register a new userQuarter-Filled Honeycomb Lattice with a Quantized Hall Conductance
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We study a generic two-dimensional hopping model on a honeycomb lattice with strong spin-orbit coupling, without the requirement that the half-filled lattice be a Topological Insulator. For quarter-(or three-quarter) filling, we show that a state with a quantized Hall conductance generically arises in the presence of a Zeeman field of sufficient strength. We discuss the influence of Hubbard interactions and argue that spontaneous ferromagnetism (which breaks time-reversal) will occur, leading to a quantized anomalous Hall effect.
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The energy spectrum of massless Dirac fermions in graphene under two dimensional periodic magnetic modulation having square lattice symmetry is calculated. We show that the translation symmetry of the problem is similar to that of the Hofstadter or TKNN problem and in the weak field limit the tight binding energy eigenvalue equation is indeed given by Harper Hofstadter hamiltonian. We show that due to its magnetic translational symmetry the Hall conductivity can be identified as a topological invariant and hence quantized. We thus extend the idea of Quantum Hall Effect to magnetically modulated two dimensional electron system. Finally we indicate possible experimental systems where this may be verified.
Majorana zero-modes hold great promise for topological quantum computing. Tunnelling spectroscopy in electrical transport is the primary tool to identify the presence of Majorana zero-modes, for instance as a zero-bias peak (ZBP) in differential-conductance. The Majorana ZBP-height is predicted to be quantized at the universal conductance value of 2e2/h at zero temperature. Interestingly, this quantization is a direct consequence of the famous Majorana symmetry, particle equals antiparticle. The Majorana symmetry protects the quantization against disorder, interactions, and variations in the tunnel coupling. Previous experiments, however, have shown ZBPs much smaller than 2e2/h, with a recent observation of a peak-height close to 2e2/h. Here, we report a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in InSb semiconductor nanowires covered with an Al superconducting shell. Our ZBP-height remains constant despite changing parameters such as the magnetic field and tunnel coupling, i.e. a quantized conductance plateau. We distinguish this quantized Majorana peak from possible non-Majorana origins, by investigating its robustness on electric and magnetic fields as well as its temperature dependence. The observation of a quantized conductance plateau strongly supports the existence of non-Abelian Majorana zero-modes in the system, consequently paving the way for future braiding experiments.
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.
Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.
Quantized conductance is reported in high-crystalline tin oxide (SnO2) nanobelt back-gate field-effect transistors, at low temperatures. The quantized conductance was observed as current oscillations in the drain current vs. gate voltage characteristics, and were analyzed considering the nanobelt as a quantum wire with rectangular cross-section hard-walls. The quantum confinement in the nanowires created conditions for the successive filling of the electron energy-subbands, as the gate voltage increases. When the source-drain voltage is changed the oscillations are not dislocated with respect to Vg, indicating flat-band subband energies at low temperatures. The subband separation was found to be in good agreement with the experimental observations, since the oscillations tend to disappear for T > 60K. Therefore, a novel quantum effect is reported in SnO2 nanobelts, which is expected to behave as bulk at zero electric gate fields.
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