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Register a new userStabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States
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The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic (FM) region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the FM region, and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different lanes, the QSH effect becomes robust against symmetry-breaking perturbations.
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The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials but has eluded spatial measurements. In this report, we map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $ u=0,pm 1$ across the quantum Hall edge boundary using atomic force microscopy (AFM). Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moire superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.
Topological edge states exhibit dissipationless transport and electrically-driven topological phase transitions, making them ideal for next-generation transistors that are not constrained by Moores law. Nevertheless, their dispersion has never been probed and is often assumed to be simply linear, without any rigorous justification. Here we determine the non-linear electrical response of topological edge states in the ballistic regime and demonstrate the way this response ascertains the presence of symmetry breaking terms in the edge dispersion, such as deviations from non-linearity and tilted spin quantization axes. The non-linear response stems from discontinuities in the band occupation on either side of a Zeeman gap, and its direction is set by the spin orientation with respect to the Zeeman field. We determine the edge dispersion for several classes of topological materials and discuss experimental measurement.
The behavior of conduction electrons on magnetic structures has been intensely investigated. A typical example is the anomalous Hall effect in a ferromagnet. However, distinguishing various anomalous and normal Hall signals induced from the time-reversal symmetry (TRS) broken by their magnetic structure or applied magnetic field is delicate. In this study, we present a method to investigate TRS broken by the magnetic structure by analyzing magnetic quantum oscillations (MQOs). As is known, if a material is nonmagnetic, the MQO phases can only be two distinct values of 0 or $pi$ from the orbits. When the magnetic structure breaks the TRS, the MQO phase deviates from these values, and the deviation is called the anomalous phase. We observed the anomalous phase in Fe-doped NbSb2, where magnetic Fe impurities break the TRS. The phase of a high-doped sample largely deviates from the phases of low-doped and pristine samples, indicating the anomalous phase. In MQOs, different types of magnetic structures afford different field dependence to the phase; this makes it easy to discern different magnetic structures, which respond differently with magnetic fields. This method can complement the Hall measurement and will provide useful information by itself for studying the magnetic structure of materials.
We report direct imaging of standing waves of the nontrivial surface states of topological insulator Bi$_2$Te$_3$ by using a low temperature scanning tunneling microscope. The interference fringes are caused by the scattering of the topological states off Ag impurities and step edges on the Bi$_2$Te$_3$(111) surface. By studying the voltage-dependent standing wave patterns, we determine the energy dispersion $E(k)$, which confirms the Dirac cone structure of the topological states. We further show that, very different from the conventional surface states, the backscattering of the topological states by nonmagnetic impurities is completely suppressed. The absence of backscattering is a spectacular manifestation of the time-reversal symmetry, which offers a direct proof of the topological nature of the surface states.
We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias voltage applied to the neighboring quantum point contact, which originates from the Luttinger liquid physics which describes the Hall fluid. General expressions are obtained using a screened Coulomb interaction. The dephasing rate is strictly proportional to the zero frequency backscattering current noise, which allows to describe exactly the weak to strong backscattering crossover using the Bethe-Ansatz solution.
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