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Register a new userSpin current pumping in helical Luttinger liquids
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We study the DC spin current induced into an unbiased quantum spin Hall system through a two-point contacts setup with time dependent electron tunneling amplitudes. By means of two external gates, it is possible to drive a current with spin-preserving and spin-flipping contributions showing peculiar oscillations as a function of pumping frequency, electron-electron interaction and temperature. From its interference patterns as a function of the Fabry-Perot and Aharonov-Bohm phases, it is possible to extract information about the helical nature of the edge states and the intensity of the electron-electron interaction.
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Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Na{i}vely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations. Here we investigate transport properties of hDWs in the $ u=2/3$ fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the na{i}ve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.
Coulomb interaction has important consequences on the physics of quantum spin Hall edge states, weakening the topological protection via two-particle scattering and renormalizing both the velocity and charge of collective plasmon modes compared to that of free electrons. Despite these effects, interactions remain difficult to quantify. We propose here simple and robust edge resonator geometries to characterize Coulomb interaction by means of high-frequency measurements. They rely on a transmission line approach, and take advantage of the impedance mismatch between the edge states and their microwave environment.
One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator, also known as a two-dimensional topological insulator, and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in semiconductors. Our focus is on the theory, though we confront it with existing experiments. We discuss various aspects of the helical states, such as their realization, topological protection and stability, or possible experimental characterization. We lay emphasis on the hallmark of these states, being the prediction of a quantized electrical conductance. Since so far reaching a well-quantized conductance remained challenging experimentally, a large part of the review is a discussion of various backscattering mechanisms which have been invoked to explain this discrepancy. Finally, we include topics related to proximity-induced topological superconductivity in helical states, as an exciting application towards topological quantum computation with the resulting Majorana bound states.
We investigate a one-dimensional electron liquid with two point scatterers of different strength. In the presence of electron interactions, the nonlinear conductance is shown to depend on the current direction. The resulting asymmetry of the transport characteristic gives rise to a ratchet effect, i.e., the rectification of a dc current for an applied ac voltage. In the case of strong repulsive interactions, the ratchet current grows in a wide voltage interval with decreasing ac voltage. In the regime of weak interaction the current-voltage curve exhibits oscillatory behavior. Our results apply to single-band quantum wires and to tunneling between quantum Hall edges.
We develop a theory of finite-temperature momentum-resolved tunneling spectroscopy (MRTS) for disordered, interacting two-dimensional topological-insulator edges. The MRTS complements conventional electrical transport measurement in characterizing the properties of the helical Luttinger liquid edges. Using standard bosonization technique, we study low-energy spectral function and the MRTS tunneling current, providing a detailed description controlled by disorder, interaction, and temperature, taking into account Rashba spin orbit coupling, interedge interaction and distinct edge velocities. Our theory provides a systematic description of the spectroscopic signals in the MRTS measurement and we hope will stimulate future experimental studies on the two-dimensional time-reversal invariant topological insulator.
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