Nuclear-spin-induced localization of the edge states in two-dimensional topological insulators

We investigate the influence of nuclear spins on the resistance of helical edge states of two-dimensional topological insulators (2DTIs). Via the hyperfine interaction, nuclear spins allow electron backscattering, otherwise forbidden by time reversal symmetry. We identify two backscattering mechanisms, depending on whether the nuclear spins are ordered or not. Their temperature dependence is distinct but both give resistance, which increases with the edge length, decreasing temperature, and increasing strength of the electron-electron interaction. Overall, we find that the nuclear spins will typically shut down the conductance of the 2DTI edges at zero temperature.Comment: 5 pages, 3 figures, revised version accepted for publication in Phys. Rev.

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.Comment: 20 pages, 11 figures; revised version accepted for publication in Phys. Rev.

Topological density wave states of non-zero angular momentum

The pseudogap state of high temperature superconductors is a profound mystery. It has tantalizing evidence of a number of broken symmetry states, not necessarily conventional charge and spin density waves. Here we explore a class of more exotic density wave states characterized by topological properties observed in recently discovered topological insulators. We suggest that these rich topological density wave states deserve closer attention in not only high temperature superconductors but in other correlated electron states, as in heavy fermions.Comment: Expanded version, 7 pages, 6 figure

General scatterings and electronic states in the quantum-wire network of moir\'e systems

We investigate electronic states in a two-dimensional network consisting of interacting quantum wires, a model adopted for twisted bilayer systems. We construct general operators which describe various scattering processes in the system. In a twisted bilayer structure, the moir\'e periodicity allows for generalized umklapp scatterings, leading to a class of correlated states at certain fractional fillings. We identify scattering processes which can lead to an insulating gapped bulk with gapless chiral edge modes at fractional fillings, resembling the quantum anomalous Hall effect recently observed in twisted bilayer graphene. Finally, the description can be useful in predicting spectroscopic and transport features to detect and characterize the chiral edge modes in the moir\'e-induced correlated states.Comment: 14 pages, 7 figure