Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

Abstract

A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

Missing Shapiro steps and the 8π -periodic Josephson effect in interacting helical electron systems

“…As described in Ref. [36], changes of sub-band come with a spin flip, which in tandem with a spinconserving interaction can generate spin-umklapp scattering when the chemical potential is at the Dirac point. This scattering converts e.g.…”

“…In the absence of TRS breaking, the wire adjacent to the edges of the superconductors will host zero-energy modes with charge e/2, which will dominate the transport at low energies and for a short junction. 36 Tunnelling of a single quasiparticle through the junction will change the parity of the end states. In order to satisfy the boundary conditions due to the applied superconducting phase difference, four e/2 quasiparticles must tunnel via the bound states, leading to an 8π periodic Josephson effect 34 .…”

“…Recently, we showed that an analogous spinumklapp scattering can open a helical gap without magnetic field in strongly interacting wires with RSOC. 36 This prompts the question of whether an 8π-periodic Josephson current can be detected in Rashba wires as well.…”

Spin-orbit coupling in quasi-one-dimensional Wigner crystals

“…This is the same condition for the opening of a helical gap in the spectrum given in Refs. [34] and [33]. Since the fluctuations about the equilibrium positions are small, we approximate cos(2mαx n ) 1, and neglect altogether the term containing sin(2mαx n ).…”

“…It is thus important to study this model as it can provide insights into the behavior of conductance and other characteristics of nanowires with Rashba SOC. 32,33 The spectrum of a quantum wire with Rashba SOC and applied magnetic field in the limit of strong electron-electron interaction was considered in Ref. [34].…”