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

Abstract

We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.

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

“…Theoretical works have also turned to unproximitized wires with RSOC, [37][38][39][40][41][42] and experimental studies have investigated transport in these wires too. Without induced superconductivity, the system only has a partial gap, and so does not contain localized bound states.…”

A Short Review of One-Dimensional Wigner Crystallization

“…Spin-orbit coupling, that can be significant in carbon nanotubes, couples the spin and the valley degree of freedom and can further enrich the physics, mainly lifting degeneracies and altering the transport properties in the Kondo regime [111][112][113][114]. Another relevant topic is the behavior of the electrons hosted by carbon nanotubes in the presence of an external magnetic field.…”

A Short Review on One Dimensional Wigner Crystallization

“…Thus, when the phonons of the chain are included in the Hamiltonian, the picture drawn for weakly interacting CNTs is recovered even for the Wigner molecule in CNTs. Spin-orbit coupling, that can be significant in carbon nanotubes, couples the spin and the valley degree of freedom and can further enrich the physics, mainly lifting degeneracies and altering the transport properties in the Kondo regime [111][112][113][114]. Another relevant topic is the behavior of the electrons hosted by carbon nanotubes in the presence of an external magnetic field.…”