Helical gaps in interacting Rashba wires at low electron densities

Schmidt, Thomas L.; Pedder, Christopher J.

doi:10.1103/physrevb.94.125420

Cited by 20 publications

(24 citation statements)

References 54 publications

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“…We continue with the spin-exchange termsV sx in Eq. (12). While those mostly yield merely corrections to the terms already present in the density-density interaction termV ρ , there remains one term which cannot be written as a density-density interaction and must thus be kept separate, namelŷ…”

Section: Bosonizationmentioning

confidence: 99%

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

et al. 2016

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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.

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Section: Bosonizationmentioning

confidence: 99%

“…1) due to an applied magnetic field. Indeed, the creation of such a gap can be understood most easily for non-interacting electrons, and the fate of this "helical gap" in the interacting case has been studied in recent years using renormalization-group (RG) arguments, numerical simulations, and Wigner crystal theory [9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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“…One of the goals of this work is to compare the properties of our microscopic model to those of the popular LL models [26][27][28][29][30][31][32][33][34][35][36][37], specifically, the spiral LL and the helical LL. The spiral LL was first introduced by Braunecker et al [38,39] to describe a LL embedded in a lattice of nuclear spins.…”

Section: Introductionmentioning

confidence: 99%

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

et al. 2017

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We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

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“…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 ).…”

Section: A Averaging Out the Charge Degrees Of Freedommentioning

confidence: 99%

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

2017

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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.

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Helical gaps in interacting Rashba wires at low electron densities

Cited by 20 publications

References 54 publications

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

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

Interaction effects in a microscopic quantum wire model with strong spin–orbit interaction

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

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