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See detailSpin-orbit coupling in quasi-one-dimensional Wigner crystals
Kornich, Viktoriia; Pedder, Christopher UL; Schmidt, Thomas UL

in Physical Review B (2017), 95(4), 045413

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 ... [more ▼]

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. [less ▲]

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See detailDynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields
Pedder, Christopher UL; Meng, Tobias; Tiwari, Rakesh et al

in Physical Review B (2016), 94(24), 245414

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 ... [more ▼]

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. [less ▲]

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See detailStability of a spin-triplet nematic state near to a quantum critical point
Hannappel, Gregor; Pedder, Christopher UL; Kruger, Frank et al

in Physical Review. B: Condensed Matter and Materials Physics (2016), 93(23), 5105

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk ... [more ▼]

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards d-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial rotational symmetries. This order results in spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a nematic state that is intertwined with a helical modulation in spin space. Such a state is closely related to d-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, p-wave superconducting state. [less ▲]

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See detailThe helical gap in interacting Rashba wires at low electron densities
Schmidt, Thomas UL; Pedder, Christopher UL

E-print/Working paper (2016)

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting ... [more ▼]

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. [less ▲]

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See detailStrongly interacting quantum wires with spin-orbit coupling
Pedder, Christopher UL; Schmidt, Thomas UL

Scientific Conference (2016, March 10)

We study the effect of Rashba spin-orbit coupling on a quantum wire with strong interactions, which can be experimentally realised by depopulating a gated InSb or GaAs wire. When the wire carries a very ... [more ▼]

We study the effect of Rashba spin-orbit coupling on a quantum wire with strong interactions, which can be experimentally realised by depopulating a gated InSb or GaAs wire. When the wire carries a very low density of electrons, it is convenient to model the system in terms of a "Wigner crystal" of electrons localised on lattice sites. At the lowest densities, the Wigner crystal is a one dimensional entity, whereas at intermediate regimes it is know that a "zigzag" crystal consisting of two parallel rows of electrons can form. We investigate the effect of Rashba spin-orbit coupling, which plays an important role for both the spin and charge degrees of freedom, in both these systems with and without an applied magnetic field. We propose detection of these effects via measurement of spin-spin correlation functions of the quantum wire, e.g. by doing STM with a polarized tip. [less ▲]

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See detailParafermion bound states and the fractional Josephson effect in Rashba spin-orbit coupled nanowires
Pedder, Christopher UL; Meng, Tobias; Tiwari, Rakesh et al

Poster (2015, September)

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See detail8pi-periodic Josephson effect in time-reversal invariant interacting Rashba nanowires
Pedder, Christopher UL; Meng, Tobias; Tiwari, Rakesh et al

E-print/Working paper (2015)

We investigate narrow quantum wires with strong Rashba spin-orbit coupling and electron-electron interactions. We show that virtual transitions between subbands lead to umklapp scattering which can open a ... [more ▼]

We investigate narrow quantum wires with strong Rashba spin-orbit coupling and electron-electron interactions. We show that virtual transitions between subbands lead to umklapp scattering which can open a partial gap in the spectrum even in the presence of time-reversal symmetry. Using the superconducting proximity effect to gap out the remaining modes, we show that the system can host zero-energy states at its edges, which are protected by time-reversal symmetry. We present the parameter regime in which these bound states will emerge. Similarly to Majorana bound states, they will produce a zero-bias peak in the differential conductance. In contrast to the Majorana fermions, however, their fourfold degeneracy leads to an 8π periodicity of the Josephson current due to tunneling of fractionalized excitations with charge e/2. [less ▲]

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