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arXiv:1411.4084 · Physical Review B

Spin correlations in quantum wires

Chen Sun, V. L. Pokrovsky

Published Apr 24, 2015• 4 citations
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Abstract

We consider theoretically spin correlations in a one-dimensional quantum wire with Rashba-Dresselhaus spin-orbit interaction (RDI). The correlations of noninteracting electrons display electron spin resonance at a frequency proportional to the RDI coupling. Interacting electrons, upon varying the direction of the external magnetic field, transit from the state of Luttinger liquid (LL) to the spin-density wave (SDW) state. We show that the two-time total-spin correlations of these states are significantly different. In the LL, the projection of total spin to the direction of the RDI-induced field is conserved and the corresponding correlator is equal to zero. The correlators of two components perpendicular to the RDI field display a sharp electron-spin resonance driven by the RDI-induced intrinsic field. In contrast, in the SDW state, the longitudinal projection of spin dominates, whereas the transverse components are suppressed. This prediction indicates a simple way for an experimental diagnostic of the SDW in a quantum wire. We point out that the Luttinger model does not respect the spin conservation since it assumes the infinite Fermi sea. We propose a proper cutoff to correct this failure.

DOI
10.1103/physrevb.91.161305

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We consider theoretically spin correlations in a one-dimensional quantum wire with Rashba-Dresselhaus spin-orbit interaction (RDI). The correlations of noninteracting electrons display electron spin resonance at a frequency proportional to the RDI coupling. Interacting electrons, upon varying the direction of the external magnetic field, transit from the state of Luttinger liquid (LL) to the spin-density wave (SDW) state. We show that the two-time total-spin correlations of these states are significantly different. In the LL, the projection of total spin to the direction of the RDI-induced field is conserved and the corresponding correlator is equal to zero. The correlators of two components perpendicular to the RDI field display a sharp electron-spin resonance driven by the RDI-induced intrinsic field. In contrast, in the SDW state, the longitudinal projection of spin dominates, whereas the transverse components are suppressed. This prediction indicates a simple way for an experimental diagnostic of the SDW in a quantum wire. We point out that the Luttinger model does not respect the spin conservation since it assumes the infinite Fermi sea. We propose a proper cutoff to correct this failure.
This is a review of theoretical works on spin resonance in a quantum wire associated with the spin-orbit interaction. We demonstrate that the spin-orbit induced internal “magnetic field” leads to a narrow spin-flip resonance at low temperatures in the absence of an applied magnetic field. An applied dc magnetic field perpendicular to and small compared with the spin-orbit field enhances the resonance absorption by several orders of magnitude. The component of applied field parallel to the spin-orbit field separates the resonance frequencies of right and left movers and enables a linearly polarized ac electric field to produce a dynamic magnetization as well as electric and spin currents. We start with a simple model of noninteracting electrons and then consider the interaction that is not weak in 1d electron system. We show that electron spin resonance in the spin-orbit field persists in the Luttinger liquid. The interaction produces an additional singularity (cusp) in the spin-flip channel associated with the plasma oscillation. As it was shown earlier by Starykh and his coworkers, the interacting 1d electron system in the external field with sufficiently large parallel component becomes unstable with respect to the appearance of a spin-density wave. This instability suppresses the spin resonance. The observation of the electron spin resonance in a thin wires requires low temperature and high intensity of electromagnetic field in the terahertz diapason. The experiment satisfying these two requirements is possible but rather difficult. An alternative approach that does not require strong ac field is to study two-time correlations of the total spin of the wire with an optical method developed by Crooker and coworkers. We developed theory of such correlations. We prove that the correlation of the total spin component parallel to the internal magnetic field is dominant in systems with the developed spin-density waves but it vanishes in Luttinger liquid. Thus, the measurement of spin correlations is a diagnostic tool to distinguish between the two states of electronic liquid in the quantum wire.
We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO 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 SO 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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We study a Luttinger Liquid in a finite one-dimensional wire with box-like boundary conditions by considering the local distribution of the single-particle spectral weight. This corresponds to the experimental probability of extracting a single electron at a given place and energy, which can be interpreted as the square of an electron wave function. For the noninteracting case, this is given by a standing wave at the Fermi wave vector. In the presence of interactions, however, the wave functions obtain additional structure with a sharp depletion near the edges and modulations throughout the wire. In the spinful case, these modulations correspond to the separate spin- and charge-like excitations in the system.