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arXiv:cond-mat/0607214 · Physical Review B

Hysteresis and spin phase transitions in quantum wires in the integer quantum Hall regime

Siarhei Ihnatsenka, Igor V. Zozoulenko

Published Jan 11, 2007• 11 citations
arXivHTMLPDF

Abstract

We demonstrate that a split-gate quantum wire in the integer quantum Hall regime can exhibit electronic transport hysteresis for up- and down-sweeps of a magnetic field. This behavior is shown to be due to phase spin transitions between two different ground states with and without spatial spin polarization in the vicinity of the wire boundary. The observed effect has a many-body origin arising from an interplay between a confining potential, Coulomb interactions, and the exchange interaction. We also demonstrate and explain why the hysteretic behavior is absent for steep and smooth confining potentials and is present only for a limited range of intermediate confinement slopes.

DOI
10.1103/physrevb.75.035318

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We demonstrate that a split-gate quantum wire in the integer quantum Hall regime can exhibit electronic transport hysteresis for up- and down-sweeps of a magnetic field. This behavior is shown to be due to phase spin transitions between two different ground states with and without spatial spin polarization in the vicinity of the wire boundary. The observed effect has a many-body origin arising from an interplay between a confining potential, Coulomb interactions, and the exchange interaction. We also demonstrate and explain why the hysteretic behavior is absent for steep and smooth confining potentials and is present only for a limited range of intermediate confinement slopes.
Motivated by the successful idea of using weakly coupled quantum electronic wires to realize the quantum Hall effects and the quantum spin Hall effects, we theoretically study two systems composed of weakly coupled quantum spin chains within the mean-field approximations, which can exhibit spin analogs of superconductivity and the integer quantum Hall effect. First, a certain bilayer of two arrays of interacting spin chains is mapped, via the Jordan-Wigner transformation, to an attractive Hubbard model that exhibits fermionic superconductivity, which corresponds to spin superconductivity in the original spin Hamiltonian. Secondly, an array of spin-orbit-coupled spin chains in the presence of a suitable external magnetic field is transformed to an array of quantum wires that exhibits the integer quantum Hall effect, which translates into its spin analog in the spin Hamiltonian. The resultant spin superconductivity and spin integer quantum Hall effect can be characterized by their ability to transport spin without any resistance.
We study the effects of electronic interactions on transport through parallel quantum dots connected symmetrically to leads, focusing on the case of an intermediate value of the on-site Coulomb interaction at each quantum dot. We apply both the mean-field (MF) approximation and the functional renormalization group (fRG) approach with using the Litim regularization scheme in frequency space to treat the effect of interaction and calculate the energy levels, the magnetization, the square of local spin as well as the linear conductance as a function of gate voltage. Already for intermediate values of the Coulomb interaction, the system exhibits a quantum phase transition from the parallel aligned (high spin state) to the paramagnetic (low spin) regime. This phase transition is accompanied by the appearance of the step discontinuities in the conductance, which can be observed in the experiment.
The spin phase diagram of interacting electrons in a quantum wire under a high magnetic field is investigated by finite-system exact diagonalization. Various phases emerge as a function of interaction strength and aspect ratio. Stable spin-polarized states correspond to two-dimensional fractional quantum Hall states of filling fractions 1/q,1/q,1/q, with qqq odd. Spin-singlet ground states for six electrons with filling fractions around 25−−12\frac{2}{5}--\frac{1}{2}52​−−21​ are inspected in detail, and a real-space singlet pairing state peculiar to wire systems is found for a larger aspect ratio.
One-dimensional (1D) quantum wires provide a versatile platform for studying strong electron-electron interactions and collective excitations under confinement. Coulomb drag between 1D systems offers a powerful probe of Tomonaga-Luttinger liquid (TLL) physics, with theoretical predictions suggesting distinct power-law in temperature dependencies between the spin-full and the spin-polarized regimes. However, experimental verification has thus far remained limited. Here, we report measurements of reciprocal and nonreciprocal Coulomb drag between vertically coupled quasi-1D quantum wires in the spin-polarized regime. Clear signatures of spin splitting are observed in both the wires conductance and the drag signal. We observed a connection between electron-hole asymmetry and negative drag, and demonstrated different power-law behaviors in spin-full and spin-polarized regimes, yielding consistent TLL interaction parameters. These results validate the theoretical predictions for backscattering induced drag in the reciprocal regime and extend them to the nonreciprocal and the multiple subband regimes. Furthermore, the nonmonotonic density dependence of the reciprocal interaction parameter correlates with the subband occupation of the drag wire, revealing the complexity of the scattering mechanisms in multichannel systems.
We study the effect of electron-electron backscattering interactions on spin transport in a quantum wire. Even if these interactions have no significant effect on charge transport, they strongly influence the transport of spin. We use the quantum Boltzmann equation in the collision approximation to derive equations of motion for spin current and magnetization. In the limit of small perturbations from equilibrium, we explain the existence of ``precessional'' and ``diffusive'' behaviors. We also discuss the low-temperature nonlinear decay of an uniform spin current outside the hydrodynamic regime.
We use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature, and a magnetic field, on the conductivity. We explain the deviations of the conductivity from 2Ne2/h{2Ne}^{2}/h2Ne2/h in wires that are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin-split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin valve that only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.