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arXiv:2311.06862 · Physical Review A

Sine-Gordon dynamics in spin transport

Anne-Maria Visuri

Published May 13, 2024• 2 citations
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Abstract

We study spin transport in a one-dimensional finite-length wire connected to fermionic leads. The interacting wire is described by the sine-Gordon model while the leads are either noninteracting or interacting Luttinger liquids. We calculate the spin current driven by a spin bias in the nonlinear regime by solving numerically the classical equation of motion, and find that the cosine term in the sine-Gordon model gives rise to an oscillating spin current when the spin bias exceeds its critical value. We discuss the results in connection with transport experiments with ultracold atoms.

DOI
10.1103/physreva.109.053310

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We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent $2K\ensuremath{-}1$ for spinless electrons, where KKK is the interaction parameter. For K<1∕2K<1∕2K<1∕2, the current grows large for special values of the bias. For noninteracting electrons with K=1K=1K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1∕21∕21∕2 electrons.
We present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model (LCLCLC line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full III-VVV characteristic of the spinless fermion model with nearest-neighbor hopping tH{t}_{\text{H}}tH​ and interaction VH{V}_{\text{H}}VH​ using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions (VH=0{V}_{\text{H}}=0VH​=0). For interacting fermions we find that in the linear regime $eV\ensuremath{\ll}4{t}_{\text{H}}$ the current III is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials VVV the steady-state current depends on the current-generating setup and as VVV increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.
We study theoretically electronic transport through an isolated local defect in a 1D conductor described in terms of the Luttinger liquid, and show that the well-known tunneling regime of electronic transport leading to power-law I-V curves takes place only in the limit of small voltage. At voltages exceeding a threshold value a new dynamic regime of transport starts in which the DC current induces AC oscillations of frequency f = /e. In gated quantum wires where interaction between electrons is short-ranged, generation linewidth is small provided the inter-electronic repulsion is strong enough, otherwise a wide-band noise is generated. In case of long-range Coulomb interaction generation is coherent at any interaction strength. The effect is related to interaction of the current with Friedel oscillations of the electronic density around the impurity. Manifestations of the effect resemble the Coulomb blockade and the Josephson effect. Oscillations of the electric current are accompanied by spin current oscillations. The results are related to semiconducting quantum wires, metallic atomic chains, carbon nanotubes, graphene nanoribbons and others.
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We study electron and spin transport in interacting quantum wires contacted by noninteracting leads. We theoretically model the wire and junctions as an inhomogeneous chain where the parameters at the junction change on the scale of the lattice spacing. We study such systems analytically in the appropriate limits based on Luttinger liquid theory and compare the results to quantum Monte Carlo calculations of the conductances and local densities near the junction. We first consider an inhomogeneous spinless fermion model with a nearest-neighbor interaction and then generalize our results to a spinful model with an on-site Hubbard interaction.