Quantum interference and spin-charge separation in a disordered Luttinger liquid

Abstract

We study the influence of spin on the quantum interference of interacting electrons in a singlechannel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful LL on an equal footing. We analyze the effect of spin-charge separation at finite temperature both on the spectral properties of single-particle fermionic excitations and on the conductivity of a disordered quantum wire. We demonstrate that the notion of weak localization, related to the interference of multiple-scattered electron waves and their decoherence due to electron-electron scattering, remains applicable to the spin-charge separated system. The relevant dephasing length, governed by the interplay of electron-electron interaction and spin-charge separation, is found to be parametrically shorter than in a spinless LL. We calculate both the quantum (weak localization) and classical (memory effect) corrections to the conductivity of a disordered spinful LL. The classical correction is shown to dominate in the limit of high temperature.

Weak localization and magnetoresistance in a two-leg ladder model

“…A weak magnetic field meanwhile has relatively little effect on the Drude (diffusive) component on the resistance, and thus allows the quantum weak localization correction to be isolated and studied experimentally. This unfortunately can not be seen in strictly one-dimensional nanowires however, as in this case the magnetic-field may be gauged out completely and will have no effect (the Zeeman coupling between the magnetic field and the spin of the electrons produces a rather different effect 15 ). However, if one turns from singlechain nanowires to double-chain nanostructures, the socalled ladder models, then interesting orbital effects of the magnetic field may be restored.…”

“…As we will show, this one parameter is responsible for both the exponent of renormalization of disorder and dephasing time, 14 and will be assumed to be small α 1.…”

Hanbury Brown and Twiss correlations in quantum Hall systems

“…We note in passing that the disentanglement of the quasiclassical trajectories and renormalization effects described above is similar to the procedure used in Refs. [56][57][58] for calculating the weak-localization correction in disordered Luttinger liquids.…”

Nonequilibrium kinetics of a disordered Luttinger liquid

“…The one-loop derivation is controlled by the parameters γ/ max{T, eU } ≪ 1 and α ≪ 1, which is assumed in the rest of the paper (U is the bias voltage). We also disregard the localization effects [5,18]. For a wire of length L v F /γ, this limits the applicability of what follows to max{T, eU } ≫ T 1 = γ/α 3−η .…”

“…Four more poles q ≃ ±ω(1±iγ/2ω)/u, associated with the "greater" part of the effective interaction with parallel spins V >, , correspond to the collective plasmon mode of the clean LL, moving with velocity u = v F (1 + ηα) 1/2 . In the spinful model,V contains an extra mode-spinon-propagating with velocity v F [18]. Importantly, the e-h and collective excitations at ω ≫ T 1 are well resolved from each other and should be treated separately, while in the opposite limit, ω ≪ T 1 , the disorder-induced quantum uncertainty makes them indistinguishable.…”