Quantum creep and variable range hopping of one-dimensional interacting electrons

TL;DR

This paper extends the theory of variable range hopping to one-dimensional interacting electrons, including charge density waves and Luttinger liquids, highlighting the role of dissipation and Coulomb interactions in quantum creep and conductivity.

Contribution

It generalizes variable range hopping results to 1D interacting systems and incorporates dissipation effects, providing new insights into quantum creep and tunneling physics.

Findings

Dissipation is essential for tunneling in 1D systems.

Hopping conductivity depends on compressibility for interacting electrons.

Coulomb interactions cause only minor logarithmic corrections.

Abstract

The variable range hopping results for noninteracting electrons of Mott and Shklovskii are generalized to 1D disordered charge density waves and Luttinger liquids using an instanton approach. Following a recent paper by Nattermann, Giamarchi and Le Doussal [Phys. Rev. Lett. {\bf 91}, 56603 (2003)] we calculate the quantum creep of charges at zero temperature and the linear conductivity at finite temperatures for these systems. The hopping conductivity for the short range interacting electrons acquires the same form as for noninteracting particles if the one-particle density of states is replaced by the compressibility. In the present paper we extend the calculation to dissipative systems and give a discussion of the physics after the particles materialize behind the tunneling barrier. It turns out that dissipation is crucial for tunneling to happen. Contrary to pure systems the new metastable state does not propagate through the system but is restricted to a region of the size of the tunneling region. This corresponds to the hopping of an integer number of charges over a finite distance. A global current results only if tunneling events fill the whole sample. We argue that rare events of extra low tunneling probability are not relevant for realistic systems of finite length. Finally we show that an additional Coulomb interaction only leads to small logarithmic corrections.