Theory of subgap interchain tunneling in quasi 1D conductors

Abstract

We suggest a theory of internal coherent tunneling in the pseudogap region when the applied voltage $U$ is below the free electron gap $2{\ensuremath{\Delta}}_{0}$. We address quasi-one-dimensional (quasi 1D) systems, where the gap is originated by spontaneous lattice distortions of the incommensurate charge density wave type. The results can be adjusted also to quasi 1D superconductors. The instanton approach allows one to calculate the interchain tunneling current both in single electron (amplitude solitons, i.e., spinons) and bielectron (phase slips) channels. Transition rates are governed by a dissipative dynamics originated by the emission of gapless phase excitations in the course of the instanton process. We find that the single-electron tunneling is allowed down to the true pair-breaking threshold at ${U}_{c1}=2{W}_{\mathit{as}}<2{\ensuremath{\Delta}}_{0}$, where ${W}_{\mathit{as}}=2∕\ensuremath{\pi}{\ensuremath{\Delta}}_{0}$ is the amplitude soliton energy. Most importantly, the bielectronic tunneling stretches down to ${U}_{c2}=0$ (in the 1D regime). In both cases, the threshold behavior is given by power laws $J\ensuremath{\sim}{(U\ensuremath{-}{U}_{c})}^{\ensuremath{\beta}}$, where the exponent $\ensuremath{\beta}\ensuremath{\sim}{v}_{F}∕u$ is as large as the ratio of the Fermi velocity ${v}_{F}$ and the phase $u$. In the two-dimensional or three-dimensional ordered phases, at temperature $T<{T}_{c}$, the one-electron tunneling current does not vanish at the threshold anymore, but saturates above it at $U\ensuremath{-}{U}_{c1}\ensuremath{\sim}{T}_{c}⪡{\ensuremath{\Delta}}_{0}$. Also the biparticle channel acquires a finite threshold ${U}_{c2}={W}_{2\ensuremath{\pi}}\ensuremath{\sim}{T}_{c}⪡{\ensuremath{\Delta}}_{0}$ at the energy of the $2\ensuremath{\pi}$ phase soliton.