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�0. We address quasi 1D systems, where the gap is originated by spontaneous lattice distortions of the Incommensurate Charge Density Wave (ICDW) type. Results can be adjusted also to quasi-1D superconductors. The instanton approach allows to calculate the interchain tunneling current both in single electron (amplitude solitons, i.e. spinons) and bi-electron (phase slips) channels. Transition rates are governed by a dissipative dynamics originated by 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 Uc = 2Was < 2�0, where Was = 2/π�0 is the amplitude soliton energy. Most importantly, the bi-electronic tunneling stretches down to Uc = 0 (in the 1D regime). In both cases, the threshold behavior is given by power laws J ∼ (U − Uc) � , where the exponent β ∼ vF /u is large as the ratio of the Fermi velocity vF and the phase one u. In the 2D or 3D ordered phases, at temperature T < Tc, the one-electron tunneling current does not vanish at the threshold anymore, but saturates above it at U − Uc ∼ Tc ≪ �0. Also the bi-particle channel acquires a finite threshold Uc = W2� ∼ Tc ≪ �0 at the energy of the 2π phase soliton.