Singularities and Pseudogaps in the Density of States of the Fluctuating Gap Model

Abstract

We review the one-dimensional fluctuating gap model (FGM) which describes non-interacting fermions subject to a static random backscattering potential. The FGM applies to the low-energy behavior of quasi one-dimensional Peierls and spin systems and has recently also been used to explain the pseudogap phenomenon in high-$T_c$ superconductors. After an elementary introduction to the FGM, we develop methods which allow for a simultaneous calculation of the density of states (DOS) and the inverse localization length. First, we recover all known results in the limits of zero and infinite correlation length of the random potential. Then, we attack the problem of finite correlation lengths. While a complex order parameter, which describes incommensurate Peierls chains, leads to a suppression of the DOS, i.e. a pseudogap, the DOS exhibits a singularity at the Fermi energy if the order parameter is real and therefore refers to a commensurate system. We confirm these results by calculating the DOS and the inverse localization length for finite correlation lengths and Gaussian statistics of the backscattering potential with unprecedented accuracy numerically. Finally, we consider the case of classical phase fluctuations which apply to low temperatures where amplitude fluctuations are frozen out. In this physically important regime which is also governed by finite correlation lengths, we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.