Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time $1/ \tau_0$. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate in the DOS $\nu ( \omega )$ but only $\ln$-singularities in the conductivity $\sigma ( \omega) $, we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If $\lim_{ \omega \rightarrow 0 } \sigma ( \omega ) > 0$, then a metallic Coulomb gap $\nu ( \omega ) \propto | \omega | / e^4$ appears in the DOS at T=0 for frequencies below a certain crossover frequency $\Omega_2$ which depends on the value of the DC conductivity $\sigma ( 0 )$. Here, $-e$ is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find $\nu(\omega) \propto (|\omega|/\Omega_1)^{1/2} \exp(-\Omega_1/|\omega|)$ at , where $\Omega_1$ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments