Transport through quasi-one-dimensional wires with correlated disorder

We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however it has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this situation we suggest a semianalytical approach which is quite effective for the description of the total transmission coefficient. Our numerical data confirm the validity of this approach.

Figure 1

Disordered Q1D wire of length $N$ and width $M$ (full circles) connected at both ends to semi-infinite ideal leads of width $M$ (open circles).

Figure 2

(a) Rescaled Lyapunov exponent $\lambda N$ as a function of the energy $E$ for a one-chain wire, $M=1$. The correlated disorder has been fixed by the stepwise power spectrum of Eq. (26) with $E_L=0.4,E_R=1.3,{\sigma }^2=0.02$, and $v=1$. (b) Average transmission coefficient $\langle T\rangle$ as a function of $E$. The continuous curve corresponds to numerical data while the dashed one is the theoretical prediction from Eqs. (22, 23, 24). The average is taken over 100 realizations of disorder for a disordered region of length $N=300$.

Figure 3

Same as in Fig. 2 for the Q1D model with (a) $M=2$, (b) $M=5$, and (c) $M=10$. The energy window where all modes in the leads are open is shown by the shaded region.

Figure 4

Transmission coefficient $T$ as a function of $E$ for the Q1D model with correlated stratified disorder of length $N=300$ having (a) $M=5$ and (b) $M=10$. Continuous curves correspond to the numerical data while dashed curves are the theoretical predictions from Eqs. (22, 23, 24). A single realization of disorder was used. The energy window where all modes in the leads are open is indicated by the shaded region.

Figure 5

Average transmission coefficient as a function of the energy for nonstratified disorder. Continuous curves represent the numerical data and dashed curves are the theoretical prediction given by Eqs. (24) and (32). The length of the system is $N=300$ with the disorder strength ${\sigma }^2=0.02$ for (a) $M=2$, (b) $M=3$, and (c) $M=4$.