Институт теоретической физики им. Л.Д. Ландау РАН

L.D. Landau Institute for Theoretical Physics RAS

L.D. Landau Institute for Theoretical Physics RAS

Two-impurity scattering in quasi-one-dimensional systems with attracting impurities

Date/Time: 16:30 29-Jun-2022

Abstract:

In a quasi-one-dimensional system (e.g., a tube) with low concentration of short-range defects the resistivity $\rho$ has peaks (Van Hove singularities), occurring when the Fermi energy $E_F$ crosses a bottom $E_N$ of some (resonant) subband of transversal quantization. Scattering smears these singularities in a very nontrivial manner. In the immediate vicinity of Van Hove singularity a plane wave is not a reasonable approximation for the electron wave functions in the resonant subband and one has to employ exact 1D results instead. Here the resistivity is dominated by scattering at rare ``twin'' pairs of close defects, while scattering at solitary defects is suppressed. The character of the relevant twin pairs crucially depends on the sign of the impurity potential (repulsive -- $\lambda>0$, or attractive -- $\lambda<0$).

In our previous paper we have studied the case of repulsing impurities, where the twins scattering has a nonresonant character: the main contribution to resistance comes from all pairs with separation $L\lesssim L_{\rm twin}\sim1/\lambda\ll \overline{L}$, $\overline{L}$ being the average distance between impurities.

In the present work we show that for attracting impurities the twins scattering is dominated by resonant twin pairs with certain sharply defined separations $L\approx L_{\rm twin}(\varepsilon)$, depending on $\varepsilon\equiv E_F-E_N$. The resonant separation $L_{\rm twin}(\varepsilon)$ is determined from the equation $E_{\rm twin}(L)=\varepsilon$, where $E_{\rm twin}(L)$ is the bound state energy for a system of two impurities with separation $L$. It is important that for $\varepsilon<0$ the above equation has solutions only in the attracting case. The resistivity in the case of attractive impurities is larger than for repulsive case due to resonant character of scattering.

In our previous paper we have studied the case of repulsing impurities, where the twins scattering has a nonresonant character: the main contribution to resistance comes from all pairs with separation $L\lesssim L_{\rm twin}\sim1/\lambda\ll \overline{L}$, $\overline{L}$ being the average distance between impurities.

In the present work we show that for attracting impurities the twins scattering is dominated by resonant twin pairs with certain sharply defined separations $L\approx L_{\rm twin}(\varepsilon)$, depending on $\varepsilon\equiv E_F-E_N$. The resonant separation $L_{\rm twin}(\varepsilon)$ is determined from the equation $E_{\rm twin}(L)=\varepsilon$, where $E_{\rm twin}(L)$ is the bound state energy for a system of two impurities with separation $L$. It is important that for $\varepsilon<0$ the above equation has solutions only in the attracting case. The resistivity in the case of attractive impurities is larger than for repulsive case due to resonant character of scattering.

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