Electron transmission through a short interacting wire: 0.7 conductance anomaly

We investigate tunneling through a short interacting wire. We identify two temperature regimes (a) $T_{Kondo}<T\le T^{wire}=\mathrm{\hslash }{v}_F\mathrm{/}{k}_{B}d$ ($d$ is the length of the short wire) and (b) $T<T_{Kondo}\ll T^{wire}$. In the first regime the effective (renormalized) electron-electron interaction is smaller than the tunneling matrix element. This is the situation at finite temperature $T$ where the single particle spectrum of the wire is characterized by a multilevel “quantum dot” system with magnetic quantum number S=0 which is higher in energy than the SU(2) spin doublet $S=\pm 1\mathrm{/}2$. Due to the single particle energy we find that the tunneling electron into the wire must have an opposite spin to the one in the short wire giving rise to a conductance, $G= G_\uparrow+G_\downarrow$,$e^2/h\le G\ll 2e^2/h$\mathrm{.}Inthesecondregime,when$T \to0$ we have a situation that the effective (renormalized) electron-electron interaction is larger than the tunneling matrix element. This problem is equivalent to a Kondo problem. We find for $T<T_{Kondo}$ that the conductance is given by $G=2e^2\mathrm{/}h$. These results are in agreement with recent experiments where for $T_{Kondo}<T<T^{wire}$ the conductance $G$ obeys $e^2/h\le G\ll 2e^2/h$,andfor$T< T_{Kondo}$,$G=2e^2/h$. In both regimes the current is not polarized and the SU(2) symmetry is not broken.