Electron transmission through a short interacting wire: $0.7$ conductance anomaly

We investigate electron transmission through a short wire with electron-electron interactions which is coupled to noninteracting metallic leads by tunneling matrix elements. We identify two temperature regimes (a) $T_{\text{Kondo}}<T⩽T^{\text{wire}}=\hslash v_F∕k_{B}d$ ($d$ is the length of the interacting wire) and (b) $T<T_{\text{Kondo}}⪡T^{\text{wire}}$. In the first regime the effective (renormalized) electron-electron interaction is smaller than the tunneling matrix element. In this situation 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 $S=\pm 1∕2$. In this regime the single particle energy is controlled by the length of the wire and the backward spin-dependent interaction. The value of the conductance is dominated by the transmitting electrons which have an opposite spin polarization to the electrons in the short wire. Since the electrons in the short wire have equal probability for spin up and spin down we find $G=G_{\uparrow }+G_{\downarrow }$, $e^2∕h⩽G<2e^2∕h$. In the second regime, when $T\to 0$ the effective (renormalized) electron-electron interaction is larger than the tunneling matrix element. This case is equivalent to a Kondo problem. We find for $T<T_{\text{Kondo}}$ the conductance is given by $G=2e^2∕h$. These results are in agreement with recent experiments where for $T_{\text{Kondo}}<T<T^{\text{wire}}$ the conductance $G$ obeys $e^2∕h⩽G<2e^2∕h$, and for $T<T_{\text{Kondo}}$, $G=2e^2∕h$. In both regimes the current is not spin polarized and the SU(2) symmetry is not broken. Our model represents a good description of the experimental situation for an interacting wire with varying confining potential in the transverse direction.

Figure 1

Conductance $\left(G\right)$ as a function of gate voltage $\left({\widehat{U}}_G\right)$ for fixed weak transmission $({\Gamma }^2=0.1)$ for three different temperatures: $\beta =1$ (dotted line), $\beta =10$ (dashed line), and $\beta =50$ (solid line). Note that decreasing the temperature to $\beta =10$ leads to the conductance reaching the value of 1.0 and in addition there is a shoulder around 0.7.

Figure 2

Conductance as a function of gate voltage for large transmission $({\Gamma }^2=5.0)$, i.e., for a short wire in the Kondo regime at very low temperature $(\beta =100)$. The conductance is about $1.0\times 2e^2∕\hslash$, as expected from the Kondo solution.