Tunneling through a short interacting wire

We investigate tunneling through a short wire with electron-electron interactions which is coupled to noninteracting leads. We identify two temperature regimes (a) TKondo < T ≤ Twire = h̄vF /kBd (d is the length of the interacting wire) and (b) T < TKondo ≪ Twire. 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 = ±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 tunneling 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↑ + G↓, e2/h ≤ G ≪ 2e2/h. In the second regime, when T → 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 < TKondo the conductance is given by G = 2e 2/h. These results are