Interaction-Induced Resonance in Conductance and Thermopower of Quantum Wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.

Figure 1

An example of interchannel scattering event discussed in this Letter. This scattering event becomes possible at the Fermi level only if the ratio of the Fermi momenta of the two channels equals $3:1$.

Figure 2

The dimensionless scaling functions $F_0(x)$ and $F_1(x)$ entering the conductance correction Eq. (1) and the interaction-induced thermopower Eq. (2), respectively.

Figure 3

Illustration of the dominant scattering events on either side of the resonance, ${\epsilon }_F={\epsilon }_R$, for a finite-temperature difference across the wire. Here the right movers are cold (blue) and left movers are warmer (red); for simplicity we consider ${\mu }_L={\mu }_R$ and $T=0$ for right movers. Because of momentum and energy conservation the scattering has to take place close to ${\epsilon }_R$ (the dotted line). In the left panel, only scattering of electrons from warm to cold is possible and, consequently, an excess of right movers is created. In contrast, in the right panel this process is blocked by a filled Fermi sea and instead a scattering, where a right mover is transformed to a left mover prevails. This explains the sign change of thermopower seen in Fig. 2.

Figure 4

Splitting of the resonance features in conductance and thermopower into four features as a function of magnetic field $B$. Dashed lines represent the evolution of the positions of single-particle peaks in the thermopower.