Thermopower with broken time-reversal symmetry

We show that when inelastic scattering effects are taken into account, the thermopower is, in general, asymmetric under magnetic field reversal, even for noninteracting systems. Our findings are illustrated in the example of a three-dot ring structure pierced by an Aharonov-Bohm flux.

Figure 1

Schematic drawing of the model. The third (probe) reservoir mimics inelastic scattering.

Figure 2

Schematic drawing of the three-dot model.

Figure 3

Ratio $x$ of the off-diagonal matrix elements $L_{12}^{\prime }$ and $L_{21}^{\prime }$ of the reduced Onsager matrix at $T=1$, $\mu =0.3$, ${\epsilon }_L=0$, ${\epsilon }_R=0.5$, ${\epsilon }_P=1$, all hopping terms $t_{pq}=-1$, and broadenings ${\gamma }_k=0.1$, independently of energy (wide-band limit). Hereafter we set $e=\hslash =k_B=1$.