Peltier effect in strongly driven quantum wires

We study a microscopic model of a thermocouple device with two connected correlated quantum wires driven by a constant electric field. In such a closed system we follow the time and position dependence of the entropy density using the concept of the reduced density matrix. At weak driving, the initial changes of the entropy at the junctions can be described by the linear Peltier response. At longer times the quasiequilibrium situation is reached with well defined local temperatures which increase due to an overall Joule heating. On the other hand, a strong electric field induces a nontrivial nonlinear thermoelectric response, e.g., the Bloch oscillations of the energy current. Moreover, we show for the doped Mott insulators that strong driving can reverse the Peltier effect.

Figure 1

(a) Sketch of TEC. (b) Entropy difference between hot and cold junctions $\Delta S^{hc}$ for ${\varepsilon }_0=1.2$ calculated for $M$-site subsystems in comparison with Heikes Eq. (3). (c) and (d) $s_i\left(t\right)-s_i\left(0\right)$ for $F=0.2$ and $F=0.4$, respectively, for $M=4$, ${\varepsilon }_0=1.6$, with line denoting $s_i\left(t\right)=s_i\left(0\right)$.

Figure 2

Results for $M=4$, $F=0.2$ and ${\varepsilon }_0=1.2$. (a) $j^N$, $j^E$ in the middle of the left wire together with $\Delta s^{hc}$. (b) The same but for $F$ switched off at $t=15$. (c) ${\beta }_i\left(t\right)$ for $i=6$, i.e., away from junctions. (d) $s_6\left(t\right)-s_6\left(0\right)$ determined directly from RDM and from $\int d{\epsilon }_6{\beta }_6$.

Figure 3

Results for $M=4$ and ${\varepsilon }_0=1.2$. (a) and (b) Parametric plots $s_i\left(t\right)$ vs ${\epsilon }_i\left(t\right)$ for cold and hot junctions, respectively. (c) and (d) Oscillations of the particle and energy densities, respectively, for $F=3.2$.

Figure 4

(a) and (b) $\Delta s^{hc}\left(t\right)$ for various $V$ and $F$, respectively, with $M=4$ and ${\varepsilon }_0=1.2$. (c) and (d) $\Delta s^{hc}\left(t\right)$ and $\langle H\left(t\right)\rangle$, respectively, for ${\varepsilon }_0=1.6$.