Nonequilibrium phenomena in multiple normal-superconducting tunnel heterostructures

Using the nonequilibrium theory of superconductivity with the tunnel Hamiltonian, we consider a meso-scopic NISINISIN heterostructure, i.e., a structure consisting of five intermittent normal-metal (N) and superconducting (S) islands separated by insulating tunnel barriers (I). Applying the bias voltage between the outer normal electrodes one can drive the central N island very far from equilibrium. Depending on the resistance ratio of outer and inner tunnel junctions, one can realize either effective electron cooling in the central N island or create highly nonequilibrium energy distributions of electrons in both S and N islands. These distributions exhibit multiple peaks at a distance of integer multiples of the superconducting chemical potential. In the latter case the superconducting gap in the S islands is strongly suppressed as compared to its equilibrium value.

Figure 1

NISINISIN structure: The central normal island (N) is placed between two superconducting islands (S) which are connected to two outer N electrodes serving as external leads. Each connection is realized through a tunnel contact with a resistance $R_{ik}$.

Figure 2

(a) Chemical and electrostatic potentials of the superconducting island as a function of bias voltage. (b) $I\text{−}V$ curves for different $\rho$. For clarity, in the case $\rho =1000$ the potentials have been multiplied by the factor 100 and the currents by the factor 1000.

Figure 3

Nonequilibrium normal-island distributions for $\rho =1000$. We use $v\equiv eV∕\Delta$ here and in Figs. 4, 5, 6, 7 below.

Figure 4

Nonequilibrium normal metal distributions for $\rho =1$.

Figure 5

Nonequilibrium normal metal distributions for $\rho =1∕1000$.

Figure 6

Effective temperature $T_{\mathrm{eff}}$ of Eq. (32).

Figure 7

Nonequilibrium superconductor distributions for various bias voltages when $\rho =1$.

Figure 8

(a) Gap $\Delta$ as a function of bias voltage for two resistance ratios $\rho =1000$ (dashed line) and $\rho =1$ (solid line). Both quantities are normalized to zero-temperature BCS gap ${\Delta }_0$. (b) Conversion between $eV∕\Delta$ and $eV∕{\Delta }_0$ for $\rho =1000$ (dashed line) and $\rho =1$ (solid line).

Figure 9

Differential conductance for (a) the probe junction and (b) the corresponding quasiparticle energy distribution in the normal-metal island when $\rho =1$, $eV∕\Delta =10$.

Figure 10

Temperature in the normal-metal island as a function of bias voltage for bath temperatures (a) $0.05\Delta$ and (b) $0.2\Delta$ when the system is in quasiequilibrium.

Figure 11

Temperature in the superconductor as a function of bias voltage for bath temperatures (a) $0.05\Delta$ and (b) $0.2\Delta$ when the system is in quasiequilibrium.

Figure 12

Chemical potential of the superconductor as a function of bias voltage for bath temperatures (a) $0.05\Delta$ and (b) $0.2\Delta$ when the system is in quasiequilibrium.

Figure 13

Electric current between S and N islands as a function of bias voltage for bath temperatures (a) $0.05\Delta$ and (b) $0.2\Delta$ when the system is in quasiequilibrium.

Figure 14

Differential conductance as a function of bias voltage for bath temperatures (a) $0.05\Delta$ and (b) $0.2\Delta$ when the system is in quasiequilibrium.