Anomalous energy transport across topological insulator superconductor junctions

We study the nonequilibrium energy transport across a topological insulator superconductor junction by deriving an interfacial heat current formula through the scattering wave approach. Several anomalous thermal properties are uncovered, such as thermal energy's Klein tunneling, asymmetric Kapitza resistance, and negative differential thermal resistance. We expect these findings will have potential applications for energy control in various hybridized mesoscopic systems.

Figure 1

Schematic illustration of the reflections and transmissions at the TI/S interfaces.

Figure 2

Thermal energy's Klein tunneling. (a) Thermal conductance as a function of the barrier strength $Z$ and the rotation angle $\alpha$ of the $d$-wave order parameter. (b) Intersections of (a) for $Z=0$, and $\pi /2$. (c) Angle-resolved thermal conductance $G_{\theta }$ for different $\alpha$ and $Z$. Solid lines are for $Z=0$ while dashed ones are for $Z=\pi /2$. Parameters are $T=70$ K, $T_c=116$ K, and ${\Delta }_0=30$ meV. Thermal conductance $G$ is in the unit of ${\Delta }_0{k}_B/h$.

Figure 3

Rectification ratios as a function of temperatures. Values apart from 1 indicate asymmetric Kapitza resistances. $\blacksquare$ ($T=35$ K), ($T=70$ K), ($T=104$ K), ($T=140$ K) are denoted for $Z=0$. Their hollow counterparts are for cases of $Z=\pi /2$. Inset shows one example of the $J_Q$ profiles depending on temperature bias for $Z=0$ (solid) and $\pi /2$ (dashed), at $T=70$ K. $\alpha =0$. Other parameters are the same as in Fig. 2. The energy current $J_Q$ is in the unit of ${\Delta }_0^2/h$.

Figure 4

NDTC for various temperatures at $\alpha =0$ (filled symbols) and $\alpha =\pi /4$ (hollow symbols). $Z=0$. Other parameters are the same as in Fig. 2. The DTC $d{J}_Q/d\delta T$ is in the unit of ${\Delta }_0{k}_B/h$.