Electrical and Thermal conductance through a Nodal Surface Semimetal-Insulator-Superconductor junction

TL;DR

This work analyzes electrical and thermal transport through a nodal surface semimetal–insulator–superconductor (NSSM-I-SC) junction in the thin-barrier limit. Using a continuum NSSM model and Bogoliubov–de Gennes formalism, the authors compute normal and Andreev reflection probabilities and derive the tunnelling conductance via a BTK-like framework, revealing a pronounced π-periodic dependence on the barrier strength β. The study further evaluates the thermal conductance κ, showing that it also oscillates with β and increases with temperature, with a strong influence from barrier-induced Fermi-surface mismatches (μ_S = μ + U_0). The results highlight distinctive transport signatures of NSSM-based heterostructures compared with graphene-based NIS junctions and offer guidance for experimental control of electric and thermal currents in topological materials.

Abstract

Motivated by the unique dispersions close to the two dimensional band crossing in a topologically charged nodal surface semimetal (NSSM) spectrum, we perform theoretical analysis of quantum tunnelling through a junction consisting of such NSSM, an insulator and a s-wave superconductor (acronymed NSSM-I-SC junction). In particular, for excitation energies both more and less than the superconducting gap potential $Δ$ we probe the normal and Andreev conductance for different incident orientations and thereby find the tunnelling electrical conductance through the heterostructure. The present work considers only the thin barrier limit which witness the conductance G to oscillate periodically with frequency $π$ as a function of the barrier strength, both in high and low doping limit. Such periodic behavior is also observed while calculating the thermal conductance $κ$ through the junction. Novelty of this problem is that the behavior of these G or $κ$ with insulator width are, in many respect, different compared to that from a normal metal - insulator - superconductor (NIS) junction on graphene or silicene. The findings can thus motivate experimentalists to culture renewed control over electric or thermal transport on topological materials.

Figures (7)

• Figure 1: Cartoon of our NSSM-I-SC junction with potential barrier profile shown above.
• Figure 2: Normal and Andreev Reflectance for $E=$ (a-c) $0.5\Delta$ and (d) $1.5\Delta$, $\mu=100\Delta$ and $U_0=30\Delta$. Incident angles are considered to be $\theta_e=$ (a,d) $\pi/8$, (b) $\pi/3$ and (c) $\pi/2$. Variations with $U_0$ at $\theta_e=\pi/8$ are demonstrated in (e) ($U_0=100\Delta$) and (f) ($U_0=1000\Delta$). (g) and (h) show same plots as (a) and (b) respectively but for a moderate doping limit with $\mu=10\Delta$.
• Figure 3: Tunneling conductance $G/G_0$ for $q_z=0.1$ and $\mu=100\Delta$. We consider (a) different value of $\beta$ with $U_0=0$ and (b) $\beta=\pi$ for different values of $U_0$.
• Figure 4: Plot tunneling conductance with the effective barrier potential $\beta$ for (a) $U_0=0$ and (b) $U_0=100\Delta$ with $E=0.5\Delta$.
• Figure 5: Thermal conductance $\kappa$ for $q_z=0.1$, $E=0.5\Delta$ and $\mu=100\Delta$. We consider different value of $\beta$ with (a) $U_0=0$ and (b) $U_0=100\Delta$ with the variation of $T/T_c$.