Quantum transport in a normal metal/odd-frequency superconductor junction

Recent experimental results indicate the possible realization of a bulk odd-frequency superconducting state in the compounds ${\text{CeCu}}_2{\text{Si}}_2$ and ${\text{CeRhIn}}_5$. Motivated by this, we present a study of the quantum transport properties of a normal metal/odd-frequency superconductor junction in a search for probes to unveil the odd-frequency symmetry. From the Eliashberg equations, we perform a quasiclassical approximation to account for the transport formalism of an odd-frequency superconductor with the Keldysh formalism. Specifically, we consider the tunneling charge conductance and the tunneling thermal conductance. We qualitatively find distinct behavior in the odd-frequency case compared to the conventional even-frequency case in both the electrical and thermal current. This serves as a useful tool to identify the possible existence of a bulk odd-frequency superconducting state.

Figure 1

(Color online) Overview of the different symmetry states will be considered in the superconducting part of the clean two-dimensional normal/superconductor junction.

Figure 2

(Color online) Plot of $G$ for isotropic, even-parity superconductors, and odd-parity superconductors for both even- and odd-frequency pairing.

Figure 3

(Color online) Plot of $\kappa$ for isotropic, even-parity superconductors, and odd-parity superconductors for both even- and odd-frequency pairings. A power-law dependence with an exponent of $\simeq 1$ is observed for both of the odd-frequency symmetries (see insets).