Mean-field description of odd-frequency superconductivity with staggered ordering vector

TL;DR

This paper develops a mean-field theoretical framework for odd-frequency superconductivity with a staggered order parameter in a two-channel Kondo lattice, revealing a weak Meissner effect with mixed paramagnetic and diamagnetic responses.

Contribution

It introduces a low-energy effective Hamiltonian that captures the essential physics of odd-frequency pairing with staggered order, supported by dynamical mean-field theory comparisons.

Findings

Reproduces low-energy behaviors of self-energy in the model

Shows a weak Meissner effect with both paramagnetic and diamagnetic contributions

Highlights the role of staggered order in determining the Meissner kernel sign

Abstract

A low-energy fixed-point Hamiltonian is constructed for the s-wave odd-frequency pairing state with staggered ordering vector in the two-channel Kondo lattice. The effective model is justified because it reproduces low-energy behaviors of self energy obtained by the dynamical mean-field theory. The retardation effect is essential for the odd-frequency pairing, which comes from the hybridization process between conduction electrons and pseudofermions originating from localized spins at low energies. Using the effective Hamiltonian, the electromagnetic response functions are microscopically calculated. The present system shows the "weak" Meissner effect, where both paramagnetic and diamagnetic parts contribute to the Meissner kernel to give a small total diamagnetic response in the superconducting state. This feature is in contrast to the ordinary s-wave BCS pairing where only the diamagnetic kernel is finite in the ground state. The staggered nature of the odd-frequency order parameter plays an important role for the sign of the Meissner kernel.