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

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 a "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.

Tunneling and Josephson effects in odd-frequency superconductor junctions: A study on multichannel Kondo chain

“…30, but it is not necessary in this paper. With spatial modulations, EF and OF components should be mixed due to a broken translational invariance.…”

“…The corresponding effective mean-field theory has also been successfully constructed [30], which qualitatively describes the pairing state at low temperatures. In this framework, we first rewrite the localized pseudospin-operator τ i by introducing pseudofermion as…”

“…However, the difference causes the channel symmetry breaking [30] and is energetically unfavorable away from half filling [29]. Hence we take the same value as in Eq.…”

“…While the numerical calculation [30] shows the diamagnetic response, here we discuss it by focusing on the structure of the Meissner kernel and do not enter the details. Following the derivation in Ref.…”

“…Following the derivation in Ref. 30, only the anomalous part contributes to the Meissner kernel K xx which can be written in the form (14) where e is an electric charge, and we define the velocity v x k = ∂ε k /∂k x along the x-direction. We have also introduced the 'daggered' anomalous Green function by…”