Odd-frequency pair density wave in the Kitaev-Kondo lattice model

TL;DR

This paper explores a novel odd-frequency pair density wave in the Kitaev-Kondo lattice model, revealing a quantum phase transition to a topologically nontrivial superconducting state with unique nodal structures and edge modes.

Contribution

It introduces an exact Majorana fermion representation for the Kitaev-Kondo model and uncovers a pair-density-wave superconducting phase with odd-frequency pairing.

Findings

Identifies a quantum phase transition from a fractionalized Fermi liquid to a nematic triplet SC phase.

Discovers that the SC phase can have Dirac points, Fermi lines, or Fermi surfaces as nodes.

Shows the SC phase is a pair-density-wave with finite momentum Cooper pairs.

Abstract

We investigate the properties of the Kitaev-Kondo lattice model defined on a bilayer honeycomb lattice by means of the SO(3) Majorana representation for spin-$1/2$ moments. We first consider the pairing of neighboring sites for the parent Kitaev spin liquid (KSL) Hamiltonian to render the Majorana and the spin-$1/2$ Hilbert spaces perfectly equivalent to each other. As a consequence, we demonstrate that this decoupling of the Kitaev interaction in terms of the SO(3) Majorana fermions reproduces exactly the spectrum of the KSL model alone. Then, by considering the effect of a local Kondo coupling $J_K$ in the model and decoupling it in terms of an order parameter that physically must have a finite staggering phase, we obtain that the system undergoes a quantum phase transition from a fractionalized Fermi liquid to a nematic triplet superconducting (SC) phase as $J_K$ is increased. Depending on the model parameters, this SC phase can exhibit either Dirac points, Bogoliubov-Fermi lines, or Bogoliubov-Fermi surfaces as nodal bulk manifolds. The surface states in this latter case are also characterized by topologically protected antichiral edge modes. The SC phase breaks time-reversal symmetry and exhibits a coexistence of a dominant odd-frequency pairing with a small even-frequency component for electronic excitations localized on sites of the same sublattice of the system. Finally, we show that this SC phase is in fact a pair-density-wave state, with Cooper pairs possessing a finite center-of-mass momentum in zero magnetic field.