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Effective model for a supercurrent in a pair-density wave

Journal article
Authors Jonatan Wårdh
Mats Granath
Published in Physical Review B Condensed Matter
Volume 96
Issue 22
ISSN 0163-1829
Publication year 2017
Published at Department of Physics (GU)
Language en
Subject categories Superconductivity, Condensed Matter Physics


We extend the standard effective model of d-wave superconductivity of a single band tight-binding Hamiltonian with a nearest-neighbor attraction to include finite range periodically modulated pair hopping. The pair hopping is characterized by a fixed wave number Q=Qx̂ breaking lattice rotational symmetry. Within self-consistent BCS theory we study the general variational state consisting of two incommensurate singlet pair amplitudes ΔQ1 and ΔQ2 and find two types of ground states; one of the Larkin-Ovchnnikov (LO) or pair-density wave (PDW) type with ΔQ1=ΔQ2 and Q1=−Q2≈Q, and one of the Fulde-Ferrell (FF) type with ΔQ2=0 and Q1≈±Q. An anomalous term in the static current operator arising from the pair hopping ensures that Bloch's theorem on ground state current is enforced also for the time-reversal and parity breaking FF state, despite no spin-population imbalance. We also consider a supercurrent by exploring the space of pair momenta Q1 and Q2 and identify characteristics of a state with multiple finite momentum order parameters. This includes the possibility of phase separation of current densities and spontaneous mirror-symmetry breaking manifested in the directional dependence of the depairing current.

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