Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides

Abstract

The possibility of realizing pair density wave (PDW) phases, in which Cooper pairs have a finite momentum, presents an interesting challenge that has been studied in a wide variety of systems. In conventional superconductors, this is only possible when external fields lift the spin degeneracy of the Fermi surface, leading to pair formation at an incommensurate momentum. Here, we study a second possibility, potentially relevant to transition metal dichalcogenides, in which the Fermi surface consists of a pair of pockets centered at the $\pm K$ points of the Brillouin zone as well as a central pocket at the $\Gamma$ point. In the limit where these three pockets are identical, the pairing susceptibility has a logarithmic divergence at the non-zero wave-vectors $\pm \mathbf{K}$, allowing for a weak-coupling analysis of the PDW instability. We find that repulsive electronic interactions combine to yield effective attractive interactions in the singlet and triplet PDW channels, as long as the $\Gamma$ pocket is present. Because these PDW channels decouple from the uniform superconducting channel, they can become the leading unconventional pairing instability of the system. Upon solving the linearized gap equations, we find that the PDW instability is robust against small trigonal warping of the $\pm K$ pockets and small detuning between the $\Gamma$ and $\pm K$ pockets, which affect the PDW transition in a similar way as the Zeeman magnetic field affects the uniform superconducting transition. We also derive the Ginzburg-Landau free energy for the PDW gaps with momenta $\pm \mathbf{K}$, analyzing the conditions for and consequences of the emergence of FF-type and LO-type PDW ground states. Our classification of the induced orders in each ground state reveals unusual phases, including an odd-frequency charge-$2e$ superconductor in the LO-type PDW.

24 pages, 11 figures

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• Superconducting Diode Effect in Multiphase Superconductors
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
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• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Friedel oscillations and chiral superconductivity in monolayer NbSe${}_2$
• Unconventional pairing in Ising superconductors: Application to monolayer NbSe${}_2$
• Local condensation of charge-$4e$ superconductivity at a nematic domain wall
• Optically active Higgs and Leggett modes in multiband pair-density-wave superconductors with Lifshitz invariant
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Electronic structure of topological defects in the pair density wave superconductor
• Interplay of magnetic field and magnetic impurities in Ising superconductors
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Unconventional superconductivity in monolayer transition metal dichalcogenides
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Pair-mixing induced Time-reversal-breaking superconductivity
• Anomalous Superfluid Density in Pair-Density-Wave Superconductors
• Spin-triplet pair density wave superconductors