Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal d -wave superconductors
Artikel i vetenskaplig tidskrift, 2025

Phase crystals are a class of nonuniform superconducting ground states characterized by spontaneous phase gradients of the superconducting order parameter. These phase gradients nonlocally drive periodic currents and magnetic fields, thus breaking both time-reversal symmetry and continuous translational symmetry. The phase crystal instability is generally triggered by negative and inhomogeneous superfluid stiffness. Several scenarios have been identified that can realize phase crystals, especially flat bands at specific edges of unconventional nodal superconductors. Motivated by omnipresent disorder in all materials, we employ the t-matrix approach within the quasiclassical theory of superconductivity to study the emergence of phase crystals at edges of a nodal d-wave superconductor. We quantify the full phase diagram as a function of the impurity scattering energy and the temperature, with full self-consistency in the impurity self energies, the superconducting order parameter, and the vector potential. We find that the phase crystal survives even up to ∼40-50% of the superconducting critical impurity strength in both the Born and unitary scattering limits. Finally, we show how mesoscopic finite-size effects induce a competition with a state still breaking time-reversal symmetry but with translationally invariant edge currents.

Författare

Kevin Marc Seja

Chalmers, Mikroteknologi och nanovetenskap, Tillämpad kvantfysik

Niclas Wennerdal

Chalmers, Mikroteknologi och nanovetenskap, Tillämpad kvantfysik

Tomas Löfwander

Chalmers, Mikroteknologi och nanovetenskap, Tillämpad kvantfysik

Annica M. Black-Schaffer

Uppsala universitet

Mikael Fogelström

Chalmers, Mikroteknologi och nanovetenskap, Tillämpad kvantfysik

Stockholms universitet

Patric Holmvall

Uppsala universitet

Physical Review B

2469-9950 (ISSN) 2469-9969 (eISSN)

Vol. 111 9 094513

Kollektiva moder och kvanttransport i kvantmaterial

Vetenskapsrådet (VR) (2019-05274), 2020-01-01 -- 2023-12-31.

Kvanttransport och dynamik i supraledande kvantmaterial

Vetenskapsrådet (VR) (2023-05112), 2024-01-01 -- 2027-12-31.

Ordnade faser och transportfenomen i 2D-material

Vetenskapsrådet (VR) (2020-05261), 2021-01-01 -- 2024-12-31.

Styrkeområden

Nanovetenskap och nanoteknik

Ämneskategorier (SSIF 2025)

Den kondenserade materiens fysik

Infrastruktur

Chalmers e-Commons (inkl. C3SE, 2020-)

DOI

10.1103/PhysRevB.111.094513

Relaterade dataset

Data for "Impurity strength–temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal d-wave superconductors" [dataset]

URI: https://zenodo.org/records/14524387

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Senast uppdaterat

2025-04-04