Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal d -wave superconductors
Journal article, 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.

Author

Kevin Marc Seja

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Niclas Wennerdal

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Tomas Löfwander

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Annica M. Black-Schaffer

Uppsala University

Mikael Fogelström

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Stockholm University

Patric Holmvall

Uppsala University

Physical Review B

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

Vol. 111 9 094513

Collective Modes and Quantum Transport in Quantum Materials

Swedish Research Council (VR) (2019-05274), 2020-01-01 -- 2023-12-31.

Quantum Transport and Dynamics in Superconducting Quantum Materials

Swedish Research Council (VR) (2023-05112), 2024-01-01 -- 2027-12-31.

Ordered phases and transport phenomena in 2D materials

Swedish Research Council (VR) (2020-05261), 2021-01-01 -- 2024-12-31.

Areas of Advance

Nanoscience and Nanotechnology

Subject Categories (SSIF 2025)

Condensed Matter Physics

Infrastructure

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

DOI

10.1103/PhysRevB.111.094513

Related datasets

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

More information

Latest update

4/4/2025 8