Spontaneous symmetry breaking at surfaces of d-wave superconductors: Influence of geometry and surface ruggedness
Journal article, 2019

Surfaces of d-wave superconductors may host a substantial density of zero-energy Andreev states. The zero-energy flat band appears due to a topological constraint, but comes with a cost in free energy. We have recently found that an adjustment of the surface states can drive a phase transition into a phase with finite superflow that breaks time-reversal symmetry and translational symmetry along the surface. The associated Doppler shifts of Andreev states to finite energies lower the free energy. Direct experimental verification of such a phase is still technically difficult and controversial, however. To aid further experimental efforts, we use the quasiclassical theory of superconductivity to investigate how the realization and the observability of such a phase are influenced by sample geometry and surface ruggedness. Phase diagrams are produced for relevant geometric parameters. In particular, critical sizes and shapes are identified, providing quantitative guidelines for sample fabrication in the experimental hunt for symmetry-breaking phases.

spontaneous symmetry breaking

andreev reflection


thin superconducting films


Patric Holmvall

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

Anton Vorontsov

Montana State University

Mikael Fogelström

Chalmers, Microtechnology and Nanoscience (MC2)

Tomas Löfwander

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

Physical Review B

24699950 (ISSN) 24699969 (eISSN)

Vol. 99 18 184511

Areas of Advance

Nanoscience and Nanotechnology


C3SE (Chalmers Centre for Computational Science and Engineering)

Subject Categories

Condensed Matter Physics



More information

Latest update