English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We report results of a microscopic calculation of a second-order phasetransition into a state breaking time-reversal and translational invariancealong pair-breaking edges of $d$-wave superconductors. By solving atight-binding model through exact diagonalization with the Bogoliubov-de~Gennesmethod, we find that such a state with current loops having a diameter of a fewcoherence lengths is energetically favorable below $T^*$ between 10%-20% of$T_{\mathrm{c}}$ of bulk superconductivity, depending on model parameters. Thisextends our previous studies of such a phase crystal within the quasiclassicaltheory of superconductivity, and shows that the instability is notqualitatively different when including a more realistic band structure and thefast oscillations on the scale of the Fermi wavelength. Effects of sizequantization and Friedel oscillations are not detrimental. We also report on acomparison with quasiclassical theory with the Fermi surfaces extracted fromthe tight-binding models used in the microscopic calculation. There arequantitative differences in for instance the value of $T^*$ between thedifferent models, but we can explain the predicted transition temperaturewithin each model as due to the different spectral weights of zero-energyAndreev bound states and the resulting gain in free energy by breakingtime-reversal and translational invariance below $T^*$.

Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory