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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We solve the Bogoliubov-de Gennes equations self-consistently for the$d$-wave order parameter in nanoscale $d$-wave systems with [110] surfaces andshow that spontaneous time-reversal symmetry (TRS) breaking occurs at lowtemperatures due to a spontaneously induced complex order parameter of extended$s$-wave symmetry. The Andreev surface bound states, which are protected by aone-dimensional (1D) topological invariant in the presence of TRS, are gappedby the emergence of this new order parameter. The extended $s$-wave orderparameter is localized within a narrow region near the surfaces, which isconsistent with the fact that topological protection of the gapless Andreevsurface states is characterized by the 1D topological invariant. In thisTRS-breaking phase, not only is the complex order parameter induced, but alsothe $d$-wave order parameter itself becomes complex. Furthermore, thedisappearance of topological protection brings about novel vortex phenomenanear the surfaces. We show that vortex-antivortex pairs are formed in theextended $s$-wave order parameter along the surfaces if the side length of ananoisland or the width of an infinitely long nanoribbon is relatively large.

Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in $d$-wave nanoislands