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<p>We theoretically investigate the superconducting gap structures in wallpaper fermions, which are surface states of topological nonsymmorphic crystalline insulators, based on a two-dimensional effective model. A symmetry analysis identifies six types of momentum-independent pair potentials. One hosts a point node, two host line nodes, and the remaining three are fully gapped. By classifying the Bogoliubov–de Gennes Hamiltonian in the zero-dimensional symmetry class, we show that the point and line nodes are protected by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> topological invariants. In addition, for the twofold-rotation-odd pair potential, nodes appear on the glide-invariant line and are protected by crystalline symmetries, as clarified by the Mackey–Bradley theorem.</p>

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Superconducting Gap Structures in Wallpaper Fermion Systems

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Kaito Yoda,
  • Ai Yamakage

摘要

We theoretically investigate the superconducting gap structures in wallpaper fermions, which are surface states of topological nonsymmorphic crystalline insulators, based on a two-dimensional effective model. A symmetry analysis identifies six types of momentum-independent pair potentials. One hosts a point node, two host line nodes, and the remaining three are fully gapped. By classifying the Bogoliubov–de Gennes Hamiltonian in the zero-dimensional symmetry class, we show that the point and line nodes are protected by \(\mathbb {Z}_2\) Z 2 topological invariants. In addition, for the twofold-rotation-odd pair potential, nodes appear on the glide-invariant line and are protected by crystalline symmetries, as clarified by the Mackey–Bradley theorem.