paper

Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality

arXiv:1809.05687 · doi:10.1103/PhysRevB.99.184512

Abstract

Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the odd-frequency Cooper pair amplitudes can be expressed by a winding number extended to a nonzero frequency, which is called a `spectral bulk-boundary correspondence,' and can be evaluated from the spectral features of the bulk. The odd-frequency Cooper pair amplitudes are classified into two categories: the amplitudes in the first category have the singular functional form (where is a complex frequency) that reflects the presence of a topological surface Andreev bound state, whereas the amplitudes in the second category have the regular form and are regarded as non-topological. We discuss the topological phase transition by using the coefficient in the latter category, which undergoes a power-law divergence at the topological phase transition point and is used to indicate the distance to the critical point. These concepts are established based on several concrete models, including a Rashba nanowire system that is promising for realizing Majorana fermions.

14 pages, 11 figures

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