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arXiv · 1612.03619

Impurity bound states in fully gapped $d$-wave superconductors with subdominant order parameters

Mahdi Mashkoori·Kristofer Björnson·Annica M. Black-Schaffer
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Abstract

Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure $d$-wave superconductor only allows virtual bound states. Fully gapped $d$-wave superconducting states have however been proposed in several cuprate systems thanks to subdominant order parameters producing $d+is$- or $d+id'$-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped $d$-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in $d+is$- and $d+id'$-wave superconductors. In a $d+is$-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a $d+id'$-wave symmetry always give rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.

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Mahdi Mashkoori, Kristofer Björnson, Annica M. Black-Schaffer. 2016-12-12. Impurity bound states in fully gapped $d$-wave superconductors with subdominant order parameters. https://doi.org/10.1038/srep44107

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