Recently, major strides have been taken towards a complete classification of gapped quantum states of matter. Yet a commonly observed gapped state—ordinary superconductors—sits awkwardly within this classification. Here we will answer the question of classification by proposing that the minimal description of a superconductor is in terms of symmetry protected topological (SPT) phases. A key role is played by the magnetic symmetry, a 1-form symmetry in three spatial dimensions, which encodes the absence of magnetic monopoles. The known properties of superconductors can be reproduced from the SPT characterization. Besides providing a minimalist derivation that is complementary to the Landau-Ginzburg approach, the non-perturbative nature of this viewpoint may be useful in situations when fluctuations are significant.
Furthermore, this approach reveals an unexpected relation between persistent currents at the surface of a superconductor and the Josephson effect on the one hand and Thouless pumps and the quantum spin Hall effect on the other.
Zoom Link: https://icts-res-in.zoom.us/j/98843194798?pwd=QIzFAJGnpB3QeOJ2FkA24xqOwHL9No.1
Meeting ID: 988 4319 4798
Passcode: 643593