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Register a new userRole of Topology and Symmetry for the Edge Currents of a 2D Superconductor
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Added by
Maximilian F. Holst
Publication date
2021
fields
Physics
and research's language is
English
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The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current as the electron number is not conserved in a Bogolyubov-de Gennes Hamiltonian. Still, edge currents are in general present. Here, we use the two-dimensional Rashba system as an example to systematically analyze the effect symmetry reductions have on the order-parameter mixing and the edge properties in a superconductor of Altland-Zirnbauer class DIII (time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). In particular, we employ both Ginzburg-Landau and microscopic modeling to analyze the bulk superconducting properties and edge currents appearing in a strip geometry. We find edge (spin) currents independent of bulk topology and associated topological edge states which evolve continuously even when going through a phase transition into a topological state. Our findings emphasize the importance of symmetry over topology for the understanding of the non-quantized edge currents.
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Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determines the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions.
Inversion symmetry is a key symmetry in unconventional superconductors and even its local breaking can have profound implications. For inversion-symmetric systems, there is a competition on a microscopic level between the spin-orbit coupling associated with the local lack of inversion and hybridizing terms that `restore inversion. Investigating a layered system with alternating mirror-symmetry breaking, we study this competition considering the spin response of different superconducting order parameters for the case of strong spin-orbit coupling. We find that signatures of the local non-centrosymmetry, such as an increased spin susceptibility in spin-singlet superconductors for $Trightarrow 0$, persist even into the quasi-three-dimensional regime. This leads to a direction dependent spin response which allows to distinguish different superconducting order parameters. Furthermore, we identify several regimes with possible topological superconducting phases within a symmetry-indicator analysis. Our results may have direct relevance for the recently reported Ce-based superconductor CeRh$_2$As$_2$ and beyond.
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