TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.2.060
TI  - Mode-shell correspondence, a unifying phase space theory in topological physics - Part I: Chiral number of zero-modes
PY  - 2024/08/23
UR  - https://scipost.org/SciPostPhys.17.2.060
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 2
SP  - 060
A1  - Jezequel, Lucien
AU  - Delplace, Pierre
AB  - We propose a theory, that we call the mode-shell correspondence, which relates the topological zero-modes localised in phase space to a shell invariant defined on the surface forming a shell enclosing these zero-modes. We show that the mode-shell formalism provides a general framework unifying important results of topological physics, such as the bulk-edge correspondence, higher-order topological insulators, but also the Atiyah-Singer and the Callias index theories. In this paper, we discuss the already rich phenomenology of chiral symmetric Hamiltonians where the topological quantity is the chiral number of zero-dimensional zero-energy modes. We explain how, in a lot of cases, the shell-invariant has a semi-classical limit expressed as a generalised winding number on the shell, which makes it accessible to analytical computations.
ER  -

@Article{10.21468/SciPostPhys.17.2.060,
	title={{Mode-shell correspondence, a unifying phase space theory in topological physics - Part I: Chiral number of zero-modes}},
	author={Lucien Jezequel and Pierre Delplace},
	journal={SciPost Phys.},
	volume={17},
	pages={060},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.2.060},
	url={https://scipost.org/10.21468/SciPostPhys.17.2.060},
}