Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping

Abstract In this paper, we study the localized states of a generic quadratic fermionic chain with finite-range couplings and an inhomogeneity in hopping (defect) that breaks translational invariance. When defect vanishes, which represents open chain, obtain simple bulk-edge correspondence: zero-energy modes at ends are related to roots polynomial determined by Hamiltonian bulk. From result, define index characterizes different topological phases system can be easily computed counting polynomial. As is turned on varied adiabatically, may cross energy gap connect valence conduction bands. We analyze robustness connection between bands against perturbations Hamiltonian. The pumping from one band other allows creation particle–hole pairs An important ingredient for our analysis transformation under standard discrete symmetries, C , P T as well fourth one, peculiar system, existence states.