Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping
- URL: http://arxiv.org/abs/2107.09720v2
- Date: Wed, 12 Jan 2022 16:58:49 GMT
- Title: Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping
- Authors: Filiberto Ares, Jos\'e G. Esteve, Fernando Falceto
- Abstract summary: We study the localized states of a generic quadratic fermionic chain with finite-range couplings.
We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
- Score: 68.8204255655161
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we study the localized states of a generic quadratic fermionic
chain with finite-range couplings and an inhomogeneity in the hopping (defect)
that breaks translational invariance. When the hopping of the defect vanishes,
which represents an open chain, we obtain a simple bulk-edge correspondence:
the zero-energy modes localized at the ends of the chain are related to the
roots of a polynomial determined by the couplings of the Hamiltonian of the
bulk. From this result, we define an index that characterizes the different
topological phases of the system and can be easily computed by counting the
roots of the polynomial. As the defect is turned on and varied adiabatically,
the zero-energy modes may cross the energy gap and connect the valence and
conduction bands. We analyze the robustness of the connection between bands
against perturbations of the Hamiltonian. The pumping of states from one band
to the other allows the creation of particle-hole pairs in the bulk. An
important ingredient for our analysis is the transformation of the Hamiltonian
under the standard discrete symmetries, $C$, $P$, $T$, as well as a fourth one,
peculiar to our system, that is related to the existence of a gap and localized
states.
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