Abstract
The bulk conductivity of a two-dimensional system is studied assuming that time-reversal symmetry is broken by internal mechanisms. The study is carried out by direct diagonalization in order to explore the nonlinear-response provoked by the inclusion of an electric field in the system’s Hamiltonian. The system displays a quantized conductivity that depends on the intensity of the field and under specific conditions the conductivity limit at zero electric field displays a nonvanishing value.
Highlights
ArXiv:2009.10001v3 [quant-ph] 22 Nov 2020An essential result from quantum mechanics prescribes that when two operators commute there exists an eigenbasis that diagonalizes them simultaneously, so that the elements of such an eigenbasis conform at the same time to both operators
The goal of the present study is to provide a numerical analysis of a single-body model where the symmetrybreaking takes place in the bulk and is generated by a strong lattice potential that acts in a way analogous to the edge of a topological insulator
The electric field responsible for charge transport has been included in the Hamiltonian and the study has been carried out by direct diagonalization in order to explore the system’s response beyond the linear approximation
Summary
An essential result from quantum mechanics prescribes that when two operators commute there exists an eigenbasis that diagonalizes them simultaneously, so that the elements of such an eigenbasis conform at the same time to both operators. Contrariwise, the suppression of backscattering paths due to quantum interference is unfeasible when the number of moving channels in one direction is even This can be seen considering a Hamiltonian that displays the common form (the constant term σ2 is included only to keep a reference to spin states). In absence of symmetry breaking mechanisms, it is at least possible to build eigenstates that be invariant under the joined effect of both symmetries These states take place both in the bulk and on the edges, as shown in figure 2. This approach intends to shed insight by helping visualize the system’s response as a complement to the more abstract analytical formulation often found in related studies This procedure yields a quantized conductivity that shows a dependence with the number of bands below the Fermi energy and in some cases this conductivity remains finite as the electric field goes to zero, suggesting in this way a superconducting state
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