Characterization of helical states in semiconductor quantum wells using quantum information quantities

Abstract

The information content of one-electron bulk and edge states in semiconductor quantum wells is calculated in the inverted regime, where edge states, topologically protected, are responsible for the conduction in Spin Quantum Hall effect experiments. To study the information content of these states we first calculate realistic two dimensional one-electron states, solving first the eight-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian to obtain the bulk states and then a four band effective Hamiltonian to obtain the edge states. The behavior of information-like quantities, as a function of the different parameters that define the quantum well, is analyzed. The results presented show that the helical edge states can be singled out using different quantities that characterize the rich phenomenology of these states.