Transporte em constrições geométricas de isolantes topológicos

Abstract

The QSHE is a quantum phase of matter defined by a pair of opposite spin currents in each edge of two-dimensional material known as helical edge states. More specifically, these pairs are Kramer states created by the time-reversal invariance and are very robust against non-magnetic impurities and lattice defects that may appear, which leads to a system to avoid backscattering phenomena. Its electronic band structure is represented by a closed Dirac-cone, which defines a metallic phase for each conducting channel at the boundaries. It is known the QSHE occurs in bidimensional topological insulators due to the bulk-edge correspondence. In particular, here we consider the topological insulator HgTe-CdTe which is described by the topological band theory through the BHZ Hamiltonian. To understand and study these materials and its electronic properties, we study Dirac-like Hamiltonians and transport concepts related to Landauer’s formalism. Additionally, we implement the BHZ Hamiltonian numerically and explore the electronic properties of a two-dimensional topological insulator with geometric constrictions. At that point, we consider an impurity potential inside that constriction region and investigate the dynamics of the spin current density. For the chosen parameters, the geometrical constriction drives to the opposite eigenstate of spins edge channels to hybridize among each other. Consequently, the Dirac energy spectrum opens a gap in the constriction region, and Fabry-Pérot resonances emerge. We observed this phenomenon is related to the creation of an integer number of the vortex within this constriction region, and our results allow us to state that these numbers are directly related to the number of resonance peaks found in the conductance. In other words, when the energy eigenvalues correspond to the first peak, we observe only one vortex being created. When we increase the energy for the second peak, we observe two vortexes, and so on. We have noticed that for an even number of vortexes, the spin current density creates a node in the central region inside this constriction. In order to investigate the dynamics of the spin current and its relations to the Fabry-Pérot phenomenon, we consider a scalar and magnetic impurity (an external lead or a magnetic contact) inside this node. We have found that placing the impurity in this node, only the odd numbers of these vortexes are affected.