Spin texture of two-dimensional topological insulators

Doctoral thesis (2017)

Since the discovery of two-dimensional topological insulators a decade ago, their one-dimensional edge states have attracted significant attention due to their unique properties. For example due to time ... [more ▼]

Since the discovery of two-dimensional topological insulators a decade ago, their one-dimensional edge states have attracted significant attention due to their unique properties. For example due to time-reversal symmetry, they are protected against elastic backscattering and they propagate such that electrons with opposite spins move in opposite directions. In fact, the only necessary symmetry to sustain the edge states is time-reversal symmetry. Moreover in experimental setups, the axial spin symmetry seems to be absent. This absence allows new processes to appear such as inelastic backscattering. However, these consequences were neglected in most theoretical works where the spins are considered to be polarized in the z direction. The aim of this thesis is to provide a more realistic model taking into account a broken axial spin symmetry. In this scheme, we show that a rotation of the spin quantization axis as a function of momentum always appears. This observation leads us to develop a deeper understanding of the size of the rotation related to the material parameters and material models, using also realistic values. It also leads us to understand the implications in real space in cases where translation invariance is lost and how to quantify the rotation in such systems. The new processes which arise when the axial spin symmetry is broken have important consequences for transport in real materials. To see this, we consider a Hall bar with a hole in its middle, i.e. an antidot. This enables us to create two tunneling regions in order to probe the effect of this generic model. We also consider the effect of Coulomb interactions around the hole, as they can be important in such geometry. We discover that it is possible to probe directly the absence of axial spin symmetry. As experimental evidence is important to investigate our theoretical findings, we propose spectroscopic means to probe the spin texture. Finally, we also consider one of the experimentally-known candidate materials, namely InAs/GaSb heterostructures. From the k.p Hamiltonian, it is possible to show that their bandstructure shows some anisotropies. The latter is also reflected in the spin texture of their edge states. [less ▲]

Transport through a quantum spin Hall antidot as a spectroscopic probe of spin textures

in Physical Review. B (2016), 94

We investigate electron transport through an antidot embedded in a narrow strip of two-dimensional topological insulator. We focus on the most generic and experimentally relevant case with broken axial ... [more ▼]

We investigate electron transport through an antidot embedded in a narrow strip of two-dimensional topological insulator. We focus on the most generic and experimentally relevant case with broken axial spin symmetry. Spin-non-conservation allows additional scattering processes which change the transport properties profoundly. We start from an analytical model for noninteracting transport, which we also compare with a numerical tight-binding simulation. We then extend this model by including Coulomb repulsion on the antidot, and we study the transport in the Coulomb-blockade limit. We investigate sequential tunneling and cotunneling regimes, and we find that the current-voltage characteristic allows a spectroscopic measurement of the edge-state spin textures. [less ▲]

Spin texture of generic helical edge states

in Physical Review. B (2015), 91

We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin symmetry. By considering honeycomb and square-lattice realizations ... [more ▼]

We study the spin texture of a generic helical liquid, the edge modes of a two-dimensional topological insulator with broken axial spin symmetry. By considering honeycomb and square-lattice realizations of topological insulators, we show that in all cases the generic behavior of a momentum-dependent rotation of the spin quantization axis is realized. Here we establish this mechanism also for disk geometries with continuous rotational symmetry. Finally, we demonstrate that the rotation of spin-quantization axis remains intact for arbitrary geometries, i.e., in the absence of any continuous symmetry. We also calculate the dependence of this rotation on the model and material parameters. Finally, we propose a spectroscopy measurement which should directly reveal the rotation of the spin-quantization axis of the helical edge states. [less ▲]