Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we revie...

Recent theory predicted that the Quantum Spin Hall Effect, a fundamentally novel quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We have fabricated such sample structures with low density and high mobility in which we can tune, through an external gate voltage, the carrier conduction from n-type to the p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nm, the insul...

Spin Hall effect can be induced both by the extrinsic impurity scattering and by the intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. This difference gives a direct mechanism to experimentally distinguish the in...

The quantum spin Hall (QSH) states discovered in an inverted band of InAs/GaSb and HgTe/CdTe quantum wells categorize them among the very superior candidates for topological insulators. In the presence of a magnetic field, these QSH states persist up to a magnetic field equal to the critical field, beyond which the edge states would consist of normal quantum Hall (QH) states. We provide the expression of this critical field which is found consistent with some previous literat...

Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states. Since their theoretical discovery, these materials have encouraged intense efforts to study their properties and capabilities. Among the most striking results of this activity are proposals to engineer a new variety of superconductor at the surfaces of topological insulators. These topological superconductors would be capable of supporti...

The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time-reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge. Recently, it has been shown that HgTe quantum wells realize this novel effect. In this work, we start from realistic tight-binding models and demonstrate the existence of the helical edge states in HgTe quantum wells and calculate their physical properties. We also show that 3d HgTe i...

HgTe quantum wells possess remarkable physical properties as for instance the quantum spin Hall state and the 'single-valley' analog of graphene, depending on their layer thicknesses and barrier composition. However, double HgTe quantum wells yet contain more fascinating and still unrevealed features. Here we report on the study of the quantum phase transitions in tunnel-coupled HgTe layers separated by CdTe barrier. We demonstrate that this system has a 3/2 pseudo spin degre...

In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field $B_\mathrm{c}$, above which only quantum Hall (QH) states can be found. Using linear-response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and possible signatures...

While the helical character of the edge channels responsible for charge transport in the quantum spin Hall regime of a two-dimensional topological insulator is by now well established, an experimental confirmation that the transport in the edge channels is spin-polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall an...

The quantum spin Hall (QSH) state is a genuinely new state of matter characterized by a non-trivial topology of its band structure. Its key feature is conducting edge channels whose spin polarization has potential for spintronic and quantum information applications. The QSH state was predicted and experimentally demonstrated to exist in HgTe quantum wells. The existence of the edge channels has been inferred from the fact that local and non-local conductance values in suffici...