Quantum Spin Hall Insulator State in HgTe Quantum Wells (0710.0582v1)

Abstract: 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 insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e^2/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nm, is also independently determined from the magnetic field induced insulator to metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

• The paper confirms the Quantum Spin Hall insulator state in HgTe quantum wells by detecting a conductance plateau near 2e²/h above the 6.3 nm threshold.
• The authors used varied quantum well thicknesses and advanced eight-band k·p simulations to match experimental results with theoretical models.
• The research shows that topologically protected edge states are disrupted by small magnetic fields, highlighting significant implications for spintronic devices.

Analysis of the Quantum Spin Hall Insulator State in HgTe Quantum Wells

This paper presents a significant experimental investigation into the realization of the Quantum Spin Hall (QSH) effect in HgTe/(Hg,Cd)Te quantum wells. The conceptual framework is grounded in the theoretical prediction that the QSH effect, a novel quantum state of matter existing without an external magnetic field, could manifest in such quantum wells. This research substantiates the existence of a QSH insulator state, contributing empirical evidence in support of this theoretical forecast.

The authors fabricated HgTe/(Hg,Cd)Te quantum wells with varied thicknesses and measured their transport properties under different conditions. A key finding is the distinct conductance behavior at the quantum phase transition thickness of around 6.3 nm. Specifically, for quantum wells with thicknesses less than this critical limit, the systems behaved as conventional insulators with diminishing conductance at low temperatures. However, for thicknesses greater than 6.3 nm, the so-called insulating regime exhibited a conductance plateau near $2e^2/h$, signifying robust, topologically protected edge states.

The experimental design considered factors such as sample thickness, gate voltage, and external magnetic field. Notably, the edge conductance observed in thicker quantum wells was independent of sample width, reinforcing the role of edge states in the QSH effect. Importantly, the QSH state was disrupted with the application of a small magnetic field, further attesting to the time-reversal symmetry underpinning the QSH edge states.

The theoretical model relies on a four-band effective Hamiltonian with a Dirac-like mass inversion, modulating from a positive to a negative value, describing an insulator to QSH transition. The transition was experimentally validated via measurements showing a phase shift from an insulating to a quantum Hall (QH) state under magnetic fields. The intricate Landau level crossings in the inverted regime further elucidated this phase transition.

Disparities between experimental observations and the simplified Dirac model were addressed through sophisticated simulations using an eight-band $k \cdot p$ model. Discrepancies in expected and observed crossing points were reconciled, corroborating the topological nature of the insulating state for critical thicknesses beyond 6.3 nm.

The empirical realization of the QSH state in HgTe/(Hg,Cd)Te quantum wells opens avenues for further research in topological insulators and their applications in spintronics. The robustness of edge states against non-magnetic perturbations holds potential for low-dissipation spintronic devices. Future investigations could delineate the spin accumulation properties and explore variations in transport behaviors near the critical transition thickness, comparing them with two-dimensional materials like graphene.

This paper significantly advances the understanding of QSH insulators, and its implications are likely to motivate ongoing developments in the exploration of topologically non-trivial materials.