[Paper Review] Ballistic Intrinsic Spin-Hall Effect in HgTe Nanostructures

Christoph Bruene, Albrecht Roth+7 more|ArXiv.org|Dec 19, 2008

Quantum and electron transport phenomena1 references3 citations

TL;DR

This paper demonstrates the first electrical detection of the ballistic intrinsic spin-Hall effect (ISHE) in HgTe nanostructures using H-shaped mesoscopic devices. By tuning carrier type via a top-gate, the authors observe a non-local resistance signal of up to ~kΩ in the p-type regime—orders of magnitude larger than in metals—confirming the ISHE through quantitative agreement with Landauer-Büttiker transport simulations.

ABSTRACT

We report the first electrical manipulation and detection of the mesoscopic intrinsic spin-Hall effect (ISHE) in semiconductors through non-local electrical measurement in nano-scale H-shaped structures built on high mobility HgTe/HgCdTe quantum wells. By controlling the strength of the spin-orbit splittings and the n-type to p-type transition by a top-gate, we observe a large non-local resistance signal due to the ISHE in the p-regime, of the order of kOhms, which is several orders of magnitude larger than in metals. In the n-regime, as predicted by theory, the signal is at least an order of magnitude smaller. We verify our experimental observation by quantum transport calculations which show quantitative agreement with the experiments.

Motivation & Objective

• To experimentally demonstrate and detect the ballistic intrinsic spin-Hall effect (ISHE) in high-mobility HgTe-based quantum wells.
• To overcome the challenges of weak electrical detection in diffusive systems by using ballistic transport in nanostructured H-shaped devices.
• To distinguish the intrinsic spin-Hall effect from extrinsic contributions using gate-tunable carrier type and non-local voltage measurements.
• To validate experimental observations with quantum transport simulations based on the Landauer-Büttiker formalism.
• To quantify the dependence of the ISHE signal on spin-orbit coupling strength and carrier density in n- and p-type regimes.

Proposed method

• Fabricated H-shaped nanostructures on high-mobility HgTe/HgCdTe quantum wells using electron beam lithography and dry-etching.
• Employed a top-gate to electrically tune carrier type from n-type through insulating to p-type, enabling control over spin-orbit coupling and carrier density.
• Performed non-local electrical measurements with current injected in one leg and voltage detected in the opposite leg to isolate the ISHE signal.
• Used Landauer-Büttiker (LB) formalism with tight-binding Hamiltonian to model quantum transport, incorporating disorder via random on-site energies.
• Calculated non-local resistance $ R_{nl} = V_{36}/I_{12} $ under linear response, with zero current boundary condition at the non-local probes.
• Compared experimental data with simulations using extracted parameters: effective mass, spin-orbit coupling, and mobility from band structure and transport measurements.

Experimental results

Research questions

• RQ1 Can the intrinsic spin-Hall effect be electrically detected in a ballistic semiconductor nanostructure with high sensitivity?
• RQ2 How does the non-local resistance signal due to the ISHE depend on carrier type (n- vs. p-type) in HgTe quantum wells?
• RQ3 To what extent does the ISHE signal scale with spin-orbit coupling and carrier mobility in the ballistic regime?
• RQ4 Can quantum transport simulations based on the Landauer-Büttiker formalism quantitatively reproduce the experimental non-local resistance signal?
• RQ5 What is the contribution of extrinsic effects (e.g., QSHE) to the observed signal, and how can they be suppressed in the measurement geometry?

Key findings

• A non-local resistance signal of up to ~1 kΩ was observed in the p-type regime, several orders of magnitude larger than in metallic systems.
• The ISHE signal was at least an order of magnitude smaller in the n-type regime, consistent with theoretical predictions.
• Quantitative agreement was achieved between experimental data and Landauer-Büttiker simulations, confirming the ballistic intrinsic spin-Hall effect as the origin of the signal.
• Theoretical simulations showed that the ISHE signal is strongly enhanced in p-type HgTe due to larger spin-orbit splitting and effective mass effects.
• The oscillatory behavior of the signal with gate voltage arises from the changing ratio of Fermi energy to spin-orbit splitting across the gate voltage sweep.
• The presence of additional voltage probes in sample Q2198 enabled effective suppression of the quasi-ballistic spin-Hall effect (QSHE), improving signal fidelity.