H. Buhmann

Quantum Spin Hall Insulator State in HgTe Quantum Wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e2/h, where e is the electron charge and h is Plancks constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field–induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.

Nonlocal Transport in the Quantum Spin Hall State

Living on the Edge Topological insulators are a recently described state of matter in which the bulk material is an insulator but with a metallic surface state that is protected by the topology of the Fermi surface. Roth et al. (p. 294; see the Perspective by Büttiker) now show that the current flow on the surface takes place in edge states around the boundary of the sample. These are similar to the current transport in high-quality two-dimensional electron gases in high magnetic field, which confirms theoretical work on these materials. A topological insulator exhibits current flow in edge states around the sample without the need for magnetic fields. Nonlocal transport through edge channels holds great promise for low-power information processing. However, edge channels have so far only been demonstrated to occur in the quantum Hall regime, at high magnetic fields. We found that mercury telluride quantum wells in the quantum spin Hall regime exhibit nonlocal edge channel transport at zero external magnetic field. The data confirm that the quantum transport through the (helical) edge channels is dissipationless and that the contacts lead to equilibration between the counterpropagating spin states at the edge. The experimental data agree quantitatively with the theory of the quantum spin Hall effect. The edge channel transport paves the way for a new generation of spintronic devices for low-power information processing.

The Quantum Spin Hall Effect: Theory and Experiment

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 review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells (QWs). By varying the thickness of the QW, the band structure changes from a normal to an “inverted” type at a critical thickness d c . We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te QWs. We review both the fabrication of the sample and the experimental setup. For thin QWs w...

Quantum Hall effect from the topological surface states of strained bulk HgTe.

We report transport studies on a three-dimensional, 70-nm-thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semimetallic HgTe, which thus becomes a three-dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.

Thermopower of a Kondo Spin-Correlated Quantum Dot

The thermopower of a Kondo-correlated gate-defined quantum dot is studied using a current heating technique. In the presence of spin correlations, the thermopower shows a clear deviation from the semiclassical Mott relation between thermopower and conductivity. The strong thermopower signal indicates a significant asymmetry in the spectral density of states of the Kondo resonance with respect to the Fermi energies of the reservoirs. The observed behavior can be explained within the framework of an Anderson-impurity model.

Quantum dot as thermal rectifier

We report the observation of thermal rectification in a semiconductor quantum dot, as inferred from the asymmetric line shape of the thermopower oscillations. The asymmetry is observed at high in-plane magnetic fields and caused by the presence of a high orbital momentum state in the dot.

Single valley Dirac fermions in zero-gap HgTe quantum wells

Most of the notable properties of graphene are a result of the cone-like nature of the points in its electronic structure where its conduction and valance bands meet. Similar structures arise in 2D HgTe quantum wells, but without the spin- and valley-degeneracy of graphene; their properties are also likely to be easier to control.

Spin polarization of the quantum spin Hall edge states

The quantum spin Hall state is predicted to consist of two oppositely polarized spin currents travelling in opposite directions around the edges of a topological insulator. Non-local measurements of the transport in HgTe quantum wells confirm the polarized nature of these edge states.

Direct observation of the Aharonov-Casher phase.

Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.

Imaging currents in HgTe quantum wells in the quantum spin Hall regime

The quantum spin Hall (QSH) state is a state of matter characterized by a non-trivial topology of its band structure, and associated conducting edge channels. The QSH state was predicted and experimentally demonstrated to be realized in HgTe quantum wells. The existence of the edge channels has been inferred from local and non-local transport measurements in sufficiently small devices. Here we directly confirm the existence of the edge channels by imaging the magnetic fields produced by current flowing in large Hall bars made from HgTe quantum wells. These images distinguish between current that passes through each edge and the bulk. On tuning the bulk conductivity by gating or raising the temperature, we observe a regime in which the edge channels clearly coexist with the conducting bulk, providing input to the question of how ballistic transport may be limited in the edge channels. Our results represent a versatile method for characterization of new QSH materials systems.