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 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. By varying the thickness of the quantum well, 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 quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width $d_{QW}< 6.3$ nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells ($d_{QW}> 6.3$ 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, $d_c= 6.3$ nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.Comment: Invited review article for special issue of JPSJ, 32 pages. For higher resolution figures see official online version when publishe

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.

Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study AharonovBohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe non-monotonic 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 magneto-conductance for a multichannel ring structure within the Landauer-Büttiker formalism. In the early 1980s it was shown that a quantum mechanical system acquires a geometric phase for a cyclic motion in parameter space. This geometric phase under adiabatic motion is called Berry phase [1], while its later generalization to include non-adiabatic motion is known as Aharonov-Anandan phase [2]. A manifestation of the Berry phase is the well known AharonovBohm (AB) phase [3] of an electrical charge which cycles around a magnetic flux. Aside from the AB effect, the first experimental observation of the Berry phase was reported in 1986 for photons in a wound optical fiber [4]. Another important Berry phase effect is the AharonovCasher (AC) effect [5], which has been proposed to occur when an electron propagates in a ring structure in an external magnetic field perpendicular to the ring plane in the presence of SO interaction [6].This AC effect can be seen when two partial waves move around the ring in different directions. They will acquire a phase difference which depends on the spin orientation with respect to the total magnetic field B tot = B ext + B ef f and the path of each partial wave. B ef f is the effective field induced by the SO interaction. The phase difference is approximately [6] where s =↑ and ↓ denote parallel and anti-parallel orientation to B tot , b = +1 for s =↑ and b = −1 for s =↓, and the superscript −(+) denotes a clockwise (counterclockwise) evolution, respectively. In the above equations, α is the SO parameter, r the ring radius, m * the effective electron mass and θ the angle between the external ( B ext ) and the total magnetic field B tot . For both equations, the first term on the right hand side can be identified with the AB phase and the second term of Eq. (1) with the geometric Berry or Aharonov-Anandan phase. The second term in Eq. (2) represents the dynamic part of the AC phase, i.e. the phase of a particle with a magnetic moment that moves around an electric field. From the expressions above, it can be seen that an increase of the AC phase will lead to a phase change that increases continuously with α, whereas the contribution due to the geometric phase results in a phase shift limited to ∆ϕ geom ≤ π.Both the AC phase [7] and the geometric phase [8, 9] depend on the SO interaction. As a result, one expects a complicated non-monotonic interference pattern as a function of magnetic field and SO interaction strength. So far, to our knowledge, apart from the AB effect no direct observation of phase related effects in solid state systems has been reported. Rec...

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.

Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa2Cu3O6.67under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along theaaxis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.

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 kΩ, 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. 1 arXiv:0812.3768v1 [cond-mat.mes-hall]

The discovery of the quantum spin Hall (QSH) state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the quantum spin Hall state have confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples, and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using scanning gate microscopy to perturb the QSH edge states on a submicron scale, we identify well-localized scattering sites which likely limit the expected nondissipative transport in the helical edge channels. In the micron-sized regions between the scattering sites, the edge states appear to propagate unperturbed, as expected for an ideal QSH system, and are found to be robust against weak induced potential fluctuations.