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

We present direct experimental evidence for nonlocal transport in HgTe quantum wells in the quantum spin Hall regime, in the absence of any external magnetic field. The data conclusively show that the non-dissipative quantum transport occurs through edge channels, while the contacts lead to equilibration between the counter-propagating spin states at the edge. We show that the experimental data agree quantitatively with the theory of the quantum spin Hall effect.The quantum spin Hall (QSH) state (1, 2) is a topologically nontrivial state of matter which exists in the absence of any external magnetic field. It has a bulk energy gap but gapless helical edge states protected by time reversal symmetry. In the QSH regime, opposite spin states forming a Kramers doublet counter-propagate at the edge (3, 4). Recently, the QSH state has been theoretically predicted in HgTe quantum wells (5). There is a topological quantum phase transition at a critical thickness d c of the quantum well, separating the trivial insulator state for

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. PACS numbers:The discovery of two (2D) and three dimensional (3D) topological insulators (TI)1-10 has generated strong activity in the condensed matter physics community 11,12 . Current research on 3D TIs is mostly focused on Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 compounds 8-10 due to their simple Dirac-like surface states, which have been observed by angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy 11 . However, these compounds show strong defect doping and low carrier mobility, and the observation of surface charge transport is obscured by the bulk conductivity. Many of the predicted novel properties of a 3D TI, such as the quantized magneto-electric effect 13,14 and the surface Majorana fermions 15 , can only be observed when bulk carriers are negligible compared to the surface states. Experimentally reaching the intrinsic TI regime, where bulk carriers are absent, is now the central focus of the field.The two dimensional TI state was first predicted and observed in 2D HgTe quantum wells (QW) 1,3 , and non-local transport measurements demonstrate edge state transport without any contributions from 2D bulk carriers.16 3D HgTe is a semi-metal which is charge-neutral when the Fermi energy is at the touching point between the light-hole and heavy-hole Γ 8 bands at the Brillouin zone center. A unique property of the band structure of HgTe is the energetic inversion of the Γ 6 and Γ 8 band ordering, which is the origin of the quantum spin Hall effect in 2D HgTe/CdTe QWs 3 . Due to the band inversion, 3D HgTe is also expected to have Dirac-like surface states 17,18 , but since the material is semi-metallic, this state is always coupled to metallic bulk states. With applied strain, a gap opens up between the light-hole and heavy-hole bands, so that strained 3D HgTe is expected to be a 3D TI 4,19 . In this paper we demonstrate experimentally that a gap opens up in in-plane strained 3D HgTe bulk layers grown by molecular beam epitaxy (MBE), and we reach the much sought after intrinsic TI regime in a material with negligible bulk carriers. In this regime, the Hall effect of the 3D HgTe bulk layer is quantized, due to the contributions from the surface states only. Theoretical considerations are in agreement with the experimental results and confirm the transport through 2D surface states with Dirac type dispersion.HgTe bulk samples have been grown by MBE on CdTe subtrates, which have a lattice constant that is 0.3 % larger than that of bulk HgTe (0.646 nm). At this mismat...

The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature deeply influences the properties of the supercurrent. In recent years, considerable efforts have focused on the coupling of superconductors to the surface states of a three-dimensional topological insulator. In such a material, an unconventional induced p-wave superconductivity should occur, with a doublet of topologically protected gapless Andreev bound states, whose energies vary 4π-periodically with the superconducting phase difference across the junction. In this article, we report the observation of an anomalous response to rf irradiation in a Josephson junction made of a HgTe weak link. The response is understood as due to a 4π-periodic contribution to the supercurrent, and its amplitude is compatible with the expected contribution of a gapless Andreev doublet. Our work opens the way to more elaborate experiments to investigate the induced superconductivity in a three-dimensional insulator.

Topological insulators are a newly discovered phase of matter characterized by a gapped bulk surrounded by novel conducting boundary states [1,2,3]. 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 [4,5]. These topological superconductors would be capable of supporting localized Majorana fermions, particles whose braiding properties have been proposed as the basis of a fault-tolerant quantum computer [6]. Despite the clear theoretical motivation, a conclusive realization of topological superconductivity remains an outstanding experimental goal.Here we present measurements of superconductivity induced in two-dimensional HgTe/HgCdTe quantum wells, a material which becomes a quantum spin Hall insulator when the well width exceeds dC = 6.3 nm [7]. In wells that are 7.5 nm wide, we find that supercurrents are confined to the one-dimensional sample edges as the bulk density is depleted. However, when the well width is decreased to 4.5 nm the edge supercurrents cannot be distinguished from those in the bulk. These results provide evidence for superconductivity induced in the helical edges of the quantum spin Hall effect, a promising step toward the demonstration of one-dimensional topological superconductivity.Our results also provide a direct measurement of the widths of these edge channels, which range from 180 nm to 408 nm.Topological superconductors, like topological insulators, possess a bulk energy gap and gapless surface states. In a topological superconductor, the surface states are predicted to manifest as zero-energy Majorana fermions, fractionalized modes which pair to form conventional fermions. Due to their non-Abelian braiding statistics, achieving control of these Majorana modes is desirable both fundamentally and for [9], and on their direct engineering using s-wave superconductors combined with topological insulators or semiconductors [10,11]. Particularly appealing are implementations in one-dimensional (1D) systems, where Majorana modes would be localized to the ends of a wire. In such a 1D system, restriction to a single spin degree of freedom combined with proximity to an s-wave superconductor would provide the basis for topological superconductivity [12]. Effort in this direction has been advanced by studies of nanowire systems [13,14,15,16,17,18] and by excess current measurements on InAs/GaSb devices [19]. Given the wide interest in Majorana fermions in one dimension, it is essential to expand the search to other systems whose properties are suited toward their control.An attractive route toward a 1D topological superconductor uses as its starting point the twodimensional (2D) quantum spin Hall (QSH) insulator. This topological phase of matter was recently predicted [20,21] and observed [22,23] in HgTe/HgCdTe quantum wells thicker than a critical thickness d C = 6...

The band structure of semimagnetic Hg1−yMnyTe/Hg1−xCdxTe type-III quantum wells has been calculated using eight-band k · p model in an envelope function approach. Details of the band structure calculations are given for the Mn free case (y = 0). A mean field approach is used to take the influence of the sp − d exchange interaction on the band structure of QW's with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a Hg0.98Mn0.02Te/Hg0.3Cd0.7Te QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the sp−d exchange interaction on the transport properties of Hg1−yMnyTe/Hg1−xCdxTe QW's.

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