Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations have non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. While signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scalable to large numbers of states. Here we present a novel experimental approach towards a two-dimensional architecture. Using a Josephson junction made of HgTe quantum well coupled to thin-film aluminum, we are able to tune between a trivial and a topological superconducting state by controlling the phase difference φ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor *

Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical character of those states is by now well established experimentally, it is a fundamental open question how those edge states interact with each other when brought in spatial proximity. We employ a topological quantum point contact to guide edge channels from opposite sides into a quasi-onedimensional constriction, based on inverted HgTe quantum wells. Apart from the expected quantization in integer steps of 2e 2 /h, we find a surprising additional plateau at e 2 /h. We explain our observation by combining band structure calculations and repulsive electron-electron interaction effects captured within the Tomonaga-Luttinger liquid model. The present results may have direct implications for the study of one-dimensional helical electron quantum optics, Majorana-and potentially para-fermions. The quantum spin Hall effect has been predicted in several systems [1][2][3][4] and was first realized in HgCdTe/HgTe quantum wells [5]. Later, this phase was observed in other material systems such as InAs/GaSb double quantum wells [6] and in monolayers of WTe 2 and bismuthene [7,8]. The defining properties of this state, related to its helical nature, are well established by numerous experiments such as the observation of conductance quantization of two spin polarized edge channels G 0 = 2e 2 /h with e the electron charge and h the Planck's constant [5]. Additionally, non-local edge transport and spin-polarization of the edge channels were demonstrated by suitable transport experiments [9,10]. We instead target a still open question, namely how helical edge states interact with each other.A quantum point contact (QPC) can be used to guide * All three authors contributed equally to this work, email: Jonas.Strunz@physik.uni-wuerzburg.de edge channels from opposite boundaries of the sample into a constriction. Such a device allows for studies of charge and spin transfer mechanisms by, e.g., adjusting the overlap of the edge states [11][12][13][14][15][16][17][18][19][20]. Besides the general interest in the study of transport processes in such a device, the appropriate model to describe the essential physics and to capture interaction effects of helical edge states is still unclear. The one-dimensionality of the helical edge modes suggests a description in terms of the Tomonaga-Luttinger liquid when electron-electron interactions are taken into account. In this respect, the QPC setup provides an illuminating platform as it may give rise to particular backscattering processes.We present the realization of a QPC based on HgTe quantum wells as evidenced by the observation of the expected conductance steps in integer values of G 0 . The newly developed lithographic process allows the fabrication of sophisticated nanostructures based on topological materials without lowering the material quality. It t...

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The HgTe quantum well (QW) is a well-characterized two-dimensional topological insulator (2D-TI). Its band gap is relatively small (typically on the order of 10 meV), which restricts the observation of purely topological conductance to low temperatures. Here, we utilize the strain-dependence of the band structure of HgTe QWs to address this limitation. We use CdTe-Cd0.5Zn0.5Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magneto-transport measurements, which demonstrate a transition from a semimetallic to a 2D-TI regime in wide QWs, when the strain is changed from tensile to compressive.Most notably, we demonstrate a much enhanced energy gap of 55 meV in heavily compressively strained QWs. This value exceeds the highest possible gap on common II-VI substrates by a factor of 2-3, and extends the regime where the topological conductance prevails to much higher temperatures.The transport properties of molecular-beam epitaxially (MBE) grown HgTe QWs embedded in Cd 0.7 Hg 0.3 Te barriers have attracted considerable attention due to the discovery of the quantum-spin-Hall (QSH) effect in these structures [1][2][3]. The QSH effect is the landmark property of a 2D-TI and is characterized by the presence of a pair of one-dimensional, counter-propagating ("helical") channels along the edges of the mesa, giving rise to a quantized longitudinal conductanceA prerequisite for the formation of edge channels is atopologically nontrivial -inverted band structure, as is present in HgTe QWs when the thickness d QW exceeds d c = 6.3 nm [1]. Inverted HgTe QWs have a relatively small band gap E G (typically lower than 15 meV), which can make it difficult to gate homogeneously into the gap over the whole mesa, and also prevents applications at elevated temperatures. Here we present a way to increase E G well above the thermal energy at room temperature (k B T = 25 meV). This is achieved by applying compressive strain to HgTe QWs through coherent growth on virtual substrates with a freely tunable lattice constant.The crucial influence of strain on the band structure of HgTe has been demonstrated previously for bulk layers (layer thickness d > 40 nm): epitaxy of HgTe on CdTe substrates exerts tensile strain (ε = −0.3 %), which causes a gap-opening of the Γ 8 doublet, transforming the bulk semimetal into a three-dimensional topological insulator [4,5]. However, these previous experiments used commercially available MBE quality substrates, limiting the options to Cd 0.96 Zn 0.04 Te[1-3] and CdTe [4,5][6]. In both cases, the lattice constant of the substrate material is larger than that of HgTe, resulting in a tensile strain in the epilayers. Under such conditions, the largest gaps that can be obtained in inverted QWs are E G = 17 meV and 25 meV for wells grown on CdTe and Cd 0.96 Zn 0.04 Te, respectively [7].The present work reports on a major progress in this situation. We use CdTe-Cd 0.5 Zn 0.5 Te (001) strainedlayer superlattices (SLS) as virtual ...

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While a detailed accessible conception exists from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Due to the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.The discovery of topological insulators has inspired a remarkably broad interest in materials whose band structures exhibit relativistic properties. The effects of a linear dispersion in one-dimensional edge channels of quantum spin Hall insulators [1], as well as in twodimensional surface states of three-dimensional topological insulators [2,3], have already been extensively studied. The implications of a linear band dispersion in threedimensional conductors, however, have only recently begun to be explored. Such materials, dubbed Dirac or Weyl semimetals, represent a condensed matter realization of the Weyl/Dirac equations, and may provide an environment for studying the properties of quasiparticles which have been postulated, but not yet unambiguously demonstrated, to exist in nature.In many of these materials [4], the Weyl or Dirac band crossing is caused by a band inversion, and is intimately connected to the point group symmetry of the crystal lattice. This lends similarities to the prototypical setup of topological insulators. In fact, both in the alkali pnictide (AB 3 , where A=(Na,K,Rb), B=(As,Sb,Bi)) and Cd 2 As 3 families that boast a number of important Weyl/Dirac compounds, the inversion occurs between metallic s-like and chalcogenic p-like orbitals, a situation very similar to that found in HgTe. The correspondence in terms of band structure between these compounds and HgTe has indeed been known since the 1970's [5]. The common motif is that, for the alkali pnictides and Cd 2 As 3 , the p-like j = 3/2 bands (Γ 8 in the T d point group) cross and yield Dirac (or Weyl) points, while in HgTe the Γ 8 bands just touch, derives from the higher (zincblende) point group symmetry of the HgTe crystal. Small crystal distortions from the zincblende symmetry, as present in Weyl/Dirac semimetals, are sufficient to crucially modify the electronic structure at low energies.In the 19...