Topological Superconductivity in a Phase-Controlled Josephson Junction

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 $\phi$ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor by measuring the tunneling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunneling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunneling conductance develops a zero-bias peak which persists over a range of $\phi$ that expands systematically with increasing magnetic fields. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and will therefore open new avenues for probing topological superconducting phases in two-dimensional systems.Comment: Supplementary contains resized figures. Original files are available upon reques

Interplay of Dirac nodes and Volkov-Pankratov surface states in compressively strained HgTe

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible 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.Comment: 8 pages, 7 figures, accepted in PRX, added kp calculation and supplementar

Counterpropagating topological and quantum Hall edge channels

The survival of the quantum spin Hall edge channels in presence of an external magnetic field has been a subject of experimental and theoretical research. The inversion of Landau levels that accommodates the quantum spin Hall effect is destroyed at a critical magnetic field, and a trivial insulating gap appears in the spectrum for stronger fields. In this work, we report the absence of this transport gap in disordered two dimensional topological insulators in perpendicular magnetic fields of up to 16 T. Instead, we observe that a topological edge channel (from band inversion) coexists with a counterpropagating quantum Hall edge channel for magnetic fields at which the transition to the insulating regime is expected. For larger fields, we observe only the quantum Hall edge channel with transverse resistance close to $h/e^2$. By tuning the disorder using different fabrication processes, we find evidence that this unexpected $\nu=1$ plateau originates from extended quantum Hall edge channels along a continuous network of charge puddles at the edges of the device.Comment: 8+3 pages, 5+2 figure

Velocity and confinement of edge plasmons in HgTe-based 2D topological insulators

High-frequency transport in the edge states of the quantum spin Hall (QSH) effect has to date rarely been explored, though it could cast light on the scattering mechanisms taking place therein. We here report on the measurement of the plasmon velocity in topological HgTe quantum wells both in the QSH and quantum Hall (QH) regimes, using harmonic GHz excitations and phase-resolved detection. We observe low plasmon velocities corresponding to large transverse widths, which we ascribe to the prominent influence of charge puddles forming in the vicinity of edge channels. Together with other recent works, it suggests that puddles play an essential role in the edge state physics and probably constitute a main hurdle on the way to clean and robust edge transport.Comment: 8 pages, 6 figures, + supplementary materia

Topological band inversion in HgTe(001): surface and bulk signatures from photoemission

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy. We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its non-trivial band topology

Residual strain in free-standing CdTe nanowires overgrown with HgTe

We investigate the crystal properties of CdTe nanowires overgrown with HgTe. Scanning electron microscopy and scanning transmission electron microscopy confirm that the growth results in a high ensemble uniformity and that the individual heterostructures are single-crystalline, respectively. We use high-resolution X-ray diffraction to investigate strain, caused by the small lattice mismatch between the two materials. We find that both CdTe and HgTe show changes in the lattice constant compared to the respective bulk lattice constants. The measurements reveal a complex strain pattern with signatures of both uniaxial and shear strains present in the overgrown nanowires

Approaching Quantization in Macroscopic Quantum Spin Hall Devices through Gate Training

Quantum spin Hall edge channels hold great promise as dissipationless one-dimensional conductors.However, the ideal quantized conductance of2e2=his only found in very short channels-in contradictionwith the expected protection against backscattering of the topological insulator state. In this Letter we showthat enhancing the band gap does not improve quantization. When we instead alter the potential landscapeby charging trap states in the gate dielectric using gate training, we approach conductance quantization formacroscopically long channels. Effectively, the scattering length increases to175μm, more than 1 order ofmagnitude longer than in previous works for HgTe-based quantum wells. Our experiments show that thedistortion of the potential landscape by impurities, leading to puddle formation in the narrow gap material,is the major obstacle for observing undisturbed quantum spin Hall edge channel transpor

Approaching quantization in macroscopic quantum spin hall devices through gate training

Quantum spin Hall edge channels hold great promise as dissipationless one-dimensional conductors. However, the ideal quantized conductance of 2e2/h is only found in very short channels-in contradiction with the expected protection against backscattering of the topological insulator state. In this Letter we show that enhancing the band gap does not improve quantization. When we instead alter the potential landscape by charging trap states in the gate dielectric using gate training, we approach conductance quantization for macroscopically long channels. Effectively, the scattering length increases to 175 μm, more than 1 order of magnitude longer than in previous works for HgTe-based quantum wells. Our experiments show that the distortion of the potential landscape by impurities, leading to puddle formation in the narrow gap material, is the major obstacle for observing undisturbed quantum spin Hall edge channel transport

Approaching quantization in macroscopic quantum spin hall devices through gate training

\u3cp\u3eQuantum spin Hall edge channels hold great promise as dissipationless one-dimensional conductors. However, the ideal quantized conductance of 2e2/h is only found in very short channels-in contradiction with the expected protection against backscattering of the topological insulator state. In this Letter we show that enhancing the band gap does not improve quantization. When we instead alter the potential landscape by charging trap states in the gate dielectric using gate training, we approach conductance quantization for macroscopically long channels. Effectively, the scattering length increases to 175 μm, more than 1 order of magnitude longer than in previous works for HgTe-based quantum wells. Our experiments show that the distortion of the potential landscape by impurities, leading to puddle formation in the narrow gap material, is the major obstacle for observing undisturbed quantum spin Hall edge channel transport.\u3c/p\u3