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 2e^{2}/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.

Hexagonal silicon grown from higher order silanes.

We demonstrate the merits of an unexplored precursor, tetrasilane (Si4H10), as compared to disilane (Si2H6) for the growth of defect-free, epitaxial hexagonal silicon (Si). We investigate the growth kinetics of hexagonal Si shells epitaxially around defect-free wurtzite gallium phosphide (GaP) nanowires. Two temperature regimes are identified, representing two different surface reaction mechanisms for both types of precursors. Growth in the low temperature regime (415 °C-600 °C) is rate limited by interaction between the Si surface and the adsorbates, and in the high temperature regime (600 °C-735 °C) by chemisorption. The activation energy of the Si shell growth is 2.4 ± 0.2 eV for Si2H6 and 1.5 ± 0.1 eV for Si4H10 in the low temperature regime. We observe inverse tapering of the Si shells and explain this phenomenon by a basic diffusion model where the substrate acts as a particle sink. Most importantly, we show that, by using Si4H10 as a precursor instead of Si2H6, non-tapered Si shells can be grown with at least 50 times higher growth rate below 460 °C. The lower growth temperature may help to reduce the incorporation of impurities resulting from the growth of GaP.

High Mobility HgTe Microstructures for Quantum Spin Hall Studies.

The topic of two-dimensional topological insulators has blossomed after the first observation of the quantum spin Hall (QSH) effect in HgTe quantum wells. However, studies have been hindered by the relative fragility of the edge states. Their stability has been a subject of both theoretical and experimental investigation in the past decade. Here, we present a new generation of high quality (Cd,Hg)Te/HgTe-structures based on a new chemical etching method. From magnetotransport measurements on macro- and microscopic Hall bars, we extract electron mobilities µ up to about 400 × 103 cm2/(V s), and the mean free path λmfp becomes comparable to the sample dimensions. The Hall bars show quantized spin Hall conductance, which is remarkably stable up to 15 K. The clean and robust edge states allow us to fabricate high quality side-contacted Josephson junctions, which are significant in the context of topological superconductivity. Our results open up new avenues for fundamental research on QSH effect as well as potential applications in spintronics and topological quantum computation.

Publisher's Note: Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates [Phys. Rev. Lett. 117, 086403 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.086403.

Strain Engineering of the Band Gap of HgTe Quantum Wells Using Superlattice Virtual Substrates.

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-Cd_{0.5}Zn_{0.5}Te strained-layer superlattices on GaAs as virtual substrates with adjustable lattice constant to control the strain of the QW. We present magnetotransport 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.

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.

Emergent quantum Hall effects below 50 mT in a two-dimensional topological insulator.

The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials, which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However, the large magnetization in conventional quantum anomalous Hall systems makes it challenging to induce superconductivity. Here, we report two different emergent quantum Hall effects in (Hg,Mn)Te quantum wells. First, a previously unidentified quantum Hall state emerges from the quantum spin Hall state at an exceptionally low magnetic field of ~50 mT. Second, tuning toward the bulk p-regime, we resolve quantum Hall plateaus at fields as low as 20 to 30 mT, where transport is dominated by a van Hove singularity in the valence band. These emergent quantum Hall phenomena rely critically on the topological band structure of HgTe, and their occurrence at very low fields makes them an ideal candidate for realizing chiral Majorana fermions.

Bottom-Up Grown 2D InSb Nanostructures.

Low-dimensional high-quality InSb materials are promising candidates for next-generation quantum devices due to the high carrier mobility, low effective mass, and large g-factor of the heavy element compound InSb. Various quantum phenomena are demonstrated in InSb 2D electron gases and nanowires. A combination of the best features of these two systems (pristine nanoscale and flexible design) is desirable to realize, e.g., the multiterminal topological Josephson device. Here, controlled growth of 2D nanostructures, nanoflakes, on an InSb platform is demonstrated. An assembly of nanoflakes with various dimensions and morphologies, thinner than the Bohr radius of InSb, are fabricated. Importantly, the growth of either nanowires or nanoflakes can be enforced experimentally by setting growth and substrate design parameters properly. Hall bar measurements on the nanostructures yield mobilities up to ≈20 000 cm2 V-1 s-1 and detect quantum Hall plateaus. This allows to see the system as a viable nanoscale 2D platform for future quantum devices.

Gapless Andreev bound states in the quantum spin Hall insulator HgTe.

In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.

Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry.

The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. This indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.