Excitonic topological order in imbalanced electron-hole bilayers.

Correlation and frustration play essential roles in physics, giving rise to novel quantum phases1-6. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement4. However, the realization of moat-band physics is still challenging. Here, we explore moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. We find that a large bulk gap exists, encompassing a broad range of density imbalances at zero magnetic field (B), accompanied by edge channels that resemble helical transport. Under an increasing perpendicular B, the bulk gap persists, and an anomalous plateau of Hall signals appears, which demonstrates an evolution from helical-like to chiral-like edge transport with a Hall conductance approximately equal to e2/h at 35 tesla, where e is the elementary charge and h is Planck's constant. Theoretically, we show that strong frustration from density imbalance leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations. Our work opens up a new direction for research on topological and correlated bosonic systems in solid states beyond the framework of symmetry-protected topological phases, including but not limited to the bosonic fractional quantum Hall effect.

Anomalous Conductance Oscillations in the Hybridization Gap of InAs/GaSb Quantum Wells.

We observe the magnetic oscillation of electric conductance in the two-dimensional InAs/GaSb quantum spin Hall insulator. Its insulating bulk origin is unambiguously demonstrated by the antiphase oscillations of the conductance and the resistance. Characteristically, the in-gap oscillation frequency is higher than the Shubnikov-de Haas oscillation close to the conduction band edge in the metallic regime. The temperature dependence shows both thermal activation and smearing effects, which cannot be described by the Lifshitz-Kosevich theory. A two-band Bernevig-Hughes-Zhang model with a large quasiparticle self-energy in the insulating regime is proposed to capture the main properties of the in-gap oscillations.

Tuning Edge States in Strained-Layer InAs/GaInSb Quantum Spin Hall Insulators.

We report on a class of quantum spin Hall insulators (QSHIs) in strained-layer InAs/GaInSb quantum wells, in which the bulk gaps are enhanced up to fivefold as compared to the binary InAs/GaSb QSHI. Remarkably, with consequently increasing edge velocity, the edge conductance at zero and applied magnetic fields manifests time reversal symmetry-protected properties consistent with the Z_{2} topological insulator. The InAs/GaInSb bilayers offer a much sought-after platform for future studies and applications of the QSHI.

Robust helical edge transport in gated InAs/GaSb bilayers.

We have engineered electron-hole bilayers of inverted InAs/GaSb quantum wells, using dilute silicon impurity doping to suppress residual bulk conductance. We have observed robust helical edge states with wide conductance plateaus precisely quantized to 2e^{2}/h in mesoscopic Hall samples. On the other hand, in larger samples the edge conductance is found to be inversely proportional to the edge length. These characteristics persist in a wide temperature range and show essentially no temperature dependence. The quantized plateaus persist to a 12 T applied in-plane field; the conductance increases from 2e^{2}/h in strong perpendicular fields manifesting chiral edge transport. Our study presents a compelling case for exotic properties of a one-dimensional helical liquid on the edge of InAs/GaSb bilayers.

Observation of a Helical Luttinger Liquid in InAs/GaSb Quantum Spin Hall Edges.

We report on the observation of a helical Luttinger liquid in the edge of an InAs/GaSb quantum spin Hall insulator, which shows characteristic suppression of conductance at low temperature and low bias voltage. Moreover, the conductance shows power-law behavior as a function of temperature and bias voltage. The results underscore the strong electron-electron interaction effect in transport of InAs/GaSb edge states. Because of the fact that the Fermi velocity of the edge modes is controlled by gates, the Luttinger parameter can be fine tuned. Realization of a tunable Luttinger liquid offers a one-dimensional model system for future studies of predicted correlation effects.

Images of edge current in InAs/GaSb quantum wells.

Quantum spin Hall devices with edges much longer than several microns do not display ballistic transport; that is, their measured conductances are much less than e(2)/h per edge. We imaged edge currents in InAs/GaSb quantum wells with long edges and determined an effective edge resistance. Surprisingly, although the effective edge resistance is much greater than h/e(2), it is independent of temperature up to 30 K within experimental resolution. Known candidate scattering mechanisms do not explain our observation of an effective edge resistance that is large yet temperature independent.

Observation of edge transport in the disordered regime of topologically insulating InAs/GaSb quantum wells.

We observe edge transport in the topologically insulating InAs/GaSb system in the disordered regime. Using asymmetric current paths we show that conduction occurs exclusively along the device edge, exhibiting a large Hall signal at zero magnetic fields, while for symmetric current paths, the conductance between the two mesoscopicly separated probes is quantized to 2e2/h. Both quantized and self-averaged transport show resilience to magnetic fields, and are temperature independent for temperatures between 20 mK and 1 K.

Andreev reflection of helical edge modes in InAs/GaSb quantum spin Hall insulator.

We present an experimental study of S-N-S junctions, with N being a quantum spin Hall insulator made of InAs/GaSb. A front gate is used to vary the Fermi level into the minigap, where helical edge modes exist [Phys. Rev. Lett. 107, 136603 (2011)]. In this regime we observe a ~2e(2)/h Andreev conductance peak, consistent with a perfect Andreev reflection on the helical edge modes predicted by theories. The peak diminishes under a small applied magnetic field due to the breaking of time-reversal symmetry. This work thus demonstrates the helical property of the edge modes in a quantum spin Hall insulator.

Observation of 1D Fermi arc states in Weyl semimetal TaAs.

Fermi arcs on Weyl semimetals exhibit many exotic quantum phenomena. Usually found on atomically flat surfaces with approximate translation symmetry, Fermi arcs are rooted in the peculiar topology of bulk Bloch bands of 3D crystals. The fundamental question of whether a 1D Fermi arc can be probed remains unanswered. Such an answer could significantly broaden potential applications of Weyl semimetals. Here, we report a direct observation of robust edge states on atomic-scale ledges in TaAs using low-temperature scanning tunneling microscopy/spectroscopy. Spectroscopic signatures and theoretical calculations reveal that the 1D Fermi arcs arise from the chiral Weyl points of bulk crystals. The crossover from 2D Fermi arcs to eventual complete localization on 1D edges was arrested experimentally on a sequence of surfaces. Our results demonstrate extreme robustness of the bulk-boundary correspondence, which offers topological protection for Fermi arcs, even in cases in which the boundaries are at the atomic-scale. The persistent 1D Fermi arcs can be profitably exploited in miniaturized quantum devices.

Evidence for helical edge modes in inverted InAs/GaSb quantum wells.

We present an experimental study of low temperature electronic transport in the hybridization gap of inverted InAs/GaSb composite quantum wells. An electrostatic gate is used to push the Fermi level into the gap regime, where the conductance as a function of sample length and width is measured. Our analysis shows strong evidence for the existence of helical edge modes proposed by Liu et al [Phys. Rev. Lett. 100, 236601 (2008)]. Edge modes persist in spite of sizable bulk conduction and show only a weak magnetic field dependence-a direct consequence of a gap opening away from the zone center.

Cryogen-free one hundred microkelvin refrigerator.

A temperature below 100 µK is achieved in a customized cryogen-free dilution refrigerator with a copper-nuclear demagnetization stage. The lowest temperature of conduction electrons of the demagnetization stage is below 100 µK as measured by using a pulsed platinum nuclear magnetic resonance thermometer, and the temperature can remain below 100 µK for over 10 h. A demagnetization magnetic field of up to 9 T and a research magnetic field of up to 12 T can be controlled independently, provided by a coaxial room-temperature-bore cryogen-free magnet.

[Nitrogen uptake, distribution, and utilization in young bearing Huangguan pear trees under 15N-urea application in spring].

We investigated the characteristics of nitrogen uptake, distribution, and utilization in the three-year-old bearing Huangguan pear trees following 15N-urea application in early spring. The results showed that the growth of pear trees was mainly depended on vegetative organs such as shoots and leaves at the stage from budbreak to shoot growth arrest, but mainly on storage organs (roots) and supplemented by the formation of fruit yield and quality at the stage from shoot growth arrest stage to fruit harvest. Meanwhile, tree biomass, especially that storage organs, substantially increased. All organs, especially newly developed shoots and leaves, acquired more N in shoot growth arrest stage due to vigorous growth, with relatively higher N derived from fertilizer (Ndff). Ndff of each organ except for root was lower at fruit maturity stage than that at shoot growth stage. Most of the labeled nitrogen was distributed in the newly developed organs (shoots and leaves) from budbreak to shoot growth arrest stage, but in the storage organs during shoot growth arrest stage to fruit maturity stage. Labeled fertilizer nitrogen was mainly distributed in the storage organs, followed by the vegetative organs. Reproductive organs had the lowest allocation in the experimental stage. For the three-years-old pear trees, the ratio of absorbed N from fertilizer was responsible for 31.1% and 21.0% of total absorbed nitrogen from budbreak to shoot growth arrest stage and from shoot growth arrest stage to fruit maturity stage, respectively, with the remaining N (68.9% and 79.0% of total) being absorbed from soil N.

Evidence for a topological excitonic insulator in InAs/GaSb bilayers.

Electron-hole pairing can occur in a dilute semimetal, transforming the system into an excitonic insulator state in which a gap spontaneously appears at the Fermi surface, analogous to a Bardeen-Cooper-Schrieffer (BCS) superconductor. Here, we report optical spectroscopic and electronic transport evidence for the formation of an excitonic insulator gap in an inverted InAs/GaSb quantum-well system at low temperatures and low electron-hole densities. Terahertz transmission spectra exhibit two absorption lines that are quantitatively consistent with predictions from the pair-breaking excitation dispersion calculated based on the BCS gap equation. Low-temperature electronic transport measurements reveal a gap of ~2 meV (or ~25 K) with a critical temperature of ~10 K in the bulk, together with quantized edge conductance, suggesting the occurrence of a topological excitonic insulator phase.