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. Introduction.-Symmetry protected topological order is a new paradigm in classification of condensed matter systems, describing certain system observables, such as charge or spin conductance, via topological invariants, i.e., distinct system characteristics which remain unchanged under smooth deformations of its band structure [1,2]. In addition to topological considerations, time reversal symmetry (TRS) has been widely believed to be a necessary ingredient for the emergence of the quantum spin Hall (QSH) insulating phase, commonly characterized via the Z 2 topological invariant [3][4][5][6]. Applying a magnetic field breaks the TRS and removes the topological protection of the helical liquid (HL) from backscattering. In fact, in the first realization of the QSH phase in HgTe=CdTe quantum wells, strong magnetic field dependence has been reported [6,7] albeit only in larger devices; nevertheless, it has been theoretically shown [8] that strong backscattering of the helical edge in magnetic field appears only in the case of sufficient disorder in the system, suggesting that the presence of magnetic fields is not a sufficient condition to gap out the edge states, and the ultimate fate of HL under TRS breaking may depend on the exact microscopic details of the system. Here we present data of robust HL edge states in engineered semiconductor systems that are immune to disordered bulk, as well as perturbations from external magnetic fields.The quantum spin Hall insulating state is here realized in InAs=GaSb quantum wells where electron-hole bilayer naturally occurs due to the unique broken-gap band alignment of InAs and GaSb [9]. In particular, the conduction band of InAs is some 150 meV lower than the valence band of GaSb, which results in charge transfer between the two layers, and emergence of coexisting 2D sheets of electrons and holes, trapped by wide gap AlSb barriers, as shown in Fig. 1(a). The positions of the electron and hole subbands

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. DOI: 10.1103/PhysRevLett.115.136804 PACS numbers: 71.10.Pm, 73.23.-b, 73.63.-b It is well known that electron-electron interactions play a more important role in one-dimensional (1D) electronic systems than in higher dimensional systems. In a 1D system, interactions cause electrons to behave in a strongly correlated way; so, under very general circumstances, 1D electron systems can be described by the TomonagaLuttinger liquid (LL) theory [1,2] instead of the meanfield Fermi liquid theory. A Luttinger parameter K characterizes the sign and the strength of the interactions: K < 1 for repulsion, K > 1 for attraction, and K ¼ 1 for the noninteracting case. Confirmations of LL have been examined in various materials, such as carbon nanotubes [3][4][5], semiconductor nanowires [6], and cleaved-edgeovergrowth 1D channels [7], as well as fractional quantum Hall edge states [8], respectively, for spinful or chiral Luttinger liquids. The experimental hallmarks of LL are a strongly suppressed tunneling conductance and a powerlaw dependence of the tunneling conductance on temperature and bias voltage [3][4][5]8]. In a weakly disordered spinful LL, transport experiments showed that the conductance reduces from the quantized value as the temperature is being decreased [6,7].The quantum spin Hall insulator (QSHI), also known as a two-dimensional (2D) topological insulator, is a topological state of matter supporting the helical edge states, which are counterpropagating, spin-momentum locked 1D modes protected by time reversal symmetry. It has recently attracted a lot of interest due to the peculiar helical edge properties and potential applications for quantum computation [9][10][11][12][13][14][15][16][17][18]. Experimentally, QSHI has been realized in HgTe quantum wells (QWs) [14] and in InAs=GaSb QWs [16][17][18]. In both cases, quantized conductance plateaus have been observed in devices with an edge length of several micrometers [14,18], implying ballistic transport in the edges. On the other hand, devices with longer edges have lower values of conductance [14,17,18], indicating certain backscattering processes occurred inside helical edges. In principle, single-particle elastic backscattering is forbidden in helical edges due to the protection of time reversal symmetry. Therefore, inelastic and/or multiparticle scattering should be the dominating sc...

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 2e 2 =h. Both quantized and self-averaged transport show resilience to magnetic fields, and are temperature independent for temperatures between 20 mK and 1 K. DOI: 10.1103/PhysRevLett.112.026602 PACS numbers: 72.25.Dc, 73.23.-b, 73.63.Hs Two-dimensional (2D) topological insulators (TI) are a novel class of materials that are insulating in the bulk but which display uniquely conductive edge channels [1][2][3][4]. These one-dimensional (1D) edge modes are helical, with the spin direction tied to the electron direction of motion, and are protected from backscattering by the time reversal symmetry (TRS) [5,6]. Applying magnetic fields breaks the TRS, removing the topological protection of the 1D helical liquid (HL) from single particle backscattering, resulting in a gap opening in the edge spectrum. Such HL channels were first observed in transport measurements in HgTe=CdTe quantum wells, and much of the HL phenomenology has been confirmed and elucidated in those first experiments [7,8]. Recently, Du et al. reported quantized transport in the inverted regime of Si-doped InAs=GaSb quantum wells in mesoscopic samples [9], where the existence of helical edge states was proposed in Ref.[10] and the first experimental evidence provided in Ref.[11] through scaling arguments due to the presence of residual bulk carriers. Unlike that observed in HgTe=CdTe [7], quantized transport in InAs=GaSb persists to magnetic fields of several Tesla [9,11], challenging the common understanding of 2D TIs in terms of TRS protected edge states and associated Z 2 topological invariant.Much remains to be learned about the nature and robustness of HL, in particular, to TRS breaking and disorder. In addition, edge transport in InAs=GaSb has so far only been indirectly assessed in ballistic samples [9,11]. In this Letter we study TI InAs=GaSb quantum wells in the disordered regime [12], where the total device size is much larger than the ballistic length of the HL, and show that transport in the topological regime manifestly occurs along the sample perimeter and is quantized to values consistent with the existence of a HL. Similar to ballistic regime studies [9,11], the conduction is also seen to be only weakly dependent on externally applied magnetic fields of up to 1 T. We argue that this behavior is due to the reduced effective g factor of the edge states originating from their small Fermi velocity v F . In addition, the edge states do not exhibit significant variation in transport properties for temperatures between 20 mK and 1 K measured. This is in contrast to theoretical studies, which have predicted power law corrections to the edge conductance as a function of temperatur...

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.

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.