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...

The interplay between topology and correlations can generate a variety of unusual quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe2 as a promising material for exploring such interplay in a highly tunable fashion. The ground state of this two-dimensional (2D) crystal can be electrostatically tuned from a quantum spin Hall insulator (QSHI) to a superconductor. However, much remains unknown about the nature of these ground states, including the gap-opening mechanism of the insulating state. Here we report systematic studies of the insulating phase in WTe2 monolayer and uncover evidence supporting that the QSHI is also an excitonic insulator (EI). An EI, arising from the spontaneous formation of electron-hole bound states (excitons), is a largely unexplored quantum phase to date, especially when it is topological. Our experiments on high-quality transport devices reveal the presence of an intrinsic insulating state at the charge neutrality point (CNP) in clean samples. The state exhibits both a strong sensitivity to the electric displacement field and a Hall anomaly that are consistent with the excitonic pairing. We further confirm the correlated nature of this charge-neutral insulator by tunneling spectroscopy. Our results support the existence of an EI phase in the clean limit and rule out alternative scenarios of a band insulator or a localized insulator. These observations lay the foundation for understanding a new class of correlated insulators with nontrivial topology and identify monolayer WTe2 as a promising candidate for exploring quantum phases of ground-state excitons.

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.fractional quantum Hall effect | 5/2 fractional quantum Hall state | edge-current tunneling | quantum point contact | non-Abelian statistics A mong the roughly 100 known fractional quantum Hall (FQH) states, the filling factor ν = 5/2 state is special. It is an evendenominator state with elementary excitations that may have nonAbelian statistics (1-10). If the ground state is non-Abelian, it would be insensitive to environmental decoherence (11) and would therefore be useful for fault-tolerant topological quantum computation. Because of this potential application, much theoretical effort has focused on the 5/2 state, and a variety of wave functions have been proposed (1-3, 5-7, 12-15). There have also been several experiments on the 5/2 state, with more of them supporting non-Abelian than Abelian statistics (16,17). All of the proposed wave functions for the 5/2 state have an effective charge e* of the quasiparticles that is a quarter of the elementary charge e, and this effective charge has been confirmed experimentally (18-21). However, the wave function of the 5/2 state is still under discussion.The proposed wave functions of the 5/2 state can be distinguished by the strength of the interaction between quasiparticles, described by a coupling constant g. This coupling constant can be obtained from experiments using weak-tunneling theory (22). The FQH effect emerges in a highly interacting 2D electron gas (2DEG) at high magnetic field and ultralow temperature. The FQH states have gapless conducting edge currents at the boundaries of the 2DEG, in which fractionally charged quasiparticles carry the current. If the counter-propagating edge currents of a FQH state are brought close enough together in a quantum point contact (QPC), back-scattering is induced. In the weak-tunneling regime, the rate of quasiparticle tunneling depend...

In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, chargeneutral fermions, e.g., spinons 1 and fermionic excitons 2,3 , that result in neutral Fermi surfaces and Landau quantization 4,5 in an insulator. While previous experiments in quantum spin liquids 1 , topological Kondo insulators [6][7][8] , and quantum Hall systems 3,9 have hinted at charge-neutral Fermi surfaces, evidence for their existence remains far from conclusive. Here we report experimental observation of Landau quantization in a two dimensional (2D) insulator, i.e., monolayer tungsten ditelluride (WTe2), a large gap topological insulator [10][11][12][13] . Using a detection scheme that avoids edge contributions, we uncover strikingly large quantum oscillations in the monolayer insulator's magnetoresistance, with an onset field as small as ~ 0.5 tesla. Despite the huge resistance, the oscillation profile, which exhibits many periods, mimics the Shubnikov-de Haas oscillations in metals. Remarkably, at ultralow temperatures the observed oscillations evolve into discrete peaks near 1.6 tesla, above which the Landau quantized regime is fully developed. Such a low onset field of quantization is comparable to high-mobility conventional two-dimensional electron gases. Our experiments call for further investigation of the highly unusual ground state of the WTe2 monolayer. This includes the influence of device components and the possible existence of mobile fermions and charge-neutral Fermi surfaces inside its insulating gap. MainBulk tungsten ditelluride (WTe2) is a compensated semimetal in which an equal number of electrons and holes co-exist 14 . The semimetallic behavior remains when the material is thinned down to the trilayers 11,15 . In bilayers and monolayers, nevertheless, an insulating gap is observed 11 , giving rise to the high-temperature quantum spin Hall effect in monolayers [10][11][12][13] . However, the mechanism for the gap opening remains mysterious 10,11,16,17 . The observation of superconductivity when the monolayer is doped with a low electron density 18,19 highlights the unusual nature of the insulating state.

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