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Exciton condensates (ECs) are macroscopic coherent states arising from condensation of electron–hole pairs1. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study ECs2,3,4. The tunnel barrier suppresses recombination, yielding long-lived excitons5,6,7,8,9,10. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of ECs in naturally occurring 2H-stacked bilayer WSe2. In this system, the intrinsic spin–valley structure suppresses interlayer tunnelling even when the separation is reduced to the atomic limit, providing access to a previously unattainable regime of strong interlayer coupling. Using capacitance spectroscopy, we investigate magneto-ECs, formed when partially filled Landau levels couple between the layers. We find that the strong-coupling ECs show dramatically different behaviour compared with previous reports, including an unanticipated variation of EC robustness with the orbital number, and find evidence for a transition between two types of low-energy charged excitations. Our results provide a demonstration of tuning EC properties by varying the constituent single-particle wavefunctions.

Exciton condensates (ECs) are macroscopic coherent states arising from condensation of electron-hole pairs

In moiré heterostructures, gate-tunable insulating phases driven by electronic correlations have been recently discovered. Here, we use transport measurements to characterize the gate-driven metal-insulator transitions and the metallic phase in twisted WSe2 near half filling of the first moiré subband. We find that the metal-insulator transition as a function of both density and displacement field is continuous. At the metal-insulator boundary, the resistivity displays strange metal behaviour at low temperature with dissipation comparable to the Planckian limit. Further into the metallic phase, Fermi-liquid behaviour is recovered at low temperature which evolves into a quantum critical fan at intermediate temperatures before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe2 as a new platform to study doping and bandwidth controlled metal-insulator quantum phase transitions on the triangular lattice.

Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behaviour that defies the Landau Fermi paradigm

Charge separated interlayer excitons in transition metal dichalcogenide heterobilayers are being explored for moir\'e exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many-body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moir\'e potential to the modestly mobile exciton gas as exciton density increases to ${n}_{ex}\ensuremath{\sim}{10}^{11}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$ and from the exciton gas to the highly mobile charge separated electron-hole plasma for ${n}_{ex}g{10}^{12}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$. The latter is the Mott transition and is confirmed in photoconductivity measurements. These findings set fundamental limits for achieving quantum states of interlayer excitons.

Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behaviour that defies the Landau Fermi paradigm1–5. In moire heterostructures, gate-tuneable insulating phases driven by electronic correlations have been recently discovered6–23. Here, we use transport measurements to characterize metal–insulator transitions (MITs) in twisted WSe2 near half filling of the first moire subband. We find that the MIT as a function of both density and displacement field is continuous. At the metal–insulator boundary, the resistivity displays strange metal behaviour at low temperatures, with dissipation comparable to that at the Planckian limit. Further into the metallic phase, Fermi liquid behaviour is recovered at low temperature, and this evolves into a quantum critical fan at intermediate temperatures, before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe2 as a new platform to study doping and bandwidth-controlled metal–insulator quantum phase transitions on the triangular lattice. Metal-to-insulator transitions are characterized in twisted WSe, revealing strange metal behaviour and quantum criticality at low temperatures.

Charge separated interlayer excitons in transition metal dichalcogenide heterobilayers are being explored for moiré exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many-body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the MoSe_{2}/WSe_{2} heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moiré potential to the modestly mobile exciton gas as exciton density increases to n_{ex}∼10^{11} cm^{-2} and from the exciton gas to the highly mobile charge separated electron-hole plasma for n_{ex}10^{12} cm^{-2}. The latter is the Mott transition and is confirmed in photoconductivity measurements. These findings set fundamental limits for achieving quantum states of interlayer excitons.

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe2, with signatures of collective phases observed over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. At a 5.1° twist, zero-resistance pockets were observed on doping away from half filling at temperatures below 3 K, which indicates a possible transition to a superconducting state. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice., Studies of the tunable correlated states in the twisted bilayer WSe2 were supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. The synthesis of the WSe2 crystals was supported by the NSF MRSEC programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The theoretical work was supported by the European Research Council (ERC-2015-AdG694097), cluster of Excellence AIM, SFB925 and Grupos Consolidados (IT1249-19). The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck–New York Center for Non-Equilibrium Quantum Phenomena.

Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity1,2, magnetism3, topological edge states4,5, exciton trapping6 and correlated insulator phases7. However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix., This work is supported by the Programmable Quantum Materials (Pro-QM) programme at Columbia University, an Energy Frontier Research Center established by the Department of Energy (grant no. DE-SC0019443). L.J.M. acknowledges support from the Swiss National Science Foundation (grant no. P400P2_186744). Synthesis of MoSe2 and WSe2 was supported by the National Science Foundation Materials Research Science and Engineering Centers programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The Flatiron Institute is a division of the Simons Foundation. C.E.D. acknowledges support from the National Science Foundation under grant no. DMR-1918455. M.S. and K.S. acknowledge the support of the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 724529), Ministerio de Economia, Industria y Competitividad through grant nos. MAT2016-77100-C2-2-P and SEV-2015-0496, and the Generalitat de Catalunya (grant no. 2017SGR 1506). We thank D. Griffin and T. Walsh from Oxford Instruments Asylum Research for confirmation of PFM results.

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe

Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin-orbit coupling. Measurements under large magnetic fields have revealed an unusual Landau level (LL) structure

Monolayer (ML) semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure -- just like graphene -- facilitates gate-tunability, while the sizable band gap and strong spin-orbit coupling hold promise for properties beyond graphene. Measurements under large magnetic fields have revealed an unusual LL structure, distinct from other 2D electron systems. However, owing to limited sample quality and poor electrical contact, probing the lowest Landau levels (LLs) has been challenging, and observation of electron correlations within the fractionally filled LLs regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of ML WSe$_2$ in the extreme quantum limit, and observe fractional quantum Hall (FQH) states in the lowest three LLs. The odd-denominator FQH sequences demonstrate a systematic evolution with the LL orbital index, which has not been observed in any other system but is consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime., typos in v1 corrected

Monolayer MoS2, among many other transition metal dichalcogenides, holds great promise for future applications in nanoelectronics and optoelectronics due to its ultrathin nature, flexibility, sizable band gap, and unique spin-valley coupled physics. However, careful study of these properties at low temperature has been hindered by an inability to achieve low-temperature Ohmic contacts to monolayer MoS2, particularly at low carrier densities. In this work, we report a new contact scheme that utilizes cobalt (Co) with a monolayer of hexagonal boron nitride (h-BN) that has the following two functions: modifies the work function of Co and acts as a tunneling barrier. We measure a flat-band Schottky barrier of 16 meV, which makes thin tunnel barriers upon doping the channels, and thus achieve low-T contact resistance of 3 kΩ.μm at a carrier density of 5.3 × 1012/cm2. This further allows us to observe Shubnikov–de Haas oscillations in monolayer MoS2 at much lower carrier densities compared to previous work.

Monolayer MoS

This chapter presents the complex in-plane dielectric function from 1.5 to 3 eV for monolayers of four transition metal dichalcogenides: MoSe2, WSe2, MoS2, and WS2. The results were obtained from optical reflection spectra using a Kramers–Kronig constrained variational analysis. From the inferred dielectric functions, we obtain the absolute absorbance of the monolayers. We also provide a comparison of the dielectric function for the monolayers with the respective bulk materials [1].