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Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/τtr = 2π λ T, where λ is a dimensionless strength of the electron--phonon coupling. The fact that measured values satisfy λ ≲ 1 has been noted in the context of a possible "Planckian" bound on transport. However, since the electron--phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally. [ABSTRACT FROM AUTHOR]

When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two-dimensional systems are predicted to spontaneously break continuous-translation symmetry and form a quantum crystal1. Efforts to observe2–12 this elusive state of matter, termed a Wigner crystal, in two-dimensional extended systems have primarily focused on conductivity measurements on electrons confined to a single Landau level at high magnetic fields. Here we use optical spectroscopy to demonstrate that electrons in a monolayer semiconductor with density lower than 3 × 1011 per centimetre squared form a Wigner crystal. The combination of a high electron effective mass and reduced dielectric screening enables us to observe electronic charge order even in the absence of a moiré potential or an external magnetic field. The interactions between a resonantly injected exciton and electrons arranged in a periodic lattice modify the exciton bandstructure so that an umklapp resonance arises in the optical reflection spectrum, heralding the presence of charge order13. Our findings demonstrate that charge-tunable transition metal dichalcogenide monolayers14 enable the investigation of previously uncharted territory for many-body physics where interaction energy dominates over kinetic energy.The signature of a Wigner crystal—the analogue of a solid phase for electrons—is observed via the optical reflection spectrum in a monolayer transition metal dichalcogenide. [ABSTRACT FROM AUTHOR]

One of the first theoretically predicted manifestations of strong interactions in many-electron systems was the Wigner crystal1–3, in which electrons crystallize into a regular lattice. The crystal can melt via either thermal or quantum fluctuations4. Quantum melting of the Wigner crystal is predicted to produce exotic intermediate phases5,6 and quantum magnetism7,8 because of the intricate interplay of Coulomb interactions and kinetic energy. However, studying two-dimensional Wigner crystals in the quantum regime has often required a strong magnetic field9–11 or a moiré superlattice potential12–15, thus limiting access to the full phase diagram of the interacting electron liquid. Here we report the observation of bilayer Wigner crystals without magnetic fields or moiré potentials in an atomically thin transition metal dichalcogenide heterostructure, which consists of two MoSe2 monolayers separated by hexagonal boron nitride. We observe optical signatures of robust correlated insulating states at symmetric (1:1) and asymmetric (3:1, 4:1 and 7:1) electron doping of the two MoSe2 layers at cryogenic temperatures. We attribute these features to bilayer Wigner crystals composed of two interlocked commensurate triangular electron lattices, stabilized by inter-layer interaction16. The Wigner crystal phases are remarkably stable, and undergo quantum and thermal melting transitions at electron densities of up to 6 × 1012 per square centimetre and at temperatures of up to about 40 kelvin. Our results demonstrate that an atomically thin heterostructure is a highly tunable platform for realizing many-body electronic states and probing their liquid–solid and magnetic quantum phase transitions4–8,17.Optical signatures reveal correlated insulating Wigner crystals—electron solids—in a bilayer of a two-dimensional transition metal dichalcogenide, MoSe2, with hexagonal boron nitride between the layers. [ABSTRACT FROM AUTHOR]