Electrostatic gating in two-dimensional materials provides a powerful tool to explore quantum phase transitions, including Mott transitions, superconducting domes, and other critical phenomena. Unlike bulk systems, where disorder and three-dimensional interactions dominate, 2D materials offer a cleaner platform to study these transitions due to their reduced dimensionality and enhanced tunability. The ability to modulate carrier density continuously with gate voltage allows for precise control over electronic correlations, leading to emergent phases of matter.
Mott transitions in 2D materials occur when electron-electron interactions drive a metal-insulator transition. In a correlated electron system, the competition between kinetic energy and Coulomb repulsion determines the ground state. When the on-site Coulomb energy exceeds the bandwidth, electrons localize, forming a Mott insulator. Electrostatic gating can tune this balance, inducing a transition from an insulating to a metallic state. For instance, in monolayer transition metal dichalcogenides, such as WSe2 or MoS2, gate-induced carrier doping can suppress the Mott gap, leading to a metallic phase. The critical behavior near the transition often follows scaling laws, with the resistivity exhibiting power-law dependence on temperature or gate voltage. Theoretical models, such as the Hubbard model with extended interactions, capture the essential physics, though disorder and inhomogeneities can complicate the interpretation.
Superconducting domes in 2D materials under gating represent another intriguing quantum phase transition. These domes typically appear as a function of carrier density, with superconductivity emerging at intermediate doping levels and vanishing at both low and high densities. The dome-shaped phase diagram suggests a competition between pairing and depairing mechanisms. In materials like magic-angle twisted bilayer graphene, electrostatic gating reveals superconductivity near correlated insulator states, hinting at a possible link between strong correlations and pairing. The BCS theory, extended to include strong-coupling effects, provides a framework for understanding these observations, though non-phonon-mediated pairing mechanisms, such as spin fluctuations, may also play a role. The critical temperature often peaks at optimal doping, with the superconducting gap following a similar trend.
Other quantum phase transitions in 2D materials include the emergence of charge density waves, ferromagnetism, and topological phases under electrostatic gating. Charge density waves, for example, can be suppressed or enhanced by tuning the Fermi level, leading to a quantum critical point where the transition temperature vanishes. Ferromagnetic ordering, observed in materials like CrI3, can be controlled by gate voltage, with critical behavior described by Ising or Heisenberg models depending on the anisotropy. Topological transitions, such as the opening of a gap in Dirac materials, can also be driven by gating, with the critical point marked by a change in Berry curvature.
Theoretical models for these transitions often rely on renormalization group techniques, which account for the scaling behavior near critical points. For Mott transitions, dynamical mean-field theory combined with density functional theory provides insights into the role of local correlations. For superconducting domes, Eliashberg theory or random phase approximation can describe the pairing instability, while for other transitions, Landau-Ginzburg theory or quantum field theory approaches are applicable. The reduced dimensionality of 2D materials simplifies some aspects of these models, as fluctuations play a more dominant role than in bulk systems.
Experimental signatures of these transitions include abrupt changes in resistivity, Hall coefficient, or optical conductivity as a function of gate voltage. In superconducting domes, the onset of zero resistance and Meissner effect mark the transition, while in Mott systems, the activation gap collapses. Critical exponents extracted from these measurements often deviate from mean-field predictions due to strong fluctuations in 2D. For example, the correlation length exponent in Mott systems may reflect the influence of disorder or inhomogeneous strain.
The interplay between different phases adds further complexity. In some cases, superconductivity coexists with magnetism or charge order, suggesting a delicate balance between competing orders. Gate-tuned quantum criticality can also lead to non-Fermi liquid behavior, with resistivity scaling linearly with temperature over a wide range. These observations challenge conventional theories and motivate the development of new frameworks to describe strongly correlated 2D systems.
Practical considerations in studying these transitions include the role of substrate effects, dielectric environment, and contact resistance. The choice of gate dielectric can influence the electrostatic screening and disorder potential, while the substrate may introduce strain or additional scattering. Optimizing these factors is crucial for isolating intrinsic material properties from extrinsic effects.
In summary, electrostatic gating in 2D materials offers a versatile platform to investigate quantum phase transitions with unprecedented control. Mott transitions, superconducting domes, and other critical phenomena reveal rich physics driven by correlations and dimensionality. Theoretical models continue to evolve to account for the unique aspects of these systems, while experiments provide stringent tests of their predictions. The study of these transitions not only advances fundamental understanding but also holds promise for novel device applications leveraging quantum criticality or emergent phases.