Upper bound on the window of density occupied by microemulsion phases in two-dimensional electron systems

Abstract

In two-dimensional electronic systems, direct first-order phase transitions are prohibited as a consequence of the long-range Coulomb interaction, which implies a stiff energetic penalty for macroscopic phase separation. A prominent proposal is that any direct first-order transition is instead replaced by a sequence of ``microemulsion" phases, in which the two phases are mixed in patterns of mesoscopic domains. In this note, we comment on the range $\Delta n$ of average electron density that such microemulsion phases may occupy. We point out that, even without knowing the value of a phenomenological parameter associated with surface tension between the two phases, one can place a fairly strong upper bound on the value of $\Delta n$. We make numerical estimates for $\Delta n$ in the case of the Fermi liquid to Wigner crystal transition and find $\Delta n$ to be on the order of $10^7$\,cm${}^{-2}$. This value is much smaller than the width of the phase transition observed in experiments, suggesting that disorder is a more likely explanation for the apparent broadening of the transition.

6 + 3 pages, 2 + 1 figures; published version (with typo corrections, added discussion on gate electrode at finite distance in the closing remarks, along with minor modifications to text and updated references.)

References in corpus (13)

• A self-consistent theory for graphene transport
• Entropic evidence for a Pomeranchuk effect in magic angle graphene
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• Competing correlated states around the zero field Wigner crystallization transition of electrons in two-dimensions
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Phase diagram for Coulomb-frustrated phase separation in systems with negative short-range compressibility
• Theory of the random potential and conductivity at the surface of a topological insulator
• A simple model of Coulomb disorder and screening in graphene
• Screening effects in Coulomb frustrated phase separation
• Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
• A simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions
• Universality classes for Coulomb frustrated phase separation

Cited by in corpus (6)

• Ground state phases of the two-dimension electron gas with a unified variational approach
• Observation of an electronic microemulsion phase emerging from a quantum crystal-to-liquid transition
• Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers
• Importance of electron-phonon coupling near the electron-liquid to Wigner-crystal transition in two-dimensional atomically thin materials
• Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals