A universal framework for the melting temperature of bubble phases (generalized Wigner crystal in high Landau levels) and its quantitative comparison with the experiments

Reentrant quantum Hall phase, also known as the bubble phases, appear in high Landau levels when the competing result of the Coulomb repulsion and the kinetic energy is to spontaneously form a solid phase made of electrons. Bubble phases can be regarded as the generalized Wigner crystal in the 2-dimensional electron gas, whose existence has been confirmed by experiments such as transport measurements, microwave resonance, and STM imaging. The theoretical studies about the bubble phases so far are limited in using Hartree-Fock (HF) mean field theory, DMRG, or Monte Carlo to study the properties of the phases at zero temperature. Here we present our framework to compute the critical melting temperature of such phases when confronting a solid-liquid phase transition. The universal framework combines the energy from Hartree-Fock computation, elastic theories in studying the solid phase, and the Kosterlitz-Thouless-Halperin-Nelson-Young's topological defect theory put forward initially in the studying of Wigner crystal and superfluid phases. The computed melting temperature fit quantitatively well with the complete temperature dependent resistance characterization through a wide range of Landau levels.