$\lambda$-Jellium Model for the Anomalous Hall Crystal

Abstract

The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental platforms that combine strong interactions with nontrivial quantum geometry. These experiments inspired the anomalous Hall crystal (AHC) -- a topological variant of the Wigner crystal. The AHC spontaneously breaks continuous translation symmetry but has a nonzero Chern number. In this work, we introduce $\lambda -$jellium, a minimal extension of the two-dimensional jellium model. Its Berry curvature distribution is controlled by a single parameter, $\lambda$, where $\lambda =0$ corresponds to the standard jellium model. This setup facilitates the systematic exploration of Berry curvature's impact on electron crystallization. The phase diagram of this model, established using self-consistent Hartree Fock calculations, reveals several interesting features: (i) The AHC phase occupies a large region of the phase diagram. (ii) Two distinct Wigner crystal phases, the latter enabled by quantum geometry, and two distinct Fermi liquid phases are present. (iii) A continuous phase transition separates the AHC and one of the WC phases. (iv) In some parts of the AHC phase, the lattice geometry is non-triangular, unlike in the classical Wigner crystal. In addition to elucidating the physics of correlated electrons with nonzero Berry curvature, we expect that the simplicity of the model makes it an excellent starting point for more advanced numerical methods.

7+12 pages, 4+4 figures

References in corpus (6)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Unrestricted Hartree-Fock theory of Wigner crystals
• Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
• Phonons in Electron Crystals with Berry Curvature
• Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems

Cited by in corpus (6)

• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Various electronic crystal phases in rhombohedral graphene multilayers
• Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals