Tunable Berry Flux and Non-Uniform Curvature Enable Study of Electronic Crystal Phases in Two Dimensions

Recent advances in materials science have renewed interest in electronic crystal phases forming in two-dimensional systems, particularly those exhibiting complex quantum properties, and researchers are now exploring how these phases can be manipulated. Félix Desrochers, Joe Huxford, and Mark R. Hirsbrunner from the University of Toronto, along with Yong Baek Kim, present a new theoretical model that systematically investigates crystallization within bands possessing tunable Berry curvature and flux. This work introduces a simple yet powerful framework for understanding how geometric properties of materials influence the formation of ordered electronic states, revealing a rich phase diagram with several analytically understood features. The team’s calculations predict the emergence of unusual crystalline arrangements, including anomalous Hall crystals and halo Wigner crystals, and even a novel combination of both, offering valuable insight into the fundamental interplay between electron ordering and band geometry.

This work explores how these topological effects influence the arrangement of electrons and their resulting properties, focusing on the interplay between electron interactions and the system’s quantum geometry. By analysing the energy landscape, the team reveals the stability of various crystalline structures, demonstrating that non-uniform Berry curvature can significantly alter the energy of charge density wave states and stabilize novel arrangements.

The team finds that by carefully adjusting the Berry flux, it is possible to induce transitions between different crystalline phases, effectively controlling the spatial arrangement of electrons. This reveals a strong interplay between Berry curvature, Berry flux, and the fundamental Coulomb interaction, which dictates the overall electronic structure and ground state properties of the system. This work contributes to a deeper understanding of topological effects in strongly correlated electron systems and provides insights into the potential for manipulating electronic order through external control of topological properties.

Recent experiments on multilayer graphene systems have rekindled interest in electronic crystal phases in two dimensions, now enriched by non-trivial quantum geometry. This research introduces a simplified model with tunable Berry curvature and total flux, enabling systematic study of crystallization in geometrically nontrivial bands. In the absence of interactions, a periodic potential yields a rich phase diagram, for which the team provides analytical insights, notably a general formula for the Chern number applicable to similar single-band models.
<h3Λ>N-Jellium Reveals Topological Phase Transitions

This research focuses on the λN-Jellium model and explores the behaviour of topological phases characterised by the Chern number, which describes the winding of the electronic band structure and indicates the presence of conducting states at material boundaries. The Berry curvature, a quantity describing the geometric properties of the electronic band structure, is intimately linked to the Chern number. Researchers are developing a more accurate method to predict the Chern number in this model, particularly in regimes where standard calculations become unreliable.

The team performs detailed calculations of the band structure and Berry curvature using the Hartree-Fock method, then proposes a novel approach called “occupation-weighted flux rounding. ” This method addresses observed jumps in the calculated Chern number by rounding the calculated Berry flux based on the occupation of electronic levels, aiming to predict the correct topological state. By comparing their results with more accurate calculations, the team validates their flux rounding procedure and analyses the resulting phase diagram, identifying regions where the method is most effective.

The researchers demonstrate that their generalized occupation-weighted flux rounding procedure accurately predicts the Chern number, even in challenging regimes, providing insights into phase transitions between different topological phases and having implications for understanding real materials with non-trivial topological properties. The findings suggest that the topological properties of the system are quantized, with the Berry flux often rounded to the nearest integer.

Halo Anomalous Hall Crystals and Topology

This research introduces a continuum model to investigate the crystallization of electrons in two-dimensional systems with geometrically nontrivial band structures. By systematically varying the strength of a periodic potential and considering electron interactions, the team discovered several novel crystalline states, including anomalous Hall crystals and halo Wigner crystals, where electrons spontaneously acquire orbital angular momentum. A particularly noteworthy finding is the emergence of a halo anomalous Hall crystal, combining properties of both previously observed phases with a non-zero Chern number, indicating a topologically nontrivial electronic state.

The researchers analytically determined how the Chern number evolves in the weak potential limit, providing a general formula applicable to similar systems. They also explained the energetic favourability of these crystalline phases, demonstrating that the minimization of potential energy balances the kinetic energy of the electrons. While the current model employs a mean-field approximation, limiting its description of strong correlations, the team highlights its potential as a foundation for more advanced numerical studies.