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The behavior of two-dimensional electron gas (2DEG) in extreme coupling limits are reasonably well-understood, but our understanding of intermediate region remains limited. Strongly interacting electrons crystalize into a solid phase known…
Ignited by the discovery of the metal-insulator transition, the behaviour of low-disorder two-dimensional (2D) electron systems is currently the focus of a great deal of attention. In the strongly-interacting limit, electrons are expected…
We consider temperature-induced melting of a Wigner solid in one dimensional (1D) and two dimensional (2D) lattices of electrons interacting via the long-range Coulomb interaction in the presence of strong disorder arising from charged…
We investigate the interplay of disorder and interaction in two-dimensional electron systems in a strong magnetic field, focusing on the transition between Wigner crystals and fractional quantum Hall liquids. We first study classical Wigner…
When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x-y), highly correlated states emerge as a result of the interplay between electron-electron interactions, confinement and…
The interrelation between disorder and interactions in two dimensional electron liquid is studied beyond weak coupling perturbation theory. Strong repulsion significantly reduces the electronic density of states on the Fermi level. This…
Strongly interacting electronic systems possess rich phase diagrams resulting from the competition between different quantum ground states. A general mechanism that relieves this frustration is the emergence of microemulsion phases, where…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/r potential. We review a series of exact numerical…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder…
The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives…
The Wigner crystal, an ordered array of electrons, is one of the very first proposed many-body phases stabilized by the electron-electron interaction. This electron solid phase has been reported in ultra-clean two-dimensional electron…
We study the consequences of Coulomb interactions on a system undergoing a putative first order phase transition. In two dimensions (2D), near the critical density, the system is universally unstable to the formation of new intermediate…
Electron Wigner solids (WSs)1-12 provide an ideal system for understanding the competing effects of electron-electron and electron-disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has…
The Fermi liquid-Wigner crystal transition in a two dimensional electronic system is revisited with a focus on the nature of the fixed node approximation done in quantum Monte Carlo calculations. Recently, we proposed (Phys. Rev. Lett. 94,…
Wigner crystals are extremely fragile, which is shown to result from very strong geometric frustration germane to long-range Coulomb interactions. Physically, this is manifested by a very small characteristic energy scale for shear density…
Multicanonical ensemble sampling simulations have been performed to calculate the phase diagram of a Lennard-Jones fluid embedded in a fractal random matrix generated through diffusion limited cluster aggregation. The study of the system at…
It is well known that the dielectric constant of two-dimensional (2D) electron system goes negative at low electron densities. A consequence of the negative dielectric constant could be the formation of the droplet state. The droplet state…
A Wigner crystal structure of the electronic ground state is induced by strong Coulomb interactions at low temperature in clean or disordered two-dimensional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, being closed to…
Critically analyzing recent STM and transport experiments [Z. Ge, et al, arXiv:2510.12009] on 2D electron systems in the presence of random quenched impurities, we argue that the resulting low-density putative "solid" phase reported…
The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a…