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Wigner crystals are predicted as the crystallization of the dilute electron gas moving in a uniform background when the electron-electron Coulomb energy dominates the kinetic energy. The Wigner crystal has previously been observed in the…
While correlated phenomena of flat bands have been extensively studied in twisted systems, the ordered states that emerge from interactions in the intrinsic flat bands of kagome lattice materials remain largely unexplored. The newly…
Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states…
Charged colloidal crystals exhibit a subtle interplay between electrostatic screening and elastic deformation. In an anisotropic elastic medium the coupling between dilation and the local ionic environment becomes direction dependent,…
In recent years, kagome materials have attracted significant attention due to their rich emergent phenomena arising from the quantum interplay of geometry, topology, spin, and correlations. However, in the search for kagome materials, it…
Spin-liquids -- an emergent, exotic collective phase of matter -- have garnered enormous attention in recent years. While experimentally, many prospective candidates have been proposed and realized, theoretically modeling real materials…
Recent technological advances in controlling materials have developed methods to produce idealized two-dimensional (2D) electron systems such as heterogeneous interfaces, molecular-beam-epitaxy (MBE) grown atomic layers, exfoliated thin…
The Bloch electron energy spectrum of a crystalline solid is determined by the underlying lattice structure at the atomic level. In a 2-dimensional (2d) crystal it is possible to impose a superlattice with nanometer-scale periodicity,…
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…
Electron-electron interactions strongly affect the behavior of low-dimensional systems. In one dimension (1D), arbitrarily weak interactions qualitatively alter the ground state producing a Luttinger liquid (LL) which has now been observed…
Geometry, whether on the atomic or nanoscale, is a key factor for the electronic band structure of materials. Some specific geometries give rise to novel and potentially useful electronic bands. For example, a honeycomb lattice leads to…
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave…
A Wigner crystal, a regular electron lattice arising from strong correlation effects, is one of the earliest predicted collective electronic states. This many-body state exhibits quantum and classical phase transitions and has been proposed…
While the ground state phase diagram of the correlated flat-band systems have been intensively investigated, the dynamic and thermodynamic properties of such lattice models are less explored, but it is the latter which is most relevant to…
Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and…
Quantum confinement has made it possible to detect and manipulate single-electron charge and spin states. The recent focus on two-dimensional (2D) materials has attracted significant interests on possible applications to quantum devices,…
Electrons in artificial lattices enable explorations of the impact of repulsive Coulomb interactions in a tunable system. We have trapped two-dimensional electrons belonging to a gallium arsenide quantum well in a nanofabricated lattice…
Time crystals are classified into discrete time crystals and continuous time crystals based on whether they spontaneously break time-translation symmetry. Continuous-time crystals do not require external driving. By introducing AdS/CFT…
The existence of a paradoxical supersolid phase of matter, possessing the apparently incompatible properties of crystalline order and superfluidity, was predicted 50 years ago. Solid helium was the natural candidate, but there supersolidity…
Exotic tiling patterns of quasicrystals have gotten a lot of attention for unique quantum phenomena such as critical state and multifractality. In this regard, finding new quasi-periodic tiling patterns and the relevant quantum states is…