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A profound manifestation of topologically non-trivial states of matter is the occurrence of fractionally charged elementary excitations. The quantum spin Hall insulator state is a fundamentally novel quantum state of matter that exists at…
In the 1960s, it was proposed that in small indirect band-gap materials, excitons can spontaneously form because the density of carriers is too low to screen the attractive Coulomb interaction between electrons and holes. The result is a…
The search for fractional quantized Hall phases in the absence of a magnetic field has primarily targeted flat-band systems that mimic the features of a Landau level. In an alternative approach, the fractional excitonic insulator (FEI) has…
Incompressible insulating phases of electronic systems at partial filling of a lattice are often associated with charge ordering that breaks lattice symmetry. The resulting phases have an enlarged unit cell with an effective integer…
We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local…
The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the…
Mott insulators with a half-filled band of electrons on the triangular lattice have been recently studied in a variety of organic compounds. All of these compounds undergo transitions to metallic/superconducting states under moderate…
Moir\'e materials have emerged as a powerful platform for exploring exotic quantum phases. While recent experiments have unveiled fractional Chern insulators exhibiting the fractional quantum anomalous Hall effect based on electrons or…
Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous…
We study the quantum phase diagram of spinful fermions on kagome lattice with half-filled lowest flat bands. To understand the competition between magnetism, flat band frustration, and repulsive interactions, we adopt an extended $t$-$J$…
A new bosonic, excitonic method for interacting electrons is developed. For two-dimensional electron liquid, it reveals a noncompensated quantum crystal phase ranging from the high density, or vanishing Coulomb interaction, limit: $r_s=0$,…
Insulators occur in more than one guise, a recent finding was a class of topological insulators, which host a conducting surface juxtaposed with an insulating bulk. Here we report the observation of an unusual insulating state with an…
Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, exotic quantum spin liquid states with topological order and anyonic excitations, and random singlet phases emerging in…
Excitonic insulators are long-sought-after quantum materials predicted to spontaneously open a gap by the Bose condensation of bound electron-hole pairs, namely, excitons, in their ground state. Since the theoretical conjecture, extensive…
We review various features of interacting Abelian topological phases of matter in two spatial dimensions, placing particular emphasis on fractional Chern insulators (FCIs) and fractional topological insulators (FTIs). We highlight aspects…
In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect…
Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of…
Recent experimental advances have uncovered fractional Chern insulator (FCI) states in twisted MoTe$_2$ (tMoTe$_2$) systems under zero magnetic field. Understanding the interaction effects on topological phases within realistic model…
In solids containing elements with f orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are…
Complexity in many-particle systems occurs through processes of qualitative differentiation. These are described by concepts such as emerging states with specific symmetries that are linked to order parameters. In quantum Hall phases of…