Related papers: Realization of an atomic quantum Hall system in fo…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
Conventional topological insulators and superconductors have topologically protected nodal points on their boundaries, and the recent interests in nodal-line semimetals only concerned bulk band structures. Here, we present a novel…
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry…
Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…
Until the late 1980s, phases of matter were understood in terms of Landau's symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was…
Topological quantum phases underpin many concepts of modern physics. While the existence of disorder-immune topological edge states of electrons usually requires magnetic fields, direct effects of magnetic field on light are very weak. As a…
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
The nondissipative (Hall) viscosity is known to play an interesting role in two-dimensional (2D) topological states of matter, in the hydrodynamic regime of correlated materials, and in classical active fluids with broken time-reversal…
The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
We investigate the longitudinal conductance of a disordered three-dimensional (3D) quantum Hall system within a tight-binding lattice model using numerical Thouless conductance calculations. For the bulk, we confirm that the mobility edges…
Studies of moire systems have elucidated the exquisite effect of quantum geometry on the electronic bands and their properties, leading to the discovery of new correlated phases. However, most experimental studies have been confined to a…
Quasiperiodically driven fermionic systems can support topological phases not realized in equilibrium. The fermions are localized in the bulk, but support quantized energy currents at the edge. These phases were discovered through an…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
The recent discovery of higher-order topological insulators (TIs) has opened new possibilities in the search for novel topological materials and metamaterials. Second-order TIs have been implemented in two-dimensional (2D) systems…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
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…
The transitions between neighbouring plateaux in the quantum Hall system are observed to follow anti-holomophic scaling with superuniversal scaling exponents, showing that the system contains an emergent sub-modular discrete symmetry and a…
In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of…