相关论文: Noncommutative Geometry, Quantum Hall Effect and B…

Recent interest in topological nature in condensed matter physics has revealed the essential role of Berry curvature in anomalous Hall effect (AHE). However, since large Hall response originating from Berry curvature has been reported in…

We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in $\nu=1/m$(m odd) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in…

A notion of the Berry phase is a powerful means to unravel the non-trivial role of topology in various novel phenomena observed in chiral magnetic materials and structures. A celebrated example is the intrinsic anomalous Hall effect (AHE)…

The Berry phase acquired by an electromagnetic field undergoing an adiabatic and cyclic evolution in phase space is a purely quantum-mechanical effect of the field. However, this phase is usually accompanied by a dynamical contribution and…

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…

Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which…

We explore the geometric phase in N=(2,2) supersymmetric quantum mechanics. The Witten index ensures the existence of degenerate ground states, resulting in a non-Abelian Berry connection. We exhibit a non-renormalization theorem which…

We experimentally study the phase diagram of the integer quantized Hall effect, as a function of density and magnetic field. We used a two dimensional hole system confined in a Ge/SiGe quantum well, where all energy levels are resolved,…

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a…

Electrons in clean macroscopic samples of graphene exhibit an astonishing variety of quantum phases when strong perpendicular magnetic field is applied. These include integer and fractional quantum Hall states as well as symmetry broken…

We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a…

For two-dimensional holographic CFTs, we demonstrate the role of Berry phases for relating the non-factorization of the Hilbert space to the presence of wormholes. The wormholes are characterized by a non-exact symplectic form that gives…

We calculate Berry's phase when the driving field, to which a spin-1/2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g., the angular…

Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the…

Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the…

Quantum geometry may enable the development of quantum phases ranging from superconductivity to correlated topological states. One powerful probe of quantum geometry is the nonlinear Hall response which detects Berry curvature dipole in…

We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity…

We report the observation of developing fractional quantum Hall states at Landau level filling factors $\nu = 1/2$ and 1/4 in electron systems confined to wide GaAs quantum wells with significantly $asymmetric$ charge distributions. The…

The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A…

We investigate an interplay between quantum geometrical effects and surface plasmons through surface plasmonic structures, based on an electron hydrodynamic theory. First we demonstrate that the quantum nonlinear Hall effect can be…