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

We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero…

Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive…

A static electric field generates circulating currents at the surfaces of a magnetoelectric insulator. The anomalous Hall part of the surface conductivity tensor describing such bound currents can change by multiples of $e^2/h$ depending on…

The problem of studying the quantum Hall effect on manifolds with nonconstant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The…

We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size…

We revisit the quantum Hall system with no Zeeman splitting energy using the noncommutative field theory. We analyze the BPS condition for the delta-function interaction near the filling factor $\nu=1$. Multi-skyrmions are shown to saturate…

Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding…

In this work a method based on a topological invariance of rational tangles commonly used in knot theory determines filling factors in the fractional quantum Hall effect. The main sustain for this hypothesis are the Schubert's theorems…

The quantum Hall effect, with a Berry's phase of $\pi$ is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. The mobility is $\sim$ 20,000 cm$^2$/V$\cdot$s at 4 K and ~15,000 cm$^2$/V$\cdot$s at 300 K…

Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with…

The anomalous velocity term in the semiclassical model of a Bloch electron deviates the trajectory from the conventional one. When the Berry curvature (alias noncommutative parameter) is a monopole in momentum space as found recently in…

In quantum mechanics it is often required to describe in a semiclassical approximation the motion of particles moving within a given energy band. Such a representation leads to the appearance of an analogues of fictitious forces in the…

Quantum geometric electronic responses are often viewed through a non-interacting lens: independent quasiparticles accumulate Berry phases as they move through a static crystal and background potential. Here we argue that the combined…

The geometric ideas underlying the Berry phase and the modern viewpoint of Karplus and Luttinger's theory of the anomalous Hall effect are discussed in an elementary way. We briefly review recent Hall and Nernst experiments which support…

Quantum oscillations can be used to determine properties of the Fermi surface of metals by varying the magnitude and orientation of an external magnetic field. Topological insulator surface states are an unusual mix of normal and Dirac…

The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not…

By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase $\gamma$ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid…

The anomalous Hall effect has considerable impact on the progress of condensed matter physics and occurs in systems with time-reversal symmetry breaking. Here we theoretically investigate the anomalous Hall effect in nonmagnetic…

We consider the Anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific we consider a model appropriate for the Copper-Oxide lattice to highlight the necessary conditions for time-reversal…

For a long period of time, we have been seeking how Berry curvature influnces the transport properties in materials breaking time-reversal symmetry. In time-reversal symmetric material, there will be no thermoelectric current induced by…