Related papers: Fractional quantum Hall interface induced by geome…
We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e. the Hall viscosity, the Wen-Zee…
Motivated by a recent experiment which synthesizes Landau levels for photons on cones [Schine {\em et al.}, Nature 534, 671 (2016)], and more generally the interest in understanding gravitational responses of quantum Hall states, we study…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…
In this work we obtain the Landau levels and the Hall conductivity at zero temperature of a two-dimensional electron gas on a conical surface. We investigate the integer quantum Hall effect considering two different approaches. The first…
Recently, quantum Hall interface has become a popular subject of research; distinct from that of the quantum Hall edge, which is constrained by external background confinement, the interface has the freedom to move, likely towards a…
The fundamental collective degree of freedom of fractional quantum Hall states is identified as a unimodular two-dimensional spatial metric that characterizes the local shape of the correlations of the incompressible fluid. Its quantum…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
We show that quantum Hall states on surfaces with conical singularities behave as conformal primaries near the singular points, with a conformal dimension controlled by the gravitational anomaly. We show that the electronic fluid at the…
The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
For topologically nontrivial and very narrow bands, Coulomb repulsion between electrons has been predicted to give rise to a spontaneous fractional quantum-Hall (FQH) state in absence of magnetic fields. Here we show that strongly…
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…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
Symmetry and topology play key roles in the identification of phases of matter and their properties. Both concepts are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken…
Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical…
The gapless edge modes of the Quantum Spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these…
The quest for universal signatures of topological phases is fundamentally important since these properties are robust to variations in system-specific details. Here we present general results for the response of quantum Hall states to…
Boundaries constitute a rich playground for quantum many-body systems because they can lead to novel degrees of freedom such as protected boundary states in topological phases. Here, we study the groundstate of integer quantum Hall systems…