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Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with…
We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the…
We study the edge transport properties of paired fractional quantum Hall (FQH) states--- the Haldane-Rezayi (HR), Moore-Read (Pfaffian) and Halperin (331) states. A table of exponents is given for the tunneling between the edges of paired…
$\nu$=1/2 is among the most enigmatic many-body phases in two-dimensional electron systems as it appears in the ground-state rather than an excited Landau level. It is observed in wide quantum wells where the electrons have a bilayer charge…
Here we report from our theoretical studies that in biased bilayer graphene, one can induce phase transitions from an incompressible fractional quantum Hall state to a compressible state by tuning the bandgap at a given electron density.…
Magnetotransport of conventional semiconductor based double layer systems with barrier suppressed interlayer tunneling has been a rewarding subject due to the emergence of an interlayer coherent state that behaves as an excitonic…
We recently proposed quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions [Phys. Rev. Lett. 125, 030504 (2020)]. Conceptually, the scheme is based on the idea that aphysical monolayer optical…
Non-Abelian anyons--particles whose exchange noncommutatively transforms a system's quantum state--are widely sought for the exotic fundamental physics they harbor as well as for quantum computing applications. There now exist numerous…
We propose a setup to directly measure the anyonic statistical angle on a single edge of a fractional quantum Hall system, without requiring independent knowledge of non-universal parameters. We consider a Laughlin edge state bent into a…
Using projective construction, a generalized parton construction, we construct many non-Abelian quantum Hall (QH) states, which include the Pfaffian state at filling fraction $\nu=1/2$. The projective construction allows us to calculate the…
Anyons are particles obeying statistics of neither bosons nor fermions. Non-Abelian anyons, whose exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a great attention because of possible…
The fractional quantum Hall (FQH) effect is a macroscopic manifestation of strong electron-electron interactions. Even denominator FQH states (FQHSs) at half-filling are particularly interesting as they are predicted to host non-Abelian…
Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting…
Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of…
Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents,…
Non-abelian anyons are prospective candidates for fault-tolerant topological quantum computation due to their long-range entanglement. Curiously these quasiparticles are charge-neutral, hence elusive to most conventional measurement…
Strong interaction between electrons in two-dimensional systems in the presence of a high magnetic field gives rise to fractional quantum Hall states that host quasiparticles with fractional charge and fractional exchange statistics. Here,…
The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent…
We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the…
The robustness of fractional quantum Hall states is measured as the energy gap separating the Laughlin ground-state from excitations. Using thermodynamic approximations for the correlation functions of the Laughlin state and the quasihole…