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Nonabelian anyons offer the prospect of storing quantum information in a topological qubit protected from decoherence, with the degree of protection determined by the energy gap separating the topological vacuum from its low lying…
Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge $q$ and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been…
We show that the fractional statistics of quasiparticles in dimerized graphene, in recent proposals for charge and statistics fractionalization, can have two realizations depending whether elementary objects can be considered as point-like…
We consider a thought experiment where two distinct species of 2D particles in a perpendicular magnetic field interact via repulsive potentials. If the magnetic field and the interactions are strong enough, one type of particles forms a…
The fractionally charged quasiparticles appearing in the 5/2 fractional quantum Hall plateau are predicted to have an extra non-local degree of freedom, known as topological charge. We show how this topological charge can block the…
The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange…
We demonstrate that the low-frequency resistance fluctuations, or noise, in bilayer graphene is strongly connected to its band structure, and displays a minimum when the gap between the conduction and valence band is zero. Using…
Anyons have exotic statistical properties, fractional statistics, differing from Bosons and Fermions. They can be created as excitations of some Hamiltonian models. Here we present an experimental demonstration of anyonic fractional…
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we…
We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling $\nu = 1/2$, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For…
Charge noise is an important factor limiting qubit coherence and relaxation in solid-state devices. In bilayer graphene (BLG) quantum dots, recently established as a promising platform for spin- and valley-based qubits, both the origin and…
Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited from the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport…
We study the in-plane acoustic phonons in twisted bilayer graphenes using the effective continuum approach. We calculate the phonon modes by solving the continuum equation of motion for infinitesimal vibration around the static relaxed…
We construct models of interacting itinerant non-Abelian anyons moving along one-dimensional chains, focusing in particular on itinerant Ising anyon chains, and derive effective anyonic t-J models for the low energy sectors. Solving these…
The recent observation of fractional quantum anomalous Hall (FQAH) states in tunable moir\'e materials encourages study of several new phenomena that may be uniquely accessible in these platforms. Here, we show that an isolated localized…
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent…
Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works…
The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream'' modes, moving against the direction of charge current…
We propose an experiment to probe the unconventional quantum statistics of quasi-particles in fractional quantum Hall states by measurement of current noise. The geometry we consider is that of a Hall bar where two quantum point contacts…
The effect of an ac perturbation on the shot noise of a fractional quantum Hall fluid is studied at finite temperature. For a normal metal, it is known that the zero-frequency noise derivative exhibits steps as a function of bias voltage.…