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Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however…
By numerical exact diagonalization techniques, we obtain the quantum phase diagram of the lattice fractional quantum Hall (FQH) systems in the presence of quenched disorder. By implementing an array of local potential traps representing the…
We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes.…
Two-dimensional topological phases are characterized by TKNN integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using…
The recent discovery of fractional quantum Hall states in graphene raises the question of whether the physics of graphene and its bilayer offers any advantages over GaAs-based materials in exploring strongly-correlated states of…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization…
Hall viscosity is a non-dissipative response function describing momentum transport in two-dimensional systems with broken parity. It is quantized in the quantum Hall regime, and contains information about the topological order of the…
We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim…
The electrical conductivity of graphene with a nonzero mass-gap parameter is investigated starting from the first principles of quantum electrodynamics in (2+1)-dimensional space-time at any temperature. The formalism of the polarization…
We show the emergence of fractional quantum Hall states in dry-transferred chemical vapor deposition (CVD) derived graphene assembled into heterostructures for magnetic fields from below 3 T to 35 T. Effective composite-fermion filling…
The scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in energy band models with nonzero…
We study dephasing in electron transport through a large quantum dot (a Fabry-Perot interferometer) in the fractional quantum Hall regime with filling factor $2/3$. In the regime of sequential tunneling, dephasing occurs due to electron…
Quantization of particle transport lies at the heart of topological physics. In Thouless pumps - dimensionally reduced versions of the integer quantum Hall effect - quantization is dictated by the integer winding of single-band Wannier…
Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance…
We study the effect of local modulation of charge density and carrier type in graphene field effect transistors using a double top gate geometry. The two top gates lead to the formation of multiple \emph{p-n} junctions. Electron transport…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…
Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to…
Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The…