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Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is…
The many-body wave-function of an interacting one-dimensional electron system is probed, focusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean,…
Two dimensional electronic systems under strong magnetic field form quantum Hall (QH) edge states, which propagate along the boundary of a sample with a dissipationless current. Engineering the pathway of these propagating one-dimensional…
We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a…
We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the…
Possible phase transitions between incompressible quantum Hall states and compressible three-dimensional states are discussed for infinite-layer electron systems in strong magnetic field. By variational Monte Carlo calculation, relative…
We demonstrate experimentally that the transitions between adjacent integer quantum Hall (QH) states are equivalent to a QH-to-insulator transition occurring in the top Landau level, in the presence of an inert background of the other…
In this article the extended Bose-Hubbard model describing ultra-cold atoms confined in a shallow, one-dimensional optical lattice is introduced and studied by the exact diagonalization approach. All parameters of the model are related to…
Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…
The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
Disorder and electron-electron interaction play essential roles in the physics of electron systems in condensed matter. In two-dimensional, quantum Hall systems, extensive studies of disorder-induced localization have led to the emergence…
Direct transitions, driven by disorder, from several integral quantum Hall states to an insulator have been observed in experiment. This finding is enigmatic in light of a theoretical phase diagram, based on rather general considerations,…
We theoretically investigate correlated electron-hole states in vertically coupled quantum dots. Employing a prototypical double-dot confinement and a configuration-interaction description for the electron-hole states, it is shown that the…
The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical…
We use an atomic force microscope tip as a local gate to study the scattering between edge channels in a 2D electron gas in the quantum Hall regime. The scattering is dominated by individual, microscopic scattering centers, which we…
The quantum Hall effect hosts quantum phase transitions in which the localization length, that is the size of disorder-induced bulk localized states, is governed by universal scaling from percolation theory. However, this universal…
The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is…
The evolution of the fractional quantum Hall state at filling 5/2 is studied in density tunable two-dimensional electron systems formed in wide wells in which it is possible to induce a transition from single to two subband occupancy. In 80…