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We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy…
Quantum antidot, a small potential hill introduced into a two-dimensional electron system, presents an attractive tool to study quantum mechanics of interacting electrons.Here, we report experiments on electron resonant tunneling via a…
A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to…
We study the behavior of the extended states of a two-dimensional electron system in silicon in a magnetic field, B. Our results show that the extended states, corresponding to the centers of different Landau levels, merge with the lowest…
We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor $\nu$=5/2 in a very high mobility specimen of $\mu=1.7 \times 10^7$ cm$^2$/Vs. We achieve an electron…
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…
Based on a thermodynamic approach, we have calculated the resistivity of a 2D electron gas, assumed $dissipationless$ in a strong quantum limit. Standard measurements, with extra current leads, define the resistivity caused by a combination…
The quantum Hall effect, which exhibits a number of unusual properties, is studied in a gated 1000-nm-thick HgTe film, nominally a three-dimensional system. A weak zero plateau of Hall resistance, accompanied by a relatively small value of…
The excess Hall conductivity, resulting from thermal fluctuations of the superconducting order parameter, is calculated for a layered superconductor for an arbitrarily strong in-plane electric field and a perpendicular magnetic field in the…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are…
The quantum anomalous Hall effect (QAHE) realizes dissipationless longitudinal resistivity and quantized Hall resistance without the need of an external magnetic field. However, when reducing the device dimensions or increasing the current…
Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is…
We explain effective charge anomalies recently observed for fractional quantum Hall edge states at $\nu=5/2$ [M. Dolev, Y. Gross, Y. C. Chung, M. Heiblum, V. Umansky, and D. Mahalu, Phys.Rev. B. \textbf{81}, 161303(R) (2010)]. The…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated disordered magnetic fields are investigated numerically. It is found that the correlation drastically changes the transport properties associated…
We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the…
The ground states of electrons in two vertically coupled quantum dots in the presence of an external magnetic field have been studied within the density functional theory. A phase diagram of the transition to the quantum Hall state in…
In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the…
We analyze here the behavior of the Hall conductivity $\sigma_{xy}$ near a $z=2$ insulator-superconductor quantum critical point in a perpendicular magnetic field. We show that the form of the conductivity is sensitive to the presence of…