Related papers: Quantum graphs and the integer quantum Hall effect
Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…
Quantum Hall effect (QHE), the ground to construct modern conceptual electronic systems with emerging physics, is often much influenced by the interplay between the host two-dimensional electron gases and the substrate, sometimes predicted…
The integer quantum Hall effect is analysed using a transport mechanism with a semi-classic wave packages of electrons in this paper. A strong magnetic field perpendicular to a slab separates the electron current into two branches with…
Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
The quantum anomalous Hall effect can occur in single and few layer graphene systems that have both exchange fields and spin-orbit coupling. In this paper, we present a study of the quantum anomalous Hall effect in single-layer and gated…
The quantum anomalous Hall (QAH) effect holds fundamental importance in topological physics and technological promise for electronics. It is generally believed that the QAH effect can only be realized in insulators. In this Letter, we…
Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by 2+1 dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity $\sigma_{xy} = - (2…
We study the critical properties of the quantum anomalous Hall (QAH) plateau transition in magnetic topological insulators. We introduce a microscopic model for the plateau transition in QAH effect at the coercive field and then map it to…
We find that mesoscopic conductance fluctuations in the quantum Hall regime in silicon MOSFETs display simple and striking patterns. The fluctuations fall into distinct groups which move along lines parallel to loci of integer filling…
Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance…
We study the optical properties of gapped two-dimensional materials which are subject to the quantum anomalous Hall effect. At sufficiently low temperatures the transmission, reflection and absorption coefficients are found to have a…
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped…
We investigate the phenomenon of integer quantum Hall effect in a square lattice, subjected to a perpendicular magnetic field, through Landauer-B\"uttiker formalism within the tight-binding framework. The oscillating nature of longitudinal…
For a three-dimensional lattice in magnetic fields we have shown that the hopping along the third direction, which normally tends to smear out the Landau quantization gaps, can rather give rise to a fractal energy spectram akin to…
In this work we report experiments on defined by shallow etching narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the…
Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal…
The spectrum of magnetic edge states and their transport properties in the presence of a perpendicular non-homogeneous magnetic field in a quantum wire formed by a parabolic confining potential are obtained. Systems are studied where the…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…