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We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…
Quantum fluctuations of periodic domain-wall arrays in two-dimensional incommensurate states at zero temperature are investigated using the elastic theory in the vicinity of the commensurate-incommensurate transition point. Both stripe and…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
We derive a framework to apply topological quantum chemistry in systems subject to magnetic flux. We start by deriving the action of spatial symmetry operators in a uniform magnetic field, which extends Zak's magnetic translation groups to…
We derive the effective theories for quantum hall droplets with attractive interaction among the constituent particles. In the absence of confining potentials such droplets are defined by their freely moving interfaces (or boundaries) with…
The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode…
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…
Controlling quantum phases of materials with vacuum field fluctuations in engineered cavities is a novel route towards the optical control of emergent phenomena. We demonstrate, using magnetotransport measurements of a high-mobility…
We present recent experimental results confirming previously predicted strong asymmetries of the current distribution in narrow Hall bars under the conditions of the integer quantum Hall effect (IQHE). Using a previously developed…
We use a fully self-consistent laterally resolved Hartree-Fock approximation for numerically addressing the electron configurations at higher Landau levels in the quantum Hall regime for near-macroscopic sample sizes. Our results give…
We show that observables in QED-type theories can be realized in terms of a combinatorial structure called chord diagrams. One advantage of this combinatorial representation is that it simplifies the study of the asymptotic behavior of…
We develop a formalism suitable for the study of transport properties of coherent multiple dots which captures and explains the experimentally observed features in terms of spectral properties of the system. The multiplet structure of the…
We predict a huge interference effect contributing to the conductance through large ultra-clean quantum dots of chaotic shape. When a double-dot structure is made such that the dots are the mirror-image of each other, constructive…
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel…
We address the study of controllability of a closed quantum system whose dynamical Lie algebra is generated by adjacency matrices of graphs. We characterize a large family of graphs that renders a system controllable. The key property is a…
In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However, unlike persistence modules indexed over a totally ordered…
We show how particle-vortex duality implies the existence of a large non-abelian discrete symmetry group which relates the electromagnetic response for dual two-dimensional systems in a magnetic field. For conductors with charge carriers…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
We use dynamic scanning capacitance microscopy (DSCM) to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to…