Related papers: Quantum graphs with vertices of a preferred orient…
We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both…
We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic…
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…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
This review presents experimental results on the inter-edge-state transport in the quantum Hall effect, mostly obtained in the regime of high imbalance. The application of a special geometry makes it possible to perform I-V spectroscopy…
Theoretically, the quantum anomalous Hall effect is characterized by a quantized Hall conductance. However, many experiments only reported the quantization of the Hall resistance, which is accompanied by a non-vanishing longitudinal…
We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
We study the quantum anomalous Hall states in the $p$-orbital bands of the honeycomb optical lattices loaded with the single component fermions. Such an effect has not been realized in both condensed matter and cold atom systems yet. By…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
We investigate the interaction between quantum anomalous Hall (QAH) phases hosted by two atomically thin hexagonal lattices and demonstrate the emergence of topological phases with large Chern numbers. Interlayer coupling between two…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
In this work we show that the simple Hamiltonians used in Quantum Graphity models are highly degenerate, having multiple ground states that are not lattices. In order to assess the distance of the resulting graphs from a lattice graph, we…
Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect…
The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices whose…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…