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The transport properties on the two-dimensional surface of coupled multilayer heterostructures are studied in the integer quantum Hall states. We emphasize the criticality of the surface state and the phase coherent transport properties in…
The peculiar nature of electron scattering in graphene is among many exciting theoretical predictions for the physical properties of this material. To investigate electron scattering properties in a graphene plane, we have created a…
Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…
In the effective mass approximation, electronic property in graphene can be characterized by the relativistic Dirac equation. Within such a continuum model we investigate the electronic transport through graphene waveguides formed by…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
This work deals with the intrinsic and extrinsic properties of the graphene layers inside the graphite structure, in particular the influence of defects and interfaces. We discuss the evidence for ballistic transport found in mesoscopic…
Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the…
We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering…
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…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
Detailed experimental and theoretical studies of the temperature dependence of the effect of different scattering mechanisms on electrical transport properties of graphene devices are presented. We find that for high mobility devices the…
The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
Coherent transport promises to be the basis for an emerging new technology. Notwithstanding, a mechanistic understanding of the fundamental principles behind optimal scattering media is still missing. Here, complex network analysis is…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…