Related papers: Topological bulk-edge effects in quantum graph tra…
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…
Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge…
The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
The experimental observation of the long-sought quantum anomalous Hall effect was recently reported in magnetically doped topological insulator thin films [Chang et al., Science 340, 167 (2013)]. An intriguing observation is a rapid…
Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the…
We consider the junction of multiple one-dimensional systems and study how conserved currents transport at the junction. To characterize the transport process, we introduce reflection/transmission coefficients by applying boundary conformal…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
The magnetic effects in ferromagnetic graphene basically depend on the principle of exchange interaction when ferromagntism is induced by depositing an insulator layer on graphene. Here we deal with the consequences of non-uniformity in the…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
Effects manifesting quantum geometry have been a focus of physics research. Here, we reveal that quantum metric plays a crucial role in nonlinear electric spin response, leading to a quantum metric spin-orbit torque. We argue that enhanced…
Edge currents of paramagnetic colloidal particles propagate at the edge between two topologically equivalent magnetic lattices of different lattice constant when the system is driven with periodic modulation loops of an external magnetic…
We consider topologically non-trivial interface Hamiltonians, which find several applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected,…
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…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
One of the most intriguing and fundamental properties of topological materials is the correspondence between the conducting edge states and the gapped bulk spectrum. So far, it has been impossible to access the full evolution of edge states…
Topological properties in condensed matter physics are often claimed to be a fruitful resource for technical applications, but so far they only play a minor role in applications. Here we propose to put topological edge states to use in…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…
The influence of plasma etched sample edges on electrical transport and doping is studied. Through electrical transport measurements the overall doping and mobility are analyzed for mono- and bilayer graphene samples. As a result the edge…