Related papers: The microscopic origin of the Quantum Hall Effect
Does quantum mechanics matter at everyday scales? We generally assume that its consequences are confined to microscopic scales. It would be very surprising if quantum effects were to be manifest in a macroscopic system. This has been…
The search for topological phases of matter is evolving towards strongly interacting systems, including magnets and superconductors, where exotic effects emerge from the quantum-level interplay between geometry, correlation and topology.…
Topological insulators are bulk electronic insulators which possess symmetry protected gapless modes on their surfaces. Breaking the symmetries that underlie the gapless nature of the surface modes is predicted to give rise to exotic new…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
Since the notion of topological insulator (TI) was envisioned in late 2000s, topology has become a new paradigm in condensed matter physics. Realization of topology as a generic property of materials has led to numerous predictions of…
We examine quantum transport in periodic quantum graphs with a vertex coupling non-invariant with respect to time reversal. It is shown that the graph topology may play a decisive role in the conductivity properties illustrating this claim…
The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional,…
We use magnetotransport in dual-gated magnetic topological insulator heterostructures to map out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical potential (primarily determined by the…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…
Since it is commonly believed that the observed large-scale structure of the Universe is an imprint of quantum fluctuations existing at the very early stage of its evolution, it is reasonable to pose the question: Do the effects of quantum…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
Owing to the enormous interest the rapidly growing field of topological states of matter (TSM) has attracted in recent years, the main focus of this review is on the theoretical foundations of TSM. Starting from the adiabatic theorem of…
The connection between topology and quantum mechanics is one of the cornerstones of modern physics. Several examples of current interest like the Aharonov-Bohm effect in quantum mechanics, monopoles and instantons in quantum field theory,…
Influences of topological defect and dislocation on conductivity behavior of charge carries in external electromagnetic fields are studied. Particularly the quantum Hall effect is investigated in detail. It is found that the nontrivial…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
Bulk-boundary correspondence is the foundational principle of topological physics, first established in the quantum Hall effect, where a $D$-dimensional topologically nontrivial bulk gives rise to $(D-1)$-dimensional boundary states. The…