Related papers: Topological Insulators -- A review
This is a series of lecture notes explaining topos theory and its application in physics.
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
Motivated by the topologically insulating (TI) circuit of capacitors and inductors proposed and tested in arXiv:1309.0878, we present a related circuit with less elements per site. The normal mode frequency matrix of our circuit is…
This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am…
Topological insulators represent a new quantum state of matter which is characterized by peculiar edge or surface states that show up due to a topological character of the bulk wave functions. This review presents a pedagogical account on…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
These are lecture notes of the QFT-I course I gave in an online mode at Chennai Mathematical Institute. The course focussed on the free relativistic quantum fields, their interactions in the perturbative scattering framework, standard…
This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic…
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the…
The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall effect. Therefore if a material is in the topological insulator state they frequently call it the quantum spin Hall state.…
The topic of photonic topological insulators and scattering-protected edge states bridges concepts from condensed matter physics and electromagnetics, and necessitates understanding the Berry potential and related concepts. These notes are…
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
We study by a consistent mean-field scheme the role on the single- and two-particle properties of a local electron-electron repulsion in the Bernevig, Hughes and Zhang model of a quantum spin Hall insulator. We find that the interaction…
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…
This is the first of the proposed sets of notes to be published in the website Gonit Sora (http://gonitsora.com). The notes will hopefully be able to help the students to learn their subject in an easy and comprehensible way. These notes…
We develop a general low-energy multiple-scattering partial-wave theory for gapless topological insulator (TI) surfaces in the presence of magnetic impurities. As applications, we discuss the differential cross section (CS)…
For D-dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D- or (D+1)-dimensional integration over a certain curvature function that is expressed in terms of…
Topological insulators (TIs) are a new quantum state of matter which have gapless surface states inside the bulk energy gap. Starting with the discovery of two dimensional TIs, the HgTe-based quantum wells, many new topological materials…