Related papers: Topological Superconductors and Category Theory
While topological superconductors are predicted to provide building blocks for fault-tolerant quantum computing, one of the remaining challenges is to find a convenient experimental platform that would allow patterning of circuits. We find…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
We investigate quantum transport and thermoelectrical properties of a finite-size Su-Schrieffer-Heeger model, a paradigmatic model for a one-dimensional topological insulator, which displays topologically protected edge states. By coupling…
This is the Ph.D. dissertation of the author. The project has been motivated by the conjecture that the Hopkins-Miller tmf spectrum can be described in terms of `spaces' of conformal field theories. In this dissertation, spaces of field…
We report on a realistic and rather general scheme where noncollinear magnetic textures proximitized with the most common $s$-wave superconductor can appear as the alternative to $p$-wave superconductor{--}the prime proposal to realize…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of…
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
Two-dimensional topological superconductivity has attracted great interest due to the emergence of Majorana modes bound to vortices and propagating along edges. However, due to its rare appearance in natural compounds, experimental…
Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state…
We review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous deformations. We study families of projections…
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases,…
We consider a mean-field Hamiltonian for a $d_{x^2-y^2}+(p+ip)$ superconductor(SC) in presence of spin-density-wave(SDW) order. This is due to the fact that the non-commutativity of any two orders produces the third one. The energy spectrum…
Linear electric circuits composed of inductors and capacitors can serve as analogues of tight-binding models that describe the electronic band structure of materials. This mapping provides a versatile approach for exploring topological…
The study of topological classes and their associated edge states has been of ongoing interest. In one dimension, the standard platform of these studies has been the conventional Kitaev wire and its realizations. In this work, we study the…
We study two coupled Su-Schrieffer-Heeger (SSH) chains system, which is shown to contain rich quantum phases associated with topological invariants protected by symmetries. In the weak coupling region, the system supports two non-trivial…
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold…