Related papers: Fractional topological phases in three-dimensional…
We study topological phases in the hyperbolic plane using noncommutative geometry and T-duality, and show that fractional versions of the quantised indices for integer, spin and anomalous quantum Hall effects can result. Generalising models…
The holographic Weyl semimetal is a model of a strongly coupled topological semi-metal. A topological quantum phase transition separates a topological phase with non-vanishing anomalous Hall conductivity from a trivial state. We investigate…
Weyl semimetals and higher-order topological insulators represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition…
We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of…
The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order…
We propose a 3D topolectrical (TE) network that can be tuned to realize various higher-order topological gapless and chiral phases. We first study a higher-order Dirac semimetal phase that exhibits a hinge-like Fermi arc linking the Dirac…
This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the $\nu =…
We present a theoretical study of the interplay between topological p-wave superconductivity, orbital magnetic fields and quantum Hall phases in coupled wire systems. First, we calculate the phase diagram and physical observables of a…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly…
One of the central tenets of the theory of the fractional quantum Hall effect is that the bulk quantized Hall response requires the existence of a gapless chiral edge mode. The field theoretical arguments for this rely on locality. While…
The quantum spin hall (QSH) phase, also known as the 2D topological insulator, is characterized by protected helical edge modes arising from time reversal symmetry. While initially proposed for band insulators, this phase can also manifest…
We consider periodically-driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This non-equilibrium system can be tuned into non-trivial phases such as of topological…
Recently there has been much effort in understanding topological phases of matter with gapless bulk excitations, which are characterized by topological invariants and protected intrinsic boundary states. Here we show that topological…
Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have…
A key hallmark of quantum Hall physics is the existence of topological chiral states at the system boundary. Signatures of these edge states have been experimentally observed in cold atoms by using different approaches, including notably…
It is well known that the Aubry-Andr{\'e} model lacks mobility edges due to its energy-independent self-duality but may exhibit edge states. When duality is broken, we show that mobility regions arise and non-trivial topological phases…
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…
This work investigates the coexistence of distinct topologically ordered phases within a single setup. We demonstrate this concept through tensor network simulations of the Hofstadter-Bose-Hubbard model under a spatially modulated chemical…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…