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Vacancies in materials structure -- lowering its atomic density -- take the system closer to the atomic limit, to which all systems are topologically trivial. Here we show a mechanism of mediated interaction between vacancies inducing a…
The modification of electronic band structures and the subsequent tuning of electrical, optical, and thermal material properties is a central theme in the engineering and fundamental understanding of solid-state systems. In this scenario,…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been…
Weyl semimetals are phases of matter with gapless electronic excitations that are protected by topology and symmetry. Their properties depend on the dimensions of the systems. It has been theoretically demonstrated that five-dimensional…
Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…
The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…
It is shown that three-dimensional systems of coupled quantum wires support fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems. These phases have topologically…
The electronic structure of a cubic $\mathcal{T}$-symmetric Weyl semimetal is analysed in the presence of atomic-sized vacancy defects. Isolated vacancies are shown to generate nodal bound states with $r^{{\scriptscriptstyle -2}}$…
Quantum material phases such as the Anderson insulator, diffusive metal, and Weyl/Dirac semimetal as well as topological insulators show specific wave functions both in real and Fourier spaces. These features are well captured by…
Topological phases of electrons such as topological insulators and quantum Hall states typically require strong spin-orbit coupling or magnetic fields. In this study, we consider an electron system coupled to a spin system, where electrons…
Recently, the structural disorder-induced topological phase transitions in periodic systems have attracted much attention. However, in aperiodic systems such as quasicrystalline systems, the interplay between structural disorder and band…
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and two-fold rotation symmetries. Contrary to the case of ordinary time-reversal…
Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well…
In non-interacting systems, disorder can drive a trivial phase into a topological one. However little is known how to construct a fractional quantum Hall ground-state, a paradigmatic topologically ordered state, that exists both in…
Recently, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a versatile and experimentally realistic approach of…
We study the effect of disorder in systems having a non-trivial Euler class. As these recently proposed multi-gap topological phases come about by braiding non-Abelian charged band nodes residing between different bands to induce stable…
This paper, based on the interdisciplinary frontiers of quantum electrodynamics, causal set theory, and the AdS/CFT holographic duality, integrates Keppler's zero point field resonance theory, the discrete causal structure and horizon…
We examine the impact of non-magnetic disorder on the electronic states of a multilayer structure comprising layers of both topological and conventional band insulators. Employing the Burkov-Balents model with renormalized tunneling…
Topological superconductivity in quasi-one-dimensional systems is a novel phase of matter with possible implications for quantum computation. Despite years of effort, a definitive signature of this phase in experiments is still debated. A…