Related papers: Missing link between the 2D Quantum Hall problem a…
The mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin-orbit torques and…
In this chapter, first we will address principal aspects of 1D quasiperiodicity with a particular focus on 1D Fibonacci chains. Further, the rest of the chapter will be dedicated to the electromagnetic counterpart of 1D Fibonacci structures…
We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings…
The search for strong topological phases in generic aperiodic materials and meta-materials is now vigorously pursued by the condensed matter physics community. In this work, we first introduce the concept of patterned resonators as a…
We develop a quasiclassical method based on the path integral formalism, to study the influence of disorder on magnetooscillations of the density of states and conductivity. The treatment is appropriate for electron systems in the presence…
The quantum anomalous Hall (QAH) effect is conventionally understood to exist only in Chern insulators, while a recent study has shown that ferromagnetic metals can also host the QAH effect. Between insulators and metals, we demonstrate…
In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the…
The search for candidate materials for fractional Chern insulators (FCIs) has mainly focused on the topological and geometrical structures of single-particle Chern bands. However, there are inherent limitations in approaches that neglect…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
Quantum duality is a far reaching concept in contemporary theoretical physics. In the present paper, we reveal the quantum dualities in quantum anomalous Hall (QAH) phases through concrete two bands Hamiltonian models. Our models can…
We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids which possess surface or bulk electronic band structures with nontrivial topologies, which…
Electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing 'forbidden' symmetries via quasiperiodic ordering with low-dimensionality into a…
In continuous topological phase transitions (CTPTs), the low-energy physics is governed by gap-closing subspaces, where approximate "higher" symmetries, termed quasisymmetries, may emerge. Here, we introduce the notion of quasisymmetry…
The chiral hinge modes are the key feature of a second order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge…
We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we…
Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In…
The quantum metric of single-particle wave functions in topological flatbands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern…
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…
We study two models for spinless fermions featuring topologically non-trivial bands characterized by Chern numbers $C=\pm1$ at fractional filling. Using exact diagonalization, we show that, even for infinitely strong nearest-neighbor…
In this work, we propose an exactly solvable two-dimensional lattice model of strongly correlated electrons that realizes a quantum anomalous Hall insulator with Chern number $\mathcal{C}=1$. First, we show that the interplay of ionic…