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Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By…
We develop a stochastic description of the topological properties in an interacting Chern insulator. We confirm the Mott transition's first-order nature in the interacting Haldane model on the honeycomb geometry, from a mean-field…
Local topological markers, topological invariants evaluated by local expectation values, are valuable for characterizing topological phases in materials lacking translation invariance. The Chern marker -- the Chern number expressed in terms…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
2+1 dimensional topological insulator described by the Kane-Mele model in the presence of Rashba spin-orbit interaction is considered. The effective action of the external fields coupled to electromagnetic and spin degrees of freedom is…
Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of…
The concept of Chern insulators is one of the most important buliding block of topological physics, enabling the quantum Hall effect without external magnetic fields. The construction of Chern insulators has been typically through an…
In this work, we propose the average spin Chern number (ASCN) as an indicator of the topological significance of the spin degree of freedom within insulating materials. Whenever this number is a non-zero even integer, it distinguishes the…
Topological quantum phase transitions in superconductivity are discussed on two dimensional lattices. The main focus is on the Chern number for superconducting states. Each superconductivity is characterized by the Chern number, and the…
The correlation of topology and disorder has attracted great intention due to appropriate disorder could induce the phase transition between trivial and nontrivial topological states. While it is widely recognized that strong disorder can…
Topological superconductors are characterized by topological invariants that describe the number and nature of their robust boundary modes. These invariants must also have observable consequences in the bulk of the system, akin to the…
We propose an approach to induce nontrivial bands with non-zero Chern numbers by utilizing strong spin-orbit coupling in transition metal dichalcogenides with dopants. We demonstrate that a doped state near the valence-band edge induces…
Chern-Simons (CS) invariant is a fundamental topological invariant describing the topological invariance of 3D space based on the Chern-Simons field theory. To date, direct measurement of the CS invariant in a physical system remains…
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs…
Here we study the instabilities of a quadratic band crossing system to Chern insulating states and uncorrelated disorder. We determined the phase diagram in the plane of topological mass versus disorder strength, characterizing the system…
The Chern number has been widely used to describe the topological properties of periodic structures in the momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new…
We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…
The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
We obtain localized field configurations with finite energy in a ($2+1$)-dimensional model with Maxwell and Chern-Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the $U(1)$…
We investigate disordered-driven transitions between trivial and topological insulator (TI) phases in two-dimensional (2D) systems. Our study primarily focuses on the BHZ model with Anderson disorder, while other standard 2DTI models…