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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…
We demonstrate that vacancies can induce topologically protected localized electronic excitations within the bulk of a topological insulator, and when sufficiently close, give rise to one-dimensional propagating chiral bulk modes. We show…
We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the…
Exotic phenomenon can be achieved in quantum materials by confining electronic states into two dimensions. For example, relativistic fermions are realised in a single layer of carbon atoms, the quantized Hall effect can result from…
The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
The discovery of the fractional quantum Hall effect in GaAs-based semiconductor devices has lead to new advances in condensed matter physics, in particular the possibility for exotic, topological phases of matter that possess fractional,…
This review provides a perspective on recent developments and their implications for our understanding of novel quantum phenomena in the physics of two-dimensional organic solids. We concentrate on the phase transitions and collective…
We study the properties of two dimensional topological spin hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal…
We consider quantum phase transitions with global symmetry breakings that result in the formation of topological defects. We evaluate the number densities of kinks, vortices, and monopoles that are produced in $d=1,2,3$ spatial dimensions…
The possibility of realizing topological insulators by spontaneous formation of electronic superstructure is theoretically investigated in a minimal two-orbital model including both the spin-orbit coupling and electron correlations on a…
We study the effect of electrostatic disorder on the conductivity of a three-dimensional antiferromagnetic insulator (a stack of quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where the…
Topological insulators are a class of band insulators with non-trivial topology, a result of band inversion due to the strong spin-orbit coupling. The transition between topological and normal insulator can be realized by tuning the…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
Topological defects play a key role in nonequilibrium phase transitions, ranging from birth of the early universe to quantum critical behavior of ultracold atoms. In solids, transient defects are known to generate a variety of hidden orders…
We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic…
Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing Kagome and pyrochlore lattices. They are known to possess three phases (trivial…
Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions…