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Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak…
Bound electron-hole pairs in semiconductors known as excitons can form a coherent state at low temperatures akin to a BCS condensate. The resulting phase is known as the excitonic insulator and has superfluid properties. Here we…
Systems of strongly correlated fermions on certain geometrically frustrated lattices at particular filling factors support excitations with fractional charges $\pm e/2$. We calculate quantum mechanical ground states, low--lying excitations…
Low lying excitations of electron liquids in the fractional quantum Hall (FQH) regime are studied by resonant inelastic light scattering methods. We present here results from charge and spin excitations of FQH states in the lowest…
Within condensed-matter systems, strong electronic interactions often lead to exotic quantum phases. A recent manifestation of this is the unexpected observation of magnetic quantum oscillations and metallic thermal transport, both…
The quantum dynamics of the intrinsic metric profoundly influence the neutral excitations in the fractional quantum Hall system, as established by Haldane in 2011 \cite{Haldane2011}, and further evidenced by a recent two-photon experiment…
We have studied transport and magnetic properties of Bi_{1-x}Sb_x, which is believed to be a topological insulator - a new state of matter where an insulating bulk supports an intrinsically metallic surface. In nominally insulating…
The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can…
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research…
Ultracold atom research presents many avenues to study problems at the forefront of physics. Due to their unprecedented controllability, these systems are ideally suited to explore new exotic states of matter, which is one of the key…
Charge excitations in a two dimensional electron gas, under a quantizing magnetic field and in the fractional quantum Hall effect regime, flow in one dimensional-like strips along the edges of the sample. These excitations (quasiparticles)…
Many-body interactions can produce novel ground states in a condensed-matter system. For example, interacting electrons and holes can spontaneously form excitons, a neutral bound state, provided that the exciton binding energy exceeds the…
The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices. It also stimulates the explorations of more…
Integer and fractional quantum anomalous Hall (QAH) effects have been widely seen in moir\'e systems. Recently there is even observation of a time reversal invariant fractional quantum spin hall (FQSH) state at filling $n=3$ in twisted…
We study the interface between a fractional topological insulator and an ordinary insulator, both described using holography. By turning on a chemical potential we induce a finite density of matter localized at the interface. These are…
Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas most of these special band-crossing points are built in the electronic structure of the non-interacting…
We study by a consistent mean-field scheme the role on the single- and two-particle properties of a local electron-electron repulsion in the Bernevig, Hughes and Zhang model of a quantum spin Hall insulator. We find that the interaction…
Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic…