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Pyramidal quantum dots (QDs) grown in inverted recesses have demonstrated over the years an extraordinary uniformity, high spectral purity and strong design versatility. We discuss recent results, also in view of the Stranski-Krastanow…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
Topological semimetals are gapless states of matter which have robust surface states and interesting electromagnetic responses. In this paper, we consider the electromagnetic response of gapless phases in $3+1$-dimensions with line nodes.…
Achieving stable, high-quality quantum dots has proven challenging within device architectures rooted in conventional solid-state device fabrication paradigms. In fact, these are grappled with complex protocols in order to balance ease of…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
A major question for condensed matter physics is whether a solid-state quantum computer can ever be built. Here we discuss two different schemes for quantum information processing using semiconductor nanostructures. First, we show how…
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular nonabelian ones.…
This article is devoted to a discussion of stripe and electron-nematic order and their connection to electronic properties in the pseudogap regime of copper-oxide superconductors. We review basic properties of these symmetry-breaking…
A multiscale approach was adopted for the calculation of confined states in self-assembled semiconductor quantum dots (QDs). While results close to experimental data have been obtained with a combination of atomistic strain and…
Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual…
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…
Flat band moir\'e graphene systems have emerged as a quintessential platform to investigate correlated phases of matter. A plethora of interaction-driven ground states have been proposed, and yet despite extensive experimental effort, there…
We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the…
Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness - topological protection,…
We present a detailed analysis of topological properties of the valence bond solid (VBS) states doped with fermionic holes. As concrete examples, we consider the supersymmetric extension of the SU(2)- and the SO(5) VBS states, dubbed…
We consider manifestations of topological order in time-reversal-symmetric fractional topological liquids (TRS-FTLs), defined on planar surfaces with holes. We derive a formula for the topological ground state degeneracy of such a TRS-FTL,…
Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two…
We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative…
We develop here a theory of the electronic properties of a finite number of valence holes in gated WSe$_2$ quantum dots, considering the influence of spin, valley, electronic orbitals, and many-body interactions. The single-particle wave…
Orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to…