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Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter. Seminal efforts are underway in the control of artificial quantum systems,…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
Quantum anomalous Hall effect has been widely explored in both ferromagnetic and antiferromagnetic systems. Here, we propose an interaction-driven paramagnetic quantum anomalous Hall effect emerging in the Fermion-Hubbard model on a dice…
Electron spin-qubits in silicon-germanium (SiGe) heterostructures are a major candidate for the realization of scalable quantum computers. A critical challenge in strained Si/SiGe quantum wells (QWs) is the existence of two nearly…
The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is…
The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH…
We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in…
Recent experiments [L. Ju et al., Nature, 2015, 520, 650] confirm the existence of gapless states at domain walls created in gated bilayer graphene, when the sublattice stacking is changed from AB to BA. These states are significant because…
A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles,…
The observation of the fractional quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary…
We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized…
Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum…
The construction of fractional quantum Hall (FQH) states from the two-dimensional array of quantum wires provides a useful way to control strong interactions in microscopic models and has been successfully applied to the Laughlin,…
Coupling superconductors to quantum Hall edge states is the subject of intense investigation as part of the ongoing search for non-abelian excitations. Our group has previously observed supercurrents of hundreds of picoamperes in graphene…
Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…
We review our recent results on the physics of quantum Hall fluids at Jain and non conventional fillings within a general field theoretic framework. We focus on a peculiar conformal field theory (CFT), the one obtained by means of the…
It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM…
Topological phases of matter are a potential platform for the storage and processing of quantum information with intrinsic error rates that decrease exponentially with inverse temperature and with the length scales of the system, such as…
We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the…