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We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…

We study the Hall conductivity in single layer gapped Dirac fermion materials including coupling to a phonon field, which not only modifies the quasi-particle dynamics through the usual self-energy term but also renormalizes directly the…

We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux-phases. For weak itineracy the flux-phase is coplanar and the electronic dispersion takes the shape of…

We consider a 2+1 dimensional model of charged fermions coupled to a $\mathbb{Z}_2$ gauge field, and study the confinement transition in this regime. To elucidate the phase diagram of this model, we introduce a method to handle the Gauss…

We study a mixture of spin-$1$ bosonic and spin-$1/2$ fermionic cold atoms, e.g., $^{87}$Rb and $^{6}$Li, confined in a triangular optical lattice. With fermions at $3/4$ filling, Fermi surface nesting leads to spontaneous formation of…

The quantum Hall effect and the quantum anomalous Hall effect both require time-reversal invariance to be broken. We show that non-equilibrium effects can cause Hall physics to arise even when the system is weakly time-reversal symmetric…

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 1D fermions with photoassociation or with a narrow Fano-Feshbach resonance described by the Boson-Fermion resonance model. Using thebosonization technique, we derive a low-energy Hamiltonian of the system. We show that at low…

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the…

Starting from a minimal model for a 2D nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase winding number of the mass gap terms on the loop. We…

We consider spontaneous symmetry breaking transitions of strongly interacting two-dimensional Dirac fermions minimally coupled to mass and emergent gauge field order parameters. Using a renormalization group analysis, we show that the…

Gross-Neveu model in 2+1 dimensions exhibits a continuous transition from gapless Dirac semimetal to the gapped quantum anomalous Hall (QAH) insulator at a finite (attractive) coupling, at which the inversion and time-reversal symmetry…

We derive a scheme for systematically enumerating the responses of gapped as well as gapless systems of free fermions to electromagnetic and strain fields starting from a common parent theory. Using the fact that position operators in the…

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization…

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual…

We consider a model of spinful fermions on the triangular lattice which exhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase…

We consider the Hall conductivity of two-dimensional non-interacting Bloch electrons when the magnetic flux per unit cell is a rational number $p/q$ where $p$ and $q$ are mutually coprime. We present a counter-example for the naive…

We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $\nu=1/2$ boson quantum Hall liquid. In the…

Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-space--time dimensions (QED$_3$), making use of the relativistic Kubo formula, we demonstrate that the filling factor accompanying the quantized electrical…

The pursuit of understanding parity anomaly in condensed matter systems has led to significant advancements in both theoretical and experimental research in recent years. In this study, we explore the parity anomaly of massless Dirac…