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Chiral fermionic quasiparticles emerge in certain quantum condensed matter systems such as Weyl semimetals, topological insulators, and spin-orbit coupled noncentrosymmetric metals. Here, a comprehensive theory of the chiral anomaly-induced…

We analyze the chiral symmetry breaking in a planar four-fermion model with non-null chemical potential, temperature and including the effect of the tilt of the Dirac cone. The system is modeled with a $(2 + 1)$-dimensional Gross-Neveu-like…

We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect…

The distinguishing feature of the quantum Hall ferromagnet is the identity between the electrical and topological charge densities of a spin distortion. In addition to the wealth of physics associated with Skyrmionic excitations of the…

Skyrmions and other chiral spin textures have been extensively studied as potential building blocks for novel spintronic devices. Hall-resistivity anomalies that deviate from magnetization scaling, known as the topological Hall effect, have…

In the normal state of high-Tc cuprates, the Hall coefficient shows remarkable temperature dependence, and its absolute value is enhanced in comparison with that value simply estimated on the basis of band structure. It has been recognized…

Semimetals exhibit intriguing characteristics attributed to the coexistence of both electrons and holes. In rhombohedral multilayer graphene, a strong trigonal warping effect gives rise to a semi-metallic state near the Fermi surface,…

Interaction driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite making its…

Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting…

Spin interactions of magnetic impurities mediated by conduction electrons is one of the most interesting and potentially useful routes to ferromagnetism in condensed matter. In recent years such systems have received renewed attention due…

Two-dimensional Dirac physics has aroused great interests in condensed matter physics ever since the discovery of graphene and topological insulators due to its importance in both fundamental physics and device applications. The ability to…

We study the problem of a single Dirac fermion in a quantizing orbital magnetic field, when the chemical potential is at the Dirac point. This can be realized on the surface of a topological insulator, such as Bi2Se3, tuned to neutrality.…

We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton…

The fractional quantum Hall (FQH) effect was discovered in two-dimensional electron systems subject to a large perpendicular magnetic field nearly four decades ago. It helped launch the field of topological phases, and in addition, because…

We investigate electrical transport in a three-dimensional massless Dirac fermion model that describes a Dirac semimetal state realized in topological materials. We derive a set of interdependent diffusion equations with eight local degrees…

Discovering Dirac fermions with novel properties has become an important front in condensed matter and materials sciences. Here, we report the observation of unusual Dirac fermion states in a strongly-correlated electron setting, which are…

We consider the minimal coupling of a thin film Dirac semimetal Hamiltonian to a generic spin-texture. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective…

The topological Hall effect (THE), as one of the primary manifestations of non-trivial topology of chiral skyrmions, is traditionally used to detect the emergence of skyrmion lattices with locally ferromagnetic order. In this work we…

We use the determinant Quantum Monte Carlo method (DQMC) to study the interaction-driven semimetal to antiferromagnetic insulator transition in a $\pi$-flux Hamiltonian with modulated hoppings, a model which has two species of Dirac…

We develop a theory of quantum spin Hall insulators with arbitrary spin $J$. Our analysis demonstrates that such systems support $J+\tfrac{1}{2}$ pairs of helical edge modes protected by nontrivial mirror Chern numbers. We establish that…