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The condensed-matter realization of chiral anomaly has attracted tremendous interest in exploring unexpected phenomena of quantum field theory. Here, we show that one-dimensional (1D) chiral anomaly (i.e., 1D nonconservational chiral…
We consider the problem of confining the famously elusive Dirac-like quasiparticles, as found in some recently discovered low-dimensional systems. After briefly surveying the existing theoretical proposals for creating bound states in Dirac…
The surface states of a topological insulator are described by an emergent relativistic massless Dirac equation in 2+1 dimensions. In contrast to graphene, there is an odd number of Dirac points, and the electron spin is directly coupled to…
We study the disorder potential induced by random Coulomb impurities at the surface of a topological insulator (TI). We use a simple model in which positive and negative impurities are distributed uniformly throughout the bulk of the TI,…
We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear…
We develop an effective bulk model with a topological boundary condition to study the surface states of topological insulators. We find that the Dirac point energy, the band curvature and the spin texture of surface states are crystal…
The surface states of 3D topological insulators in general have negligible quantum oscillations when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators can support surface states with…
We address the problem of identifying families of discrete models naturally flowing in continuum limit to relativistic quantum field theories. We call them Dirac graphs. In this work, we require the graphs to obey spectrality property,…
Magnetic topological insulators can host chiral 1D edge channels at zero magnetic field, when a magnetic gap opens at the Dirac point in the band structure of 2D topological surface states, leading to the quantum anomalous Hall effect in…
We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence…
From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac…
Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not…
Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and…
The quantum anomalous Hall effect (QAHE) realizes dissipationless longitudinal resistivity and quantized Hall resistance without the need of an external magnetic field. However, when reducing the device dimensions or increasing the current…
Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and $T-$linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead…
We propose a framework for applying on-shell scattering amplitude methods to emergent relativistic phases of quantum matter. Many strongly correlated systems, from Dirac and Weyl semimetals to topological-insulator surfaces, exhibit…
The discovery of the quantum Hall effect founded the field of topological condensed matter physics. Its amazingly accurate quantisation of the Hall conductance, now enshrined in quantum metrology, is topologically protected: it is stable…
Dirac's method for constraints is used for solving the problem of exclusion of double occupancy for Correlated Electrons. The constraints are enforced by the pair operator $Q(\vec{x})=\psi_{\downarrow}(\vec{x})\psi_{\uparrow}(\vec{x})$…
The quantum anomalous Hall effect in magnetic topological insulators has been recognized as a promising platform for applications in quantum metrology. The primary reason for this is the electronic conductance quantization at zero external…
Oscillations are ubiquitous wave phenomena in physical systems ranging from electromagnetic and acoustic to gravitational waves. The behavior of finite-size systems is traditionally understood to be governed by fundamental oscillatory modes…