Sharif Digital Repository

In a nanoscopic thin film of a strong topological insulator (TI) the Coulomb interaction in the channel that exchanges the two electrons with the same chirality in two different planes of the slab takes advantage of the minus sign resulting from such "exchange" and gives rise to a bound state between the positive-energy states in one surface and the negative-energy states in the opposite surface. Therefore particle and hole pairs in the undoped Dirac cone of the TI thin film form an inter-surface spin-singlet state that lies below the continuum of free particle-hole pairs. This mode is similar to the excitons of semiconductors, albeit formed between the electron and hole pairs from two... 

The particle-hole continuum (PHC) for massive Dirac fermions provides an unprecedented opportunity for the formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel, when the short-range interactions are added to the undoped system. Both states are close in energy and are separated from the continuum of free particle-hole excitations by an energy scale of the order of the gap parameter Δ. They both disperse linearly with two different velocities, reminiscent of spin-charge separation in Luttinger liquids. When the strength of Hubbard interactions is stronger than a critical value, the velocity of singlet excitation, which we interpret as a... 

We present a formulation for the nonlinear optical response in gapped graphene, where the low-energy single-particle spectrum is modeled by massive Dirac theory. As a representative example of the formulation presented here, we obtain a closed form formula for the third harmonic generation in gapped graphene. It turns out that the covariant form of the low-energy theory gives rise to peculiar logarithmic singularities in the nonlinear optical spectra. The universal functional dependence of the response function on dimensionless quantities indicates that the optical nonlinearity can be largely enhanced by tuning the gap to smaller values  

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the XYZ spin chain. First, we identify the Ising order along ◯ or ŷ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the XY interaction and the coupling Δ of the Δσzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1, depending on whether the Ising order parameter is... 

We show that the continuum limit of the tilted Dirac cone in materials such as 8-Pmmn borophene and layered organic conductor α-(BEDT-TTF)2I3 corresponds to deformation of the Minkowski space-time of Dirac materials. From its Killing vectors we construct an emergent tilted-Lorentz (t-Lorentz) symmetry group for such systems. As an example of the t-Lorentz transformations we obtain the exact solution of the Landau bands for a crossed configuration of electric and magnetic fields. For any given tilt parameter 0≤ζ<1, if the ratio χ=vFBz/Ey of the crossed magnetic and electric fields satisfies χ≥1+ζ, one can always find appropriate t-boosts in both valleys labeled by τ=±1 in such a way that the... 

Dirac cone can be tilted in condensed matter setting. As a result of tilt, the Lorentz symmetry is reduced to what we call tilted-Lorentz symmetry. In this paper, we derive the tilted-Lorentz transformations that leave a world with tilted Dirac cone invariant. © 2020, Isfahan University of Technology. All rights reserved