Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

Abstract

The full spectrum of two-dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of the novel 2D materials, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in 2D materials. We extend the analytical methods developed in the context of 1+1 field theories to explore the effect of the Lorentz symmetry breaking in the charge carrier density of 2D materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. Our findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.

Dynamical gauge symmetry breaking in lower-dimensional Lorentz-violating supersymmetric theory

“…is the Jacobian of the transformation. In low dimensional materials, ∆ can be interpreted as a quantity that renormalizes the propagation velocity of the bosonic mode with respect to the Fermi velocity [18].…”

“…Also, we expect to apply our studies for condensed matter systems, especially lower-dimensional superconductors and topological insulators. In low dimensional materials, the aether parameter ∆ can be interpreted as a quantity that renormalizes the propagation velocity of the bosonic mode with respect to the Fermi velocity [18].…”

“…Apparently, the simplest Lorentz-breaking term in 3D (as well as in 2D) is the aether term [6]. It is worth to mention that the aether term in scalar-spinor theory with Yukawa coupling, but without supersymmetry yet, has been considered within the context of 2D materials in [7]. Therefore, it is natural to develop a supersymmetric theory involving it as an ingredient, with an intention to apply it further within the condensed matter context.…”

A General Method for Transforming Nonphysical Configurations in BPS States

“…Topological defects are present in several scenarios of physics, covering areas like braneworld models, quintessence cosmological approaches, condensed matter, among others [1][2][3][4][5][6][7][8]. As examples of the applicability of defects solutions, we refer to studies involving defects in massive integrable field theories in 1+1 dimensions [9], in systems where the Lorentz symmetry is violated [10,11], in 2D materials [12], and in Yang monopoles [13].…”

Dirac field in the background of a planar defect

“…The massless Dirac fermions emerge as the quasiparticles in various novel materials such as graphene and topological insulators exhibiting intriguing behaviors [18,19]. In the context of 2D materials like graphene, it is important to study the band structure and properties of the trapped Dirac electron states and the consequent electronic properties of the material in the presence of a defect (see for instance [11,20,21]).…”