相关论文: Reflectionless pseudospin-1 Dirac systems via Darb…
Darboux transformation is a powerful tool for the construction of new solvable models in quantum mechanics. In this article, we discuss its use in the context of physical systems described by $4\times4$ Dirac Hamiltonians. The general…
We introduce a systematic method to spectrally design quasi-one-dimensional crystal models described by the Dirac equation in the low-energy regime. The method is based on the supersymmetric transformation applied to an initially known…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of…
We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian…
The collective electronic properties of various types of pseudospin-$1$ Dirac-cone materials with a flat band and finite bangaps in their energy spectra are the subject of our reported investigation. Specifically, we have calculated the…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures have been shown to be readily removed by employing a first-order difference scheme. This approach is…
We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
The energy spectra for the tight-binding models on the Lieb and kagom\'e lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band…
Spin-1 condensed matter systems characterized by the combination of a Dirac-like dispersion and flat bands are ideal for realizing high-temperature electronics and spintronic technologies in the absence of external magnetic field. In this…
We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for…
Two-dimensional Dirac materials with a flat band have been demonstrated to possess a plethora of unusual electronic properties, but the optical properties of these materials are less studied. Utilizing $\alpha$-$\mathcal{T}_3$ lattice as a…
In this paper, we are concerned with a a semi-discrete complex short pulse (CSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz-Ladik (AL) lattice in the ultra-short pulse regime. By using…
The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair…
This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center. In this sequel, we extend our computations in two significant ways. The first is to a…
We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding…
Mode conversion of transverse electromagnetic waves into longitudinal oscillations and the associated resonant absorption of wave energy in inhomogeneous plasmas is a phenomenon that has been studied extensively in plasma physics. We show…
The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to…
The Dirac equation is a paradigmatic model that describes a range of intriguing properties of relativistic spin-1/2 particles, from the existence of antiparticles to Klein tunneling. However, the Dirac-like equations have found application…
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…