arXiv subjects

Mohamed M. Elsayed

Publications and source records attributed to Mohamed M. Elsayed.

5 recordsLinked to original sources

arXiv2026

Colloquium: Semi-Dirac Fermions in Quantum Matter

This article reviews the recent progress on the subject of semi-Dirac fermions, two dimensional quasiparticles that disperse quadratically, as Galilean invariant particles, or linearly, as massless relativistic particles, depending on their direction of motion. These particles exist at a phase boundary set by the continuous change in the connectivity of Fermi surfaces, known as topological Lifshitz transitions. The basic properties and the current experimental evidence of the existence of these particles in both synthetic lattices and quantum materials are presented. The many-body problem of semi-Dirac fermions is discussed from a theoretical perspective with an eye to physical observables of relevance to experiments.

cond-mat.str-el↗

arXiv2026

Interacting type-II semi-Dirac quasiparticles

Type-II semi-Dirac fermions in two dimensions have been proposed to describe topologically nontrivial low-energy excitations in titanium/vanadium oxide heterostructures. These quasiparticles appear at the merger of three Dirac cones, resulting in a non-zero Berry phase. We find, by employing Hartree-Fock, renormalization group and Random Phase Approximation (RPA) techniques, that the spectrum is very sensitive to long-range electron-electron interactions and can undergo a profound transformation. Our results indicate that at the topological phase boundary, long-range correlations stabilize a hybrid electronic phase displaying both Dirac and type-II semi-Dirac qualities, with physical characteristics exhibiting continuously varying critical exponents as a function of the Fermi energy; for example Landau levels in a magnetic field vary with the energy scale: $|\varepsilon_n(B)|\sim (nB)^{1/2} \rightarrow (nB)^{3/4}, n\in \mathbb{N}_0$. The quasiparticle spectrum evolves, driven by interactions, from anisotropic Dirac dispersion at the lowest energies, towards the characteristic type-II semi-Dirac boomerang shape as the energy increases. The corresponding density of states concomitantly varies between linear and power one third ($\rho(\varepsilon) \sim |\varepsilon| \rightarrow |\varepsilon|^{1/3}$). The crossover scale is controlled by the interaction strength $\alpha = e^2/(\hbar v)$ and the specifics of the effective interacting Hamiltonian.

cond-mat.str-el↗

arXiv2025

Microscopic lattice model for quartic semi-Dirac fermions in two dimensions

We propose a lattice model for the realization of exotic quartic semi-Dirac fermions, i.e. quasiparticles exhibiting a dispersion with quartic momentum dependence in a given direction, and a linear dependence in the perpendicular direction. A tight binding model is employed, allowing for hopping between up to fourth nearest neighbors and anisotropic hopping parameters. In addition, we introduce short range electron-electron interactions which are necessary to stabilize the quartic semi-Dirac phase. Without interactions, or in the presence of long range correlations, the lattice is unstable towards formation of either anisotropic Dirac cones, or simple (quadratic) semi-Dirac phase.

cond-mat.mes-hall↗

arXiv2024

Coulomb interactions in systems of generalized semi-Dirac fermions

Interactions have strong effects in systems with flat bands. We examine the role of Coulomb interactions in two dimensional chiral anisotropic quasiparticles that disperse linearly in one direction and have relatively flat bands near the neutrality point in the other direction, dispersing with an arbitrary positive even power law $2n\geq2$. As in the conventional semi-Dirac case $(n=1$), we show using renormalization group that strong logarithmic divergences in the self-energy of generalized semi-Dirac fermions resum and lead to a restoration of linearity in the spectrum for arbitrary $n$ over a sizable energy window in the perturbative regime. We discuss those results in light of previous non-perturbative large $N_{f}$ results and address the implications for physical observables.

cond-mat.str-el↗

arXiv2023

Polarization Charge around Impurities in Two-Dimensional Anisotropic Dirac Systems

Introducing quasiparticle anisotropy in graphene via uniaxial strain has a profound effect on the polarization charge density induced by external impurities, both Coulomb and short-range. In particular, the charge distribution induced by a Coulomb impurity exhibits a power law tail modulated by a strain-dependent admixture of angular harmonics. The appearance of distributed charge is in sharp contrast to the response in pristine/isotropic graphene, where for subcritical impurities the polarization charge is fully localized at the impurity position. It is also interesting to note that our results are obtained strictly at zero chemical potential, and the behavior is distinct from the familiar Friedel oscillations observed at finite chemical potential. We find that over a wide range of strain, the $d$-wave symmetry is dominant. The presence of Dirac cone tilt, relevant to some 2D materials beyond graphene, can also substantially affect the induced charge distribution. Finally we consider impurities with short range potentials, and study the effect of strain on the charge response. Our results were obtained in the continuum via perturbation theory valid for weak (subcritical) potentials, and supported by numerical lattice simulations based on density functional theory.

cond-mat.mes-hall↗