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The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction has been extensively explored in isotropic Dirac systems with linear dispersion, which typically follows an exponent decaying rate with the impurity distance R , i.e., J ∝ 1/ R d (1/ R 2 d −1 ) in d -dimensional systems at finite (zero) Fermi energy. This fast decay makes it rather difficult to be detected and limits its application in spintronics. Here, we theoretically investigate the influence of anisotropic dispersion on the RKKY interaction, and find that the introduction of non-relativistic dispersion in semi-Dirac semimetals (S-DSMs) can significantly prolong the decay of the RKKY interaction and can remarkably enhance the Dzyaloshinskii–Moriya interaction around the relativistic direction. The underlying physics is attributed to the highly increased density of states in the linear-momentum direction as a result of the interplay of relativistic and non-relativistic electrons. Furthermore, we propose a general formula to determine the decaying rate of the RKKY interaction, extending the typical formula for isotropic DSMs. Our results suggest that the S-DSM materials are a powerful platform to detect and control the magnetic exchange interaction, superior to extensively adopted isotropic Dirac systems.

In the framework of Bogoliubov–de Gennes equation, we theoretically study the transport properties in normal-superconducting junctions based on semi-Dirac materials (SDMs). Owing to the intrinsic anisotropy of SDMs, the configuration of Andreev reflection (AR) and the differential conductance are strongly orientation-dependent. For the transport along the linear dispersion direction, the differential conductance exhibits a clear crossover from retro AR to specular AR with increasing the bias-voltage, and the differential conductance oscillates with the interfacial barrier strength without a decaying profile. Conversely, for the transport along the quadratic dispersion direction, the boundary between the retro AR and specular AR becomes ambiguous when the orientation angle increases, and the differential conductance decays with increasing the momentum mismatch or the interfacial barrier strength. We illustrate the pseudo-spin textures to reveal the underling physics behind the anisotropic coherent transport properties. These results enrich the understanding of the superconducting coherent transport in SDMs.

Modifying the hexagonal lattices of graphene enables the repositioning and merging of the Dirac cones which proves to be a key element in the use of these materials for alternative electronic applications such as valleytronics. Here we study the nonequilibrium transport of carriers within a system containing two Dirac cones in both standard graphene and semi-Dirac graphene. In the latter, the lattice modifications cause the relativistic and parabolic dispersion bands to coexist, furnishing the Fermi surface with a rich pseudospin texture and a versatile Dirac cones separation. We construct a kinetic theory to investigate the carrier diffusion and uncover that the pseudospin index contributes to the particle current and, like the real spin, can induce a magnetoelectric effect, and argue that the pseudospin–charge coupling can be utilized to design a pseudospin filter. We explore the charge dynamics inside a quasi-one-dimensional conductor using the drift-diffusion model and detect the pseudospin accumulation at the sample boundaries. We find that, while, for graphene, the accumulation contributes to an extra voltage drop between the sample interfaces, the semi-Dirac system presents a similar accumulation that is strikingly equipped with valley polarization, signifying an essential tool for the control of valley manipulation and chirality transport using the pseudospin.

One of the most striking predictions of quantum electrodynamics is that vacuum fluctuations of the electromagnetic field can lead to spontaneous emission of atoms as well as photon-mediated interactions among them. Since these processes strongly depend on the nature of the photonic bath, a current burgeoning field is the study of their modification in the presence of photons with non-trivial energy dispersions, e.g. the ones confined in photonic crystals. A remarkable example is the case of isotropic Dirac-photons, which has been recently shown to lead to non-exponential spontaneous emission as well as dissipation-less long-range emitter interactions. In this work, we show how to further tune these processes by considering anisotropic Dirac cone dispersions, which include tilted, semi-Dirac, and the recently discovered type II and III Dirac points. In particular, we show how by changing the anisotropy of the lattice one can change both the spatial shape of the interactions as well as its coherent/incoherent nature. Finally, we theoretically analyze a possible implementation based on subwavelength atomic arrays where these energy dispersions can be engineered and interfaced with quantum emitters.

Semi-Dirac materials in 2D present an anisotropic dispersion relation, linear along one direction and quadratic along the perpendicular one. This study explores the topological properties and the influence of disorder in a 2D semi-Dirac Hamiltonian. Energy-dependent edge states appear only in one direction, localized on either the upper or lower edge of the nanoribbon determined by their particle or hole character. Their topological protection can be rigorously founded on the Zak phase of the one-dimensional reduction of the semi-Dirac Hamiltonian, that depends parametrically on one of the momenta. In general, only a single value of the momentum, corresponding to a zero energy mode, is topologically protected. We explore the dependence on the disorder of the edge states and the robustness of the topological protection in these materials. We also explore the consequences of the topological protection of the zero-momentum state in the transport properties for a two-terminal configuration.

Floquet spectrum of charge carriers in a 2 D -crystal with initially displaced Dirac points has been derived. The phase and amplitude dependences of the energy gap induced by elliptically polarized and bichromatic high-frequency fields has been investigated. In contrast to graphene the linearly polarized electric field has been shown to be able to transform the initially semi-metallic state of Dirac crystal into the Floquet-insulator state. The conditions for such a transition are indicated, one of which is the mismatch between the orientation of the field polarization line and the direction of the crystallographic axes.

Zero-index materials, characterized by near-zero permittivity and/or permeability, represent a distinctive class of materials that exhibit a range of novel physical phenomena and have potential for various advanced applications. However, conventional zero-index materials are often hindered by constraints such as narrow bandwidth and significant material loss at high frequencies. Here, we numerically demonstrate a scheme for realizing low-loss all-dielectric dual-band anisotropic zero-index materials utilizing three-dimensional terahertz silicon photonic crystals. The designed silicon photonic crystal supports dual semi-Dirac cones with linear-parabolic dispersions at two distinct frequencies, functioning as an effective double-zero material along two specific propagation directions and as an impedance-mismatched single-zero material along the orthogonal direction at the two frequencies. Highly anisotropic wave transport properties arising from the unique dispersion and extreme anisotropy are further demonstrated. Our findings not only show a novel methodology for achieving low-loss zero-index materials with expanded operational frequencies but also open up promising avenues for advanced electromagnetic wave manipulation.

We consider the polaron dynamics driven by Froḧlich type, long wavelength dominated electron-phonon interaction at zero temperature, for three different semi-metals: single and bilayer graphene, and semi-Dirac, all grown on polar substrates such as, SiC. Single layer graphene (henceforth called SL graphene), bilayer graphene (henceforth called BL graphene), and semi-Dirac have two dimensional band-structures with point Fermi surfaces in their natural undoped conditions. When these materials are grown on polar substrates, their electrons can interact with the optical phonons (LO) at the surface of the substrates. That gives rise to the possibility of polaron formation in the context of these semi-metals, although they themselves are non-polar. Starting from the Froḧlich type electron-phonon interaction Hamiltonian, perturbation theory is employed to calculate the self energy of the electron due to polaron formation for the three aforementioned systems. The electron self energy, or the polaron energy, calculated analytically for BL graphene, is shown to vary linearly with the electron momentum for small electron momenta. Whereas for ordinary polar crystals (both two and three dimensional), for small electron momentum, the polaron energy is quadratic leading to the mass correction of the electron, for BL graphene the polaron energy disperses linearly, rendering the massive BL graphene electrons effectively massless. Energies for Froḧlich polarons in SL graphene and semi-Dirac on polar substrates, are numerically evaluated. Also, the electron relaxation rate, related to the imaginary part of the analytically continued electron self energy expression, is calculated for the three systems.

We consider the polaron dynamics driven by Froḧlich type, long wavelength dominated electron-phonon interaction at zero temperature, for three different semi-metals: single and bilayer graphene, and semi-Dirac, all grown on polar substrates such as, SiC . Single layer graphene (henceforth called SL graphene), bilayer graphene (henceforth called BL graphene), and semi-Dirac have two dimensional band-structures with point Fermi surfaces in their natural undoped conditions. When these materials are grown on polar substrates, their electrons can interact with the optical phonons (LO) at the surface of the substrates. That gives rise to the possibility of polaron formation in the context of these semi-metals, although they themselves are non-polar. Starting from the Froḧlich type electron-phonon interaction Hamiltonian, perturbation theory is employed to calculate the self energy of the electron due to polaron formation for the three aforementioned systems. The electron self energy, or the polaron energy, calculated analytically for BL graphene, is shown to vary linearly with the electron momentum for small electron momenta. Whereas for ordinary polar crystals (both two and three dimensional), for small electron momentum, the polaron energy is quadratic leading to the mass correction of the electron, for BL graphene the polaron energy disperses linearly, rendering the massive BL graphene electrons effectively massless. Energies for Froḧlich polarons in SL graphene and semi-Dirac on polar substrates, are numerically evaluated. Also, the electron relaxation rate, related to the imaginary part of the analytically continued electron self energy expression, is calculated for the three systems.