Exploring interacting Floquet states in black phosphorus: Anisotropy and bandgap laser tuning

Abstract

The dressed states arising from the interaction between electrons and holes, and off-resonant electromagnetic radiation have been investigated for recently fabricated gapped and anisotropic black phosphorus. Our calculations were carried out for the low-energy electronic subbands near the Γ point. States for both linear and circular polarizations of the incoming radiation have been computed. However, our principal emphasis is on linearly polarized light with arbitrary polarization since this case has not been given much attention for dressing fields imposed on anisotropic structures. We have considered various cases for one-and few-layer phosphorus, including massless Dirac fermions with tunable in-plane anisotropy. Initial Hamiltonian parameters are renormalized in a largely different way compared to those for previously reported for gapped Dirac structures and, most importantly, existing anisotropy which could be modified in every direction.

Peculiar electronic states, symmetries, and Berry phases in irradiated α−T3 materials

“…We would now like to point out that if the initial model Hamiltonian is linear in k, which is the case for nearly all Dirac and gapped Dirac structures, such as gapped or gapless graphene, buckled honeycomb lattices and transition metal dichalcogenides, the resulting Hamiltonian for the dressed states is obtained by adding a single interaction term, independent of the wave vector k. However, the situation is drastically different for phosphorene with a more complicated anisotropic wave vector dependence in the unperturbed Hamiltonian. 17 In order to solve this eigenvalue problem, we are going to apply perturbation theory. Nearly all off-resonant systems, subjected to external periodic fields with ε d (k) ω, could be effectively described by a perturbation expansion of the interaction Hamiltonian in powers of 1/( ω).…”

“…which could be obtained as a limiting case of vanishing anisotropy for multi-layer black phosphorus, 17 or setting to zero all the band gaps for transition metal dichalcogenides which were investigated in Ref. [16].…”

“…Being essentially anisotropic, such fields are known to transform the Dirac cone into an asymmetric elliptical cone without creating a gap between the valence and conduction bands. 34 Whereas in initially anisotropic phosphorene, the direction of the linear polarization was important, 17 for the isotropic energy dispersions in α − T 3 we can assume that the polarization vector lies along the x axis without any loss of generality so that…”

“…[8][9][10][11] Based on these theories, researchers have developed numerous techniques to modify the existing electronic properties of condensed matter materials, which was subsequently referred to as Floquet engineering of various nanostructures [12][13][14] and especially for the novel low-dimensional Dirac cone materials. [15][16][17][18][19][20][21][22] Considerable effort has been given to find a way to generate topological insulator properties in such systems under irradiation 12,23,24 Optical dressing can also alter the tunneling and conductance 25 properties of a topological insulator, leading to tunable spin transport on their surfaces 26 with potential applications in spintronics, as well as result in an optically-stimulated Lifshitz transition. 27 Another important property of such electronic dressed systems for operating an optoelectronic device is the challenge of confining such electron states in a specific region.…”

Floquet engineering of Dirac cones on the surface of a topological insulator

“…It is worth noticing that it has been already shown for example that an in-plane, circularly polarized field leads to gap openings, 21 a feature that has been also observed in graphene. 22,[30][31][32] In view of previous studies based on graphene, 33,34 phosphorene, 35 α−T 3 materials 36 and three-dimensional topological insulators, 37 other in-plane configurations are expected to preserve the Dirac point, isotropically or anisotropically widening the Dirac cone. In this paper, we will confirm these results on the surface of a topological insulator and, furthermore, we will extend previous studies with a detailed characterization of i) Dirac cones on the topological surface when a time-periodic out-of-plane field is applied and ii) the dependence of the main magnitudes of interest, the Fermi velocity and the gap, on the field parameters.…”