Doping and gap size dependence of high-harmonic generation in graphene: Importance of consistent formulation of light-matter coupling

Abstract

High-harmonic generation (HHG) in solids is a fundamental nonlinear phenomenon, which can be efficiently controlled by modifying system parameters such as doping level and temperature. To correctly predict the dependence of HHG on these parameters, consistent theoretical formulation of the light-matter coupling is crucial. Recently, contributions to the current that are often missing in the HHG analysis based on the semiconductor Bloch equations have been pointed out [Wilhelm et al., Phys. Rev. B 103, 125419 (2021)]. In this paper, by systematically analyzing the doping and gap-size dependence of HHG in gapped graphene, we discuss the practical impact of such terms. In particular, we focus on the role of the current J (2) ra , which originates from the change of the intraband dipole via interband transition. When the gap is small and the system is close to half filling, intraband and interband currents mostly cancel, thus suppressing the HHG signal-an important property that is broken when neglecting J (2) ra . Furthermore, without J (2) ra , the doping and gap-size dependence of HHG becomes qualitatively different from the full evaluation. Our results demonstrate the importance of the consistent expression of the current to study the parameter dependence of HHG for the small gap systems.

Influence of Laser Intensity and Location of the Fermi Level on Tunneling Processes for High-Harmonic Generation in Arrayed Semiconducting Carbon Nanotubes

“…An effective two-band model has been assumed for the semiconducting SWCNT with a diameter of 1.4 nm, including the lowest conduction and highest valence bands with E g = 0.6 eV and the Dirac band structures . While irradiating the system with a 60 fs MIR laser pulse, the time evolutions of the two types of currents, i.e., the interband polarization and intraband current, were evaluated using the semiconductor Bloch equation. ,− The Fermi–Dirac distribution was implemented using E F as the initial state, which was systematically varied. If E F was situated in the middle of the band gap, then its value was set to zero.…”

“…The intraband dynamics of carriers contribute to HHG. However, when the carriers cannot traverse through the K -point in the 1D-Dirac band structure (tunneling-off condition), their velocities change negligibly; hence, the contribution of this mechanism to HHG is small. ,, Consequently, in the tunneling-off condition, the carrier cannot generate high harmonics through the recombination mechanism with tunneling and intraband mechanisms (the details of the relationships among the intensity of HHG, E F , and F L are shown in Figure S14 in the SI). In the absence of the tunneling processes and negligible interband mechanisms for HHG, the majority of high harmonics should be generated through multiple photon excitation processes described by using perturbative optical processes.…”

“…Recently, HHG has been observed in various crystalline solids owing to recent advancement in intense mid-infrared lasers . HHG in solids functions as a probe for various essential physical parameters, such as the distribution of valence electrons, band dispersion, , and topology, and has been investigated in one- or two-dimensional materials in both experimental and theoretical aspects. − In addition, it can be used for extreme UV sources and ultrafast optoelectronics, − , and thus, HHG has great potential for next-generation optoelectronic science and technologies. Numerous approaches have been proposed to control HHG in solids by varying the excitation laser parameters ,, and characteristics of the solid, such as the nanostructure, crystal orientation, , electronic phase, − and electronic structure. ,, Using semiconductor device techniques, researchers have recently controlled HHG by applying a static electric field, such as by tuning the location of Fermi level E F − and inversion symmetry .…”