Abstract
Two-dimensional materials with hexagonal symmetry such as graphene and transition metal dichalcogenides are unique materials to study light-field-controlled electron dynamics inside of a solid. Around the K-point, the dispersion relation represents an ideal system to study intricately coupled intraband motion and interband (Landau-Zener) transitions driven by the optical field of phase-controlled few-cycle laser pulses. Based on the coupled nature of the intraband and interband processes, we have recently observed in graphene repeated coherent Landau-Zener transitions between valence and conduction band separated by around half an optical period of ∼1.3 fs (Higuchi et al Nature 550, 224 (2017)). Due to the low temporal symmetry of the applied laser pulse, a residual current density and a net electron polarization are formed. Here we show extended numerical data on the temporal evolution of the conduction band population of 2D materials with hexagonal symmetry during the light–matter interaction, yielding deep insights to attosecond-fast electron dynamics. In addition, we show that a residual ballistic current density is formed, which strongly increases when a band gap is introduced. Both, the sub-cycle electron dynamics and the resulting residual current are relevant for the fundamental understanding and future applications of strongly driven electrons in two-dimensional materials, including graphene or transition metal dichalcogenide monolayers.
Highlights
Two-dimensional materials with hexagonal symmetry such as graphene and transition metal dichalcogenides are unique materials to study light-field-controlled electron dynamics inside of a solid
A Bloch trajectory for an electron driven with an x-polarized few-cycle laser pulse Ex(t) = E0 exp −2 ln(2)(t/τp)2 cos (2πf0t + ΦCEP), with a pulse duration of τp = 6 fs, a driving frequency of f0 = 0.375 PHz and a carrier-envelope phase of ΦCEP = π/2 is shown in Fig. 1 (a)
For a peak electric field strength of E0 = 2.4 V/nm acting on graphene, which is reachable with a commercial few cycle laser oscillator, the electron wave number is changed by ∆kx = 1.6 nm−1
Summary
Two-dimensional materials with hexagonal symmetry such as graphene and transition metal dichalcogenides are unique materials to study light-field-controlled electron dynamics inside of a solid. A Bloch trajectory for an electron driven with an x-polarized few-cycle laser pulse Ex(t) = E0 exp −2 ln(2)(t/τp)2 cos (2πf0t + ΦCEP), with a pulse duration of τp = 6 fs, a driving frequency of f0 = 0.375 PHz and a carrier-envelope phase of ΦCEP = π/2 is shown in Fig. 1 (a).
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