Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Taya, Hidetoshi; Hongo, Masaru; Ikeda, Tatsuhiko N.

doi:10.1103/physrevb.104.l140305

Title: Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Journal Article · Thu Oct 21 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.l140305· OSTI ID:1979695

^[1];

^[2];

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RIKEN (iTHEMS), Wako (Japan); Keio University, Yokohama (Japan)
University of Illinois, Chicago, IL (United States); RIKEN (iTHEMS), Wako (Japan)
University of Tokyo (Japan)

Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E₀ and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE₀ℏΩ², with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE₀,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States); University of Illinois, Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); Japan Society for the Promotion of Science (JSPS)

Grant/Contract Number:: FG02-01ER41195; JP18K13495; JP21K13852

OSTI ID:: 1979695

Journal Information:: Physical Review. B, Vol. 104, Issue 14; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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