Abstract
We theoretically investigate mechanisms of higher-order harmonic generation in solid-state materials under a high-intensity ac electric field. A new theoretical framework presented in this Letter holds the legitimacy of Bloch's theorem even under the influence of the high-intensity electric field and provides an exact treatment of the diabatic processes of Bloch electrons. Utilizing this framework, we first discovered that the diabatic processes, namely, ac Zener tunneling and semimetallization of semiconductors, are key factors for nonperturbative mechanisms of HHG. These mechanisms are classified by the field intensity and could be understood by an extended simple man model based on an analogy between tunnel ionization in gaseous media and Zener tunneling in semiconductors. These conclusions would stimulate the universal understanding of HHG mechanisms in both atomic and solid cases.
Highlights
We theoretically investigate mechanisms of higher-order harmonic generation in solid-state materials under a high-intensity ac electric field
These mechanisms are classified by the field intensity and could be understood by an extended simple man model based on an analogy between tunnel ionization in gaseous media and Zener tunneling in semiconductors
The differences are based on the periodic arrangement of atoms and collective properties of electrons in solid-state materials. These experiments show a band-gap dependence of a cutoff energy in higher-order harmonic generation (HHG) spectra [4,5], whose definition is a threshold between a constant intensity region and strong decay region, while, in atomic cases, that is determined by the relation with ionization energy of a single atom
Summary
Week ending 8 JANUARY 2016 high-intensity ac electric field. In spite of these failures, some previous works [5,11,12], where transport processes are introduced by the scalar potential, constructed their theoretical frameworks based on assumptions of the completeness of Bloch functions as well as the concepts of band structures and Bloch electrons. We should take care of the Hamiltonian not always leading to the classical kinetic equation for the Bloch wave vector ħkðtÞ 1⁄4 −eEðtÞ, especially when treating excitation and transport processes together Based on this scheme, we first discovered that diabatic processes, namely, ac Zener tunneling and semimetallization of semiconductors, determine the characteristics of HHG in solid-state materials. The first term on the right hand side in Eq (2) indicates the intraband transition in which the Bloch wave vector k is a kinetic constant and it can be renormalized in the single-particle energy εσk, where εσkðtÞ 1⁄4 Eσk þ Eg=2 þ ħΩRðtÞ cos θk These modifications caused by an ac electric field mean a temporal variation of the band structure, which is consistent with the above discussion.
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