Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and <i>ab initio</i> calculations

Goano, Michele; Bertazzi, Francesco; Penna, Michele; Bellotti, E.

doi:10.1063/1.2794380

Cited by 83 publications

(64 citation statements)

References 148 publications

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“…The energy bands of bulk crystal ZnO are reproduced from Ref. [20,28]. To establish the relation between electric fields of inside and outside of the solids, we need to take into account the reflection of incident pulses at the surface.…”

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confidence: 99%

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids

Du¹,

Bian²

2017

Opt. Express

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We study numerically the Bloch electron wave-packet dynamics in periodic potentials to simulate laser-solid interactions. We introduce a quasi-classical model in the k space combined with the energy band structure to understand the high-order harmonic generation (HHG) process occurring in a subcycle timescale. This model interprets the multiple plateau structure in HHG spectra well and the linear dependence of cutoff energies on the amplitude of vector potential of the laser fields. It also predicts the emission time of HHG, which agrees well with the results by solving the timedependent Schrödinger equation (TDSE). It provides a scheme to reconstruct the energy dispersion relations in Brillouin zone and to control the trajectories of HHG by varying the shape of laser pulses. This model is instructive for experimental measurements.PACS numbers: 42.65. Ky, 42.65.Re, 72.20.Ht High-order harmonic generation (HHG) in atomic and molecular systems in the gas phase has been well studied theoretically and experimentally [1,2]. It can be understood by a semi-classical three-step model [3]. The bound electron may be ionized by tunneling, then driven by the external laser field. When it recombines with the parent ion, harmonics are emitted. The cutoff energy is around I p +3.17U p (U p is the ponderomotive energy, which is proportional to A 2 0 , where A 0 is the amplitude of the vector potential of the laser fields). The HHG has resulted in the birth of attosecond (1 as = 10 −18 s) pulses [4,5] and new imaging tools, such as molecular tomography [6] and spectroscopy [7]. Recent experiments have demonstrated that light-solid interactions offer a wide range of other phenomena and applications to be explored [8][9][10], including HHG from solid-state materials [11][12][13][14][15].Experimental results present a recollision feature in two-color laser fields [16], which is similar to HHG from the gas phase. However, it is also found that the cutoff of HHG from the solid phase depends on the strength E 0 of the laser fields linearly [11], rather than quadratically in the gas phase. Theoretical studies [17,18] show that the cutoff energy of HHG from the solid phase also depends on the laser wavelength λ linearly, rather than λ 2 in the gas phase. Multi-plateau structure in solid HHG has also been found theoretically [17,18] This work introduces a quasi-classical model to investigate the electron dynamic processes under the laser fields in the wave vector k space, which is similar to the three-step model for HHG generated from the atomic and molecular systems in the coordinate space [3].It is also described into three steps: Zener tunneling, electron wave packet oscillation in conduction bands, and an instantaneous electron-hole pair recombination. Since the electron and hole are delocalized, it is unnecessary for them to return to their original positions to emit HHG. The interband nonresonant and resonant Zener tunneling had been studied previously [21,[24][25][26]. The electronhole recollisions have also been observed in e...

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confidence: 99%

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids

Du¹,

Bian²

2017

Opt. Express

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“…[20]. (C 2 ); however, there is no coupling between V and C 2 .Atthe Ŵ point the bandgap between V and C 1 is 3.3 eV.…”

Section: A Description Of Zno Modelmentioning

confidence: 99%

“…The bands were determined by the nonlocal empirical pseudopotential method (NL-EPM) [20]; the complete 3D band in the first Brillouin zone is approximated as the sum over the three one-dimensional bands. Since the wave vector (k ẑ) is much smaller in magnitude than the reciprocal lattice vectors, the dipole approximation is used.…”

Section: A Description Of Zno Modelmentioning

confidence: 99%

Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals

et al. 2015

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Access and use of this website and the material on it are subject to the Terms and Conditions set forth at Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals McDonald, C. R.; Vampa, G.; Corkum, P. B.; Brabec, T.http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=fr L'accès à ce site Web et l'utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D'UTILISER CE SITE WEB. NRC Publications Record / Notice d'Archives des publications de CNRC:http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?action=rtdoc&an=21276996&lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?action=rtdoc&an=21276996&lang=fr READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. Questions? Contact the NRC Publications Archive team atPublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information. NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. For the publisher's version, please access the DOI link below./ Pour consulter la version de l'éditeur, utilisez le lien DOI ci-dessous.http://doi.org/10.1103/PhysRevA.92.033845Physical Review A: Atomic, Molecular, and Optical Physics, 92, 3, 2015-09-23 PHYSICAL REVIEW A 92, 033845 (2015) Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals High harmonic generation in semiconductors is analyzed for high mid-infrared laser intensities for which the electron-hole pair is driven beyond the first Brillouin zone and exhibits Bloch oscillations. We find that even a two-band analysis exhibits second and higher plateaus. Whereas the first plateau is shown to be consistent with high harmonic generation through electron-hole recollision, the higher plateaus arise from dynamic Bloch oscillations; however, the driving process is interband in nature, in contrast to the generally accepted intraband Bloch oscillation mechanism. Energy conservation is fulfilled, as harmonics beyond the first plateau come from a cascaded nonlinearity.

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“…26. Figure 5d also shows the calculated spectra for a cosine band ( (k) = 2.5(1 − coskd) (eV)) demonstrating the sensitivity of the spectrum to the small variation in the band structure.…”

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Observation of high-order harmonic generation in a bulk crystal

et al. 2010

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Harmonic generation is a general feature of driven nonlinear systems. In particular high-order harmonic generation (HHG) in atomic gases 1 is the basis for producing attosecond pulses 2,3 . In molecules and clusters, the existence of multiple ionization and recombination sites makes for richer dynamics allowing imaging of molecular orbitals 4,5 , higher conversion efficiency 6 and the possibility of extending the high-energy cutoff 7 . In the strong-field limit, HHG in bulk crystals is fundamentally different from that in the atomic case owing to the high density and periodic structure. Here we present the first observation of HHG in a bulk crystalline solid using a long-wavelength few-cycle laser. The harmonics spectra extend well beyond the band edge of the ZnO crystal, show a clear non-perturbative character and exhibit a cutoff that scales linearly with the electric field of the drive laser. Our results have important implications for the understanding of attosecond electron dynamics and other non-equilibrium band-structure-related phenomena in strongly driven bulk solids.The HHG spectrum from a gas typically comprises a region of rapidly decreasing low orders that scale perturbatively followed by a slowly varying succession of higher orders that scale nonperturbatively with the strength of the drive laser 1 . At the tunnelling limit of strong-field ionization 8 , the non-perturbative harmonic generation process has been described semiclassically in a recollision model 9,10 consisting of three steps: tunnel ionization of an electron, its acceleration in the laser field, and its recombination to the parent ion with an energy release in the form of higher-energy photons-a coherent process that occurs on successive half-cycles of the laser pulse, leading to emission of odd harmonics. The single-atom maximum photon energy is 9,11h ω max = I p + 3.2U p , where I p is the ionization potential and U p = e 2 E 2 λ 2 /16π 2 mc 2 is the ponderomotive energy of the electron in the laser field. The amplitude of the maximum excursion of a recolliding electron is r max = eEλ 2 /4π 2 mc 2 . For the conditions of our experiments, E = 0.6 V Å −1 at λ = 3.25 µm, the atomic case would be U p = 5 eV and r max = 32 Å. The latter is many times the lattice constant of a typical crystal. Thus, we expect the possibility of ionization from one site and recombination on another; however, because of the lattice periodicity the process would still be coherent. We note that at this field strength, the potential across a lattice constant is comparable to the bandgap of a typical insulator. Therefore, the field cannot be thought of as a small perturbation to the crystal. The non-perturbative HHG from bulk crystals has been considered theoretically 12-14 but has never been observed experimentally until now.Previously, experimental observation of non-perturbative HHG in solids was only in reflection geometry [15][16][17][18] perturbative harmonics below the band edge up to the seventh order were produced by exciting semiconducting ZnSe with...

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Electronic structure of wurtzite ZnO: Nonlocal pseudopotential and ab initio calculations

Cited by 83 publications

References 148 publications

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids

Quasi-classical analysis of the dynamics of the high-order harmonic generation from solids

Interband Bloch oscillation mechanism for high-harmonic generation in semiconductor crystals

Observation of high-order harmonic generation in a bulk crystal

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