Optical second-harmonic generation selection rules and resonances in buried oxide interfaces: the case of LaAlO_3/SrTiO_3

Abstract

Despite an intense research effort, the physical mechanism underlying the formation of a quasi-two-dimensional electron gas at the interface between the band insulators LaAlO 3 and SrTiO 3 is still not fully understood. Interfacesensitive optical second-harmonic spectroscopy can shed light on this mechanism, by accessing specific information on the orbital and structural reconstruction taking place at the interface that is not accessible by other techniques, and in particular by transport measurements. Here we present a detailed theoretical analysis of the spectral transitions that are most relevant in the second-order nonlinear optical response of oxide interfaces with a square symmetry, in general. In particular, we discuss the case of LaAlO 3 ∕SrTiO 3 interfaces, using symmetry arguments to derive specific selection rules, which have strong consequences on the second-harmonic spectra recorded with different input/output polarization combinations of light. These selection rules may in particular explain recent experimental findings.

Investigation of Electric Field–Induced Structural Changes at Fe-Doped SrTiO3 Anode Interfaces by Second Harmonic Generation

“…Solving for $P\left(2\omega \right)$, the effective second-order susceptibility for the interface can be written out explicitly using [15,23,24]: ${\chi }_{eff}^{\left(2\right)}=false\langle \overleftrightarrow{L}\left(2\omega \right)\cdot \hat{e}\left(2\omega \right)false\rangle \cdot \frac{P\left(2\omega \right)}{2{\epsilon }_o{\left(E^{\omega }\right)}^2}$…”

“…The SHG intensities, $I_p^{2\omega }\left(\phi \right)$ and $I_s^{2\omega }\left(\phi \right)$, can then be written as functions of the incident light polarization angle, $\phi$, by following $I^{2\omega }\propto {\left|E\left(2\omega \right)\right|}^2\propto {\left|{\chi }_{eff}^{\left(2\right)}\right|}^2$ and selecting outgoing SHG electric field polarizations either parallel to the y -axis ( s -polarized) or the xz -plane ( p -polarized) [24,25]: $I_p^{2\omega }\left(\phi \right)={\left|{\chi }_{pp}co{s}^2\phi +{\chi }_{sp}si{n}^2\phi \right|}^2$ $I_s^{2\omega }\left(\phi \right)={\left|{\chi }_{ds}sin\left(2\phi \right)\right|}^2$ where ${\chi }_{sp}={\chi }_{zxx}^{eff}{L}_{zz}^{2\omega }{\left(L_{yy}^{\omega }\right)}^2\sin \theta$${\chi }_{pp}={\chi }_{zzz}^{eff}{L}_{zz}^{2\omega }{\left(L_{zz}^{\omega }\right)}^{2}si{n}^3\theta -2{\chi }_{xxz}^{eff}{L}_{xx}^{2\omega }{L}_{xx}^{\omega }{L}_{zz}^{\omega }\sin \theta co{s}^{}$…”

Formation of structural defects and strain in electrodegraded Fe‐doped SrTiO3 crystals due to oxygen vacancy migration

“…As a non‐destructive nonlinear technique, optical second harmonic generation (SHG) has been successfully utilized to study structural symmetry at perovskite‐type oxide surfaces, interfaces, and bulk regions . Most recently, our group used the optical SHG technique to characterize ionic defect and strain distributions across the electrodegraded interfaces and bulk regions of Fe‐doped SrTiO 3 (Fe:STO) single crystals .…”

Potential-well depth at amorphous-LaAlO3/crystalline-SrTiO3 interfaces measured by optical second harmonic generation

“…These two types of interfaces are investigated here by resorting to optical second harmonic generation (SHG), a technique which recently has been applied to studying c-LAO/STO interfaces. [16][17][18][19][20][21][22] In SHG, an optical wave with frequency 2x is generated from an incident wave of frequency x. For this process to occur, a breaking of the material inversion symmetry is needed.…”

“…In accordance with the four-fold rotational symmetry of the interface, we measured the only three independent non-vanishing SHG components: P-in Pout (PP), S-in P-out (SP), and D-in S-out (DS). 21 In Fig. 1, we show the sheet conductance and the SHG intensity as a function of t LAO .…”