Optical second-harmonic generation selection rules and resonances in buried oxide interfaces: the case of LaAlO<sub>3</sub>/SrTiO<sub>3</sub>

Domenico Paparo; Andrea Rubano; Lorenzo Marrucci

doi:10.1364/JOSAB.30.002452

Journal of the Optical Society of America B
Vol. 30,
Issue 9,
pp. 2452-2460
(2013)
•https://doi.org/10.1364/JOSAB.30.002452

Optical second-harmonic generation selection rules and resonances in buried oxide interfaces: the case of LaAlO₃/SrTiO₃

Domenico Paparo, Andrea Rubano, and Lorenzo Marrucci

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Domenico Paparo, Andrea Rubano, and Lorenzo Marrucci, "Optical second-harmonic generation selection rules and resonances in buried oxide interfaces: the case of LaAlO₃/SrTiO₃," J. Opt. Soc. Am. B 30, 2452-2460 (2013)

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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. Interface-sensitive 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.

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$χ^{2}$ Elements	Resonant State $a$	Resonant State $b$	Nonresonant State $n$
$ω$ resonance
$χ_{z z z}$	S	S	S
$χ_{z z z}$	E	E	E
$χ_{z x x}$	S	E	E
	S	E	S
	E	S	E
	E	S	S
$χ_{x x z}$	S	S	E
	E	E	S
	S	E	S
	S	E	E
	E	S	S
	E	S	E
$2 ω$ resonance
$χ_{z z z}$	S	S	S
$χ_{z z z}$	E	E	E
$χ_{z x x}$	S	S	E
$χ_{z x x}$	E	E	S
$χ_{x x z}$	S	E	S
	E	S	S
	E	S	E
	S	E	E

$χ^{2}$ Elements	Resonant State $a$	Resonant State $b$	Nonresonant State $n$
$χ_{z z z}$	O $p_{z}$ ( $A_{1}$ )	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$A_{1}$
	O $p_{z}$ ( $B_{1}$ )	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$B_{1}$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$E$	$⋄$
$χ_{z x x}$	O $p_{z}$ (2 $A_{1}$ sin.)	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$E$
	O $p_{z}$ ( $B_{1}$ )	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$A_{1}$ , $A_{2}$ , $B_{1}$ , $B_{2}$	$⋄$
$χ_{x x z}$	O $p_{z}$ (2 $A_{1}$ sin.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$A_{1}$ , $E$	$⋄$
	O $p_{z}$ ( $B_{1}$ )	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$B_{1}$ , $E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x y}$ ( $B_{2}$ )	$B_{2}$ , $E$	$⋄$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$A_{1}$ , $E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$B_{1}$ , $E$

$χ^{2}$ Elements	Resonant State $a$	Resonant State $b$	Nonresonant State $n$
$ω$ resonance
$χ_{z z z}$	S	S	S
$χ_{z z z}$	E	E	E
$χ_{z x x}$	S	E	E
	S	E	S
	E	S	E
	E	S	S
$χ_{x x z}$	S	S	E
	E	E	S
	S	E	S
	S	E	E
	E	S	S
	E	S	E
$2 ω$ resonance
$χ_{z z z}$	S	S	S
$χ_{z z z}$	E	E	E
$χ_{z x x}$	S	S	E
$χ_{z x x}$	E	E	S
$χ_{x x z}$	S	E	S
	E	S	S
	E	S	E
	S	E	E

$χ^{2}$ Elements	Resonant State $a$	Resonant State $b$	Nonresonant State $n$
$χ_{z z z}$	O $p_{z}$ ( $A_{1}$ )	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$A_{1}$
	O $p_{z}$ ( $B_{1}$ )	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$B_{1}$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$E$	$⋄$
$χ_{z x x}$	O $p_{z}$ (2 $A_{1}$ sin.)	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$E$
	O $p_{z}$ ( $B_{1}$ )	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$A_{1}$ , $A_{2}$ , $B_{1}$ , $B_{2}$	$⋄$
$χ_{x x z}$	O $p_{z}$ (2 $A_{1}$ sin.)	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$A_{1}$ , $E$	$⋄$
	O $p_{z}$ ( $B_{1}$ )	Ti- $t_{2 g} d_{x z}$ , $d_{y z}$ ( $E$ )	$B_{1}$ , $E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $t_{2 g} d_{x y}$ ( $B_{2}$ )	$B_{2}$ , $E$	$⋄$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $e_{g} d_{z^{2}}$ ( $A_{1}$ )	$A_{1}$ , $E$
	O $p_{x}$ , $p_{y}$ (3 $E$ dup.)	Ti- $e_{g} d_{x^{2} - y^{2}}$ ( $B_{1}$ )	$B_{1}$ , $E$

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Equations (16)

Journal of the Optical Society of America B