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Revealing Hidden Order in the Pseudogap Region using Nonlinear Optics
David Hsieh Institute for Quantum Information and Matter
Department of Physics, Caltech
Frontiers of Quantum Materials Rice University
11/4/2016
The pseudogap phase in the cuprates and iridates
Nonlinear optical harmonic generation
Results on Sr2IrO4
Outline
Comparison to YBa2Cu3Oy
The cuprate phase diagram
B. Keimer et al., Nature Review 518, 179 (2015)
Nematic order
Loop-current order
Sr2IrO4
T*
Pseudogap Te
mpe
ratu
re
AFM
insu
lato
r
TN
Pseudogap observations
Exotic phases in iridates?
Doping
d-wave gap observations Y. K. Kim et al., Nature Phys. 12, 37 (2016)
Y. J. Yan et al., Phys. Rev. X 5, 041018 (2015)
Y. Cao et al., Nat. Commun. 7, 11367 (2016)
A. de la Torre et al., PRL 115, 176402 (2015)
Y. K. Kim et al., Science 345, 187 (2014)
Neumann’s principle
A tensor describing any physical property of a crystal must be invariant under all symmetry operations of the crystal
𝜒𝜒𝑥𝑥𝑥𝑥 𝜒𝜒𝑥𝑥𝑦𝑦 𝜒𝜒𝑥𝑥𝑧𝑧𝜒𝜒𝑦𝑦𝑥𝑥 𝜒𝜒𝑦𝑦𝑦𝑦 𝜒𝜒𝑦𝑦𝑧𝑧𝜒𝜒𝑧𝑧𝑥𝑥 𝜒𝜒𝑧𝑧𝑦𝑦 𝜒𝜒𝑧𝑧𝑧𝑧
𝜒𝜒𝑥𝑥𝑥𝑥 0 0
0 𝜒𝜒𝑥𝑥𝑥𝑥 00 0 𝜒𝜒𝑥𝑥𝑥𝑥
7
6
3
4
3*
0
0
Tetragonal Trigonal Hexagonal 2
# elem.
R. W. Boyd Nonlinear Optics (Academic Press 2003)
Higher rank tensors → greater symmetry resolution
Nonlinear optics
Multipole expansion of radiation source term
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ...+++++= ωωχωωχωωχωχωχ kjemmijkkj
eemijkkj
eeeijkj
emijj
eeiji HHHEEEHEP
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ...+++++= ωωχωωχωωχωχωχ kjmmmijkkj
memijkkj
meeijkj
mmijj
meiji HHHEEEHEM
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ...ˆ +++++= ωωχωωχωωχωχωχ lkqmmijkllk
qemijkllk
qeeijklk
qmijkk
qeijkij HHHEEEHEQ
1st order responses 2nd order responses
Expansion of electric dipole (P), magnetic dipole (M) and electric quadrupole (Q) contributions
2ω
( ) ( ) ( )ωωχω kjEDijki EEP =2
( ) ( )ωωχ lkjEQijkl EE ∇+
...+
even if system has inversion symmetry much weaker than ED contribution (~λ/a)
0≠EQijklχ
if system has inversion symmetry 0=EDijkχ
Optical second harmonic generation (SHG)
ω
ω
( ) ( )ωχω jEDiji EP =
T
Iω
Global inversion breaking
Nor
m. i
nten
sity
( )ωχ jEDij E
( )ωχ jEDij E
I2ω
( ) ( )ωωχ kjEDijk EE+
( ) ( )ωωχ lkjEQijkl EE ∇
( ) ( )ωωχ lkjEQijkl EE ∇
Signature of global inversion symmetry breaking
Sample environment challenge: Low temperature High magnetic field High pressure
Technical limitations of conventional RA experiments
Alignment challenge: Beam walk on sample Precession of reflected light Need large area flat single crystals (e.g. epitaxial thin-films)
100μm
Rh-Sr2IrO4
GaAs wafer qdlaser.com
Rotating scattering plane based RA technique
J. Harter et al., Opt. Lett. 40, 4671 (2015)
D. H. Torchinsky et al., Rev. Sci. Instrum. 85, 083102 (2014)
Ti:sapph regen pumped OPA (~100 fs)
J. Harter et al., Opt. Lett. 40, 4671 (2015)
High speed/ high sensitivity RA data acquisition
RA-SHG from GaAs(001)
RA-SHG data from Sr2IrO4 (001) at T = 295 K
4/mmm Proposed
Q. Huang et al., J. Sol. State. Chem. 112, 355 (1994)
centrosymmetric (bulk EQ)
1 2
D. H. Torchinsky et al. PRL 114, 096404 (2015)
corroborated by neutron: Ye et al. PRB 92, 201112(R) (2015)
4/m centrosymmetric (bulk EQ)
1 2
RA-SHG data at T = 295 K
C4 Rotational sym.
χEQ E E Δ
cryst. 4/m (C4h)
Inversion sym.
L. Zhao et al. Nature Phys. 12, 32 (2016)
I SS(ω
) Nor
m.
Hidden symmetry breaking below TΩ
ω
T ( K ) L. Zhao et al. Nature Phys. 12, 32 (2016)
Hidden symmetry breaking below TΩ
I PS (2
ω) N
orm
.
T ( K )
TΩ ∼ 232K 2ω
ω
I SS(ω
) Nor
m.
L. Zhao et al. Nature Phys. 12, 32 (2016)
RA-SHG data at T = 170 K
χEQ E E + χED E E Δ
cryst. 4/m
magn. 2′/m (m1′) C1
Rotational sym.
Inversion sym.
L. Zhao et al. Nature Phys. 12, 32 (2016)
Ir
O
+
−
C4 C1 & Broken Inv. & T. R. +
−
+
− +
−
180o
Ref: C. M. Varma PRB, 55, 14554 (1997) C. M. Varma PRL, 83, 3538 (1999) C. M. Varma PRB, 73, 155113 (2006) C. Weber et al. PRL, 102, 017005 (2009) J. Orenstein PRL, 107, 067002 (2011) V. Yakovenko Physica B, 460, 159 (2015)
Properties: Q = 0 ; No Net Magnetization per unit cell;
Non-Dipolar; Domain Average.
Symmetries of ΘII loop current order (magneto-electric)
Phase diagram of Sr2Ir1-xRhxO4
L. Zhao et al. Nature Phys. 12, 32 (2016)
T. Qi et al., PRB 86, 125105 (2012)
J. P. Clancy et al., PRB 89, 054409 (2014)
Y. Cao et al., Nat. Commun. 7, 11367 (2016)
polar Kerr effect
Xia 2008
superconductivity
pseudogap
Tc
50
150
250
350
0.05 0.10 0.15 0.20 0.25
T ( K
)
p (per planar Cu atom)
CDW onset from X-ray diffraction
Blanco-Canosa 2014 Hucker 2014
6.34 6.55 6.86 7.00
y (oxygen doping)
Strange metal
Orthorhombic mmm (centrosymmetric)
resonant ultrasound (Shekhter 2013)
Thermodynamic phase transition
Across T*, evidence for:
polarized neutron scattering (Fauque 2006 , Mook 2008)
Time-reversal symmetry breaking
THz polarimetery (Lubashevsky 2014)
Mirror (ac & bc) symmetry breaking
Nernst effect (Daou 2010)
Rotational symmetry breaking C4 → C2
Symmetry breaking across T* in YBa2Cu3O6+x
( )ωχ jEDij E
( ) ( )ωωχ lkjEQijkl EE ∇
Experimental layout and anticipated results for T > T*
L. Zhao et al. Nature Phys. (in press)
Nor
mal
ized
Inte
nsiti
es
T ( K )
y = 6.67
TΩ ~ 205 K
100 150 200 250
1
1.5
2.0 Iω I2ω
Broken inversion symmetry
Evidence for broken inversion symmetry
L. Zhao et al. Nature Phys. (in press)
polarized neutron scattering
Nernst effect
THz polarimetery
resonant ultrasound
polar Kerr effect
superconductivity
pseudogap
Tc
50
150
250
350
0.05 0.10 0.15 0.20 0.25
T ( K
)
p (per planar Cu atom)
CDW onset from X-ray diffraction
6.34 6.55 6.86 7.00
y (oxygen doping)
y = 7.0
TΩ ~ 60 K
y = 6.92
TΩ ~ 110 K
y = 6.75
TΩ ~ 190 K
y = 6.67
TΩ ~ 205 K
1
1.5
2.0
100 150 200 250
50 100 150 200 100 150 200 250
1
1.5
2.0
Nor
mal
ized
Inte
nsiti
es
T ( K ) 50 100 150
Iω I2ω
No anomalies at Tc, TCDW or TKerr
SHG (current work)
Evidence for broken inversion symmetry below T*
L. Zhao et al. Nature Phys. (in press)
Nonlinear optical response is a highly sensitive probe of bulk structural and electronic symmetry breaking.
Conclusions and Outlook
Complementary to neutron and (non-) resonant x-ray diffraction. Small crystals Spatial resolution Multipolar order parameters Strong neutron absorbers (e.g. Ir)
Recently extended to ultrafast time domain to search for dynamically induced symmetry breaking
A. de la Torre et al., in preparation
Pseudogap in both Sr2IrO4 and YBa2Cu3Oy consistent with loss of inversion and all rotational symmetries.
U. Kentucky Gang Cao Tongfei Qi
U. Minnesota Natalia Perkins Yuriy Sizyuk
Acknowledgements
Iowa State U. Rebecca Flint
U. Tel Aviv Ron Lifshitz Dr. Liuyan Zhao Dr. John Harter
Hao Chu Dr. Darius Torchinsky (Asst. Prof Temple U.)
UCSB Stephen Wilson
Tom Hogan
UBC Ruixing Liang
Doug Bonn Walter Hardy
Johns Hopkins Peter Armitage Carina Belvin, Lauren Niu, Anthony Woss