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 (Single-layer perovskite structure)

La2CuO4 Sr2IrO4

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

Rotational anisotropy

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)

100μm

Nonlinear optical microscopy images

L. Zhao et al. Nature Phys. 12, 32 (2016)

T = 295 K

Nonlinear optical microscopy images

100μm

L. Zhao et al. Nature Phys. 12, 32 (2016)

T = 175 K

Hidden order domain orientations in Sr2IrO4

Hole doped Sr2Ir1-xRhxO4

J. P. Clancy et al., PRB 89, 054409 (2014)

Doping dependence of TΩ in Sr2Ir1-xRhxO4

L. Zhao et al. Nature Phys. 12, 32 (2016)

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)

a

b a

b

Loss of ac and bc mirror symmetries above 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