Superscattering of pseudospin-1 wave in a photonic lattice

Ying-Cheng Lai Arizona State University Collaborator: Dr. Hongya Xu, ASU Funding: • F9550-15-1-0151 (AFOSR) • N00014-16-1-2828 (Vannevar Bush Faculty Fellowship) DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 1 Born approximation

Incident field ~ total field, as the driving field at each point in the scatterer - weak scattering field

Conventional wisdom: · 2D spinor wave system (e.g., ) a weak scatterer Wu and Fogler, PRB 90, 235402 (2014) -> a small scattering cross section 2 2 -> weak scattering Str / R @ (p / 4)(V0 R) (kR) · Optics - equivalent to the Rayleigh-Gans approximation Newton, Scattering Theory of Waves and Particles, Springer (1982) S / (p R2 ) @ n -1 2 (kR)4 for kR n -1 <<1

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 2 A photonic lattice to realize superscattering

Al2O3 rods triangular photonic lattice

dielectric constant 8.8

a1 = 17 mm r1 = 0.203 a1

a2 = 0.8 a1 r2 =0.203 a2

degeneracy at ~11.22 GHz

Pseudo-angular momentum operator

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 3 Superscattering

x pseudospin-1 resonances

none Born Scatterer size Scatterer Approx. resonances pseudospin-1/2 x º kR

weak strong

Scatterer Strength r ºV0R

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 4 Superscattering

r ºV0R = 0.1

Theory BA Theory 10-3 < x < 0.1 DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 5 Superscattering – intuitive understanding

Magnification

pseudospin-1/2 wave pseudospin-1 wave

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 6 Why is superscattering remarkable?

Conventional wisdom Scattering Cross Section r 2 x2 - light (Rayleigh-Gans Approximation [1]) µ{ Geometric Section r 2 x - 2D matter wave (Born Approximation [2]) for x <<1 and r <<1 풏 − ퟏ 풙, 풍풊품풉풕 𝝆 = 푽ퟎ푹, 풎풂풕풕풆풓 풘풂풗풆 Our result 풙 = 풌푹 Scattering Cross Section 16 µ H.-Y. Xu and Y.-C. Lai, “Superscattering of Geometric Section r pseudospin-1 wave in a photonic lattice,” for x » 0.5r Phys. Rev. A 95, 012119 (2017).

Take-home message : Strong scattering can occur for arbitrarily weak scatterer

[1] R. Newton, Scattering Theory of Waves and Particles, (Dover Publications, 1982). [2] L. I. Schiff, (McGraw-Hill, 1968), 3rd ed.

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 7 Valley quantum numbers

Valleys: extrema points in a bandstructure Application: Valleytronics

Graphene MoS2

K K’ Valleys in graphene act as an ideal two state system (analogous to )

K Spin up 0  two states: K’ down 1

 large separation a = 0.246nm, K~ퟒ/풂

Valleys are another uncharged degree of freedom (DOF) K

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 8 Appealing features of valleytronics

Valleytronics [c.f. ]: an emerging frontier research field based on promising “multi-valley” materials, e.g. graphene, MoS2 etc. K’ K

Motivations • Information encoding: (alternative carriers of information) robust against charged or valley-free perturbations/disorders

• Energy issue (low dissipation): valley currents can be charge neutral  no/low Joule (ohmic) heat K’ e- Charge current Valley current J ≠ 0 , J = 0 K e- v c Jc = JK + Jk’ Jv = JK – JK’

Objective: manipulate and harness the valleys to generate valley polarization/filtering and currents  information storage, valley-current generators

How ?  Valley Hall effect [c.f. Spin Hall effect]: charge – valley currents conversion D. Xiao, et al., PRL 99, 236809 (2007)

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 9 Geometric Valley Hall Effect: Intuitive Understanding

Berry Connection (k-space) Vector field (real space) gauge dependent 휦 =< 휓|푖훻풌|휓 > A(r)

Berry curvature Magnetic field 휴 = 훻 × 휦 Deflecting Force gauge B = 훻 × 푨 invariant Berry’s “Lorentz force” Lorentz force Anomalous/spin/valley Hall effect Ordinary Hall effect (intrinsic type) Berry phase AB phase gauge Φ = 풅풓 ∙ 푨 = 풅풔 ∙ 푩 Φ퐵= 풅풌 ∙ 횲 = 풅𝝈 ∙ 휴 퐴퐵 invariant

Magnetic flux Berry flux Confined/singular magnetic flux: Singular Berry flux vanishing B-force, but AB effect persists

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 10 Geometric Valley Hall Effect (gVHE)

Flux tube: singular Berry flux Flux tube: generated by a particular singular/confined Magnetic conical intersection/singularity flux generated by an (Dirac-like point) infinitely narrow solenoid

Our finding: Singular fractional Berry flux defined geometric valley Hall effect (gVHE)

Features of gVHE

• Vanishing Berry curvatures: no anomalous “deflecting force” • Exceptional skew scattering mechanism: skewing valleys using scalar-type potentials without any valley-resolved perturbations, leading to valley-contrasting spatial interference patterns at scattering resonances  efficient valley filters • Still, it is Berry (geometric) phase which underlies valley-contrasting transport: robustness

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 11 Valley filtering

Result: Efficient valley filtering through resonant skew scattering

Far-field

Near field

Valley-independent scalar-type scatterer!

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 12 Valley filtering

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 13 What materials can be used to realize gVHE?

훼 − 푇3 Lattice: Interpolation between honeycomb and dice lattice First proposed by Raoux et al. in PRL 112, 026402 (2014)

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 14 Potential experimental realization

Proposal of experiment realization: Optical lattice & ultracold gas of fermionic atoms Raoux et al., PRL 112, 026402 (2014) • Three pairs of lasers beams of 2π/3 apart, with electric field linearly polarized in the xy plane: interfere to produce an optical potential with intensity given by

Dice lattice potential

• Dephasing one of the three pairs of lasers by φ gives

훼 − 푇3 lattice

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 15 Geometric valley Hall effect & valley filtering: summary

Finding: geometric valley Hall effect arising from fractional Berry phase y

x e- Transverse - e Jc = JK + Jk’

Jv = JK – JK’

Finite valley Hall current with zero • Vanishing Berry curvatures Hall voltage • Bulk gapless phase with massless carriers  faster valley transport (vanishing charge • Valley skew scattering from valley-free scatterers: more tunable Hall current) • Berry-phase based geometric origin: robust against disorder averaging & thermal fluctuations • H.-Y. Xu and Y.-C. Lai, “Geometric valley Hall effect and filtering with singular fractional Berry flux,” preprint (2017). • Effects of many body interactions on gVHE & valley filtering – ongoing collaborative work with Dr. Danhong Huang, AFRL

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 16 Publications after 2016 PI meeting (FA9550-15-1-0151, N00014-16-1-2828 )

2D Dirac material systems • H.-Y,. Xu and Y.-C. Lai, “Revival resonant scattering, perfect caustics and isotropic transport of pseudospin-1 particles,” Physical Review B 94, 165405 (2016). • P. Yu, Z.-Y. Li, H.-Y. Xu, L. Huang, B. Dietz, C. Grebogi, and Y.-C. Lai, “Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiarads,” Physical Review E 94, 062214 (2016). • L. Ying and Y.-C. Lai, “Robustness of persistent currents in two-dimensional Dirac systems with disorders,” Physical Review B, revised. Photonic systems and optomechanics • G.-L. Wang, Y.-C. Lai, and C. Grebogi, “Transient chaos – a resolution of breakdown of quantum-classical correspondence in optomechanics,” Scientific Reports 6, 35381 (2016). • H.-Y. Xu and Y.-C. Lai, “Superscattering of pseudospin-1 wave in a photonic lattice,” Physical Review A 95, 012119 (2017). • G.-L. Wang, H.-Y. Xu, L. Huang, and Y.-C. Lai, “Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems,” New Journal of Physics, in press. Complex fluids • S. Altmeyer, Y.-H. Do, and Y.-C. Lai, “Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio,” Scientific Reports 7, 40012 (2017).

DISTRIBUTION STATEMENT A – Unclassified, Unlimited Distribution 17