Photoelectron from surfaces and nanoparticleswith attosecond-nanometer resolutionQing Liao Aihua Liu Jason Li Hongyu Shi Francisco NavarreteChang-hua Zhang Erfan Saydanzad Marcelo Ambrosio Uwe Thumm

Kansas State University

This work was supported by US National Science Foundation grants PHY 1464417 and PHY 1802085, the Air Force Office ofScientific Research award FA9550-17-1-0369, the Chemical Sciences, Geosciences, and Biosciences Division, Office of BasicEnergy Sciences, Office of Science, U.S. DOE under award DE-FG02-86ER13491, and the Alexander von HumboldtFoundation.

Outline

1. Streaked photoemission

• Methods: S-matrix, SFA,TDSE, semi-class.• Examples: Mg(0001), Mg/W, plasmon dynamics

2. RABBITT interferograms• Electronic structure & dielectric response• Examples: Cu(100/111), Ag(111), Au(111)

3. Plasmonic near-field imaging• Methods: CTMC, S-matrix• Examples: Au, Ag, Cu nanospheres

Ener

gy (

eV)

without Eplas.

Time delay (fs)

PE

Ener

gy

Attosecond physics at the nanoscale Uwe Thumm, KSU 2

Cavalieri,…,Heinzmann, Nature 449 (2007) and refs.

Generation of attosecond XUV pulses

IR pulse

Higherharmonics

as XUV pulse

as XUV (t) + IR (t+τ)target(gas/ solid)

Attosecond physics at the nanoscale 3Uwe Thumm, KSU

Attosecond streak camera

Detector

Atom

IR pulse

Delay τ

XUV pulse Photoelectron

IR pulse @ t=0

XUV pulse @ t=τ

Atom Delay τ

PhotoelectronEnergy

“Attosecond physics of atoms and solids”, U.T., Liao, et al., Handbook of Photonics, Vol.1, Chap. XIII (Wiley, 2015)

Attosecond physics at the nanoscale Uwe Thumm, KSU 4

∆τ

Ph

oto

ele

ctro

n E

ne

rgy

XUV-IR Delay τ

Photoelectron streaking → relative time delays

Level 2

Level 1

Atom

Bin

din

g E

ne

rgy

“Attosecond physics of atoms and solids”, U.T., Liao, et al., Handbook of Photonics, Vol.1, Chap. XIII (Wiley, 2015)

Attosecond physics at the nanoscale Uwe Thumm, KSU 5

amplitude

probability

Liao, U.T., PRL 112, 023602 (2014)

Time-resolved IR-streaked XUV photoemission from metal surfaces

Tk ∼ −∞∞dt ψf t 𝐩 ⋅ 𝐀XUV t + τ ψ𝐤(t)

P = 𝐤 ∈1.𝐵𝑍 Tk2

Initial state: tight-binding, DFT,…

ψ𝐤 𝐫, t ∼ e−i E𝐤 t +i 𝐤 ⋅ 𝐫 u𝐤 (r) + refl. wave

u𝐤 (r) = u𝐤 (r + 𝐑n)

Final state: damped Volkov wave (~SFA)

ψf(𝐫, t)∼ ei [ 𝐤f+ 𝐀IR ] ⋅ 𝐫 + i ϕV(𝐤f,t)

kf,z = 𝑅𝑒 { kf,z } - i / [2 λ(kf)]

ϕV 𝐤f, t =1

2 t∞dτ 𝐤f+ 𝐀IR (τ)

2

damping factor (z<0)

Volkov phase

Attosecond physics at the nanoscale

XUV

IR

bulk vacuum

IR

XUV IAP

|ψ𝐤

|ψf

Uwe Thumm, KSU 6

eikonal approximation

position

Start at (x,t) time

CLSFAEA SSS

),(2/2

~),( txSitikEA

f

EA

etx

Coulomb force

enhanced amplitude relative temporal shift

Zhang, U.T., PRA 82, 043405 (2010) → Generalization (any inhomogeneous external fields): Li, U.T., in preparation

SFA

)''('')',,()',,()',('

tAdtttxxttxxttx IR

t

tfreeIR

Photoemission time delays: analysis of final state modification beyond the SFA (Strong-Field Approx.)

])([

)('

])('[)(

|)(|),(),(

xAK

tAx

txVdtA

k

xVk

t

txSxE

IR

IRIon

IRIon

EAEA

COE

“Coulomb-laser” phase

)()'()]',([

),( 2xOtxx

txxVtdtxS

tfree

freeIonCL

VIon: residual ion potential

“Laser (~Volkov)” phase

Attosecond physics at the nanoscale Uwe Thumm, KSU 7

4f

Time-resolved photoemission from metal surfaces

XUV (t+ τ )

+ IR (t)

XUV (t)

+ IR (t)

IR puls

e

Zhang, Thumm, PRL 102, 123601 (2009)PRA 84, 063403 (2011)

W surface(single crystal)

Attosecond physics at the nanoscale 8Uwe Thumm, KSU

Theory:

Streaked photoemission from W(110) surfaces

as 110a.u. 5~

en

erg

y (e

V)

Zhang, U.T., PRL 102, 123601 (2009)PRA 84, 063403 (2011)

Experiment:

Cavalieri et al., Nature 449, 1029(2007)

as 70110

cond. band

4f core levels

delay (fs)

en

erg

y (e

V)

en

erg

y (e

V)

en

erg

y (e

V)

delay (fs)

cond. band

4f core levels

nm31.0 eV,6.33eV,5.4 eV,35.4 aIE pF

Attosecond physics at the nanoscale

Ossiander et al., Nature 561, 374 (2018)“Absolute” timing of the photoeffect

Δ𝜏 = 63 ± 6 𝑎𝑠 @ ℏ𝜔𝑋𝑈𝑉 = 105 𝑒𝑉

ℏ𝜔𝑋𝑈𝑉 = 91 𝑒𝑉

9Uwe Thumm, KSU

TheoryLiao, U.T., PRL 112,

023602 (2014)

Valence band (VB)

2p core level

ExperimentNeppl et al., PRL 109,

087401 (2012)

XUV: 435 as, 118 eV

NIR: 800 nm, 5 fsCEP = 0

IR-skin depth = 2 ÅMFPs: 4.9 Å for VB

3.7 Å for Mg(2p)

Centers of energy

VB – 2p streaking time delay = 0

Streaked photoemission from Mg(0001) surfaces

Attosecond physics at the nanoscale Uwe Thumm, KSU 10

[1] Neppl et al., Nature 517, 342 (2015)[2] Liao, U.T., PRL 112, 023602 (2014); PRA 92, 031401(R) (2015)

Experiment[1]: 4 ML Theory [2]: 4 ML

Theory [2]: 1 MLExperiment[1]: 1 ML

Mg-coverage-dependent streaking delays

relative to Mg(2p) photoelectrons

Spectra & delays are sensitive to

• electron dispersion in adsorbate

• substrate-adsorbate-interface properties

Streaked photoemission from heterogeneous structures: Mg/W(110)

W(4f) – Mg(2p)

CB – Mg(2p)

substrate adsorbate

Attosecond physics at the nanoscale Uwe Thumm, KSU 11

Sensitivity to collective (plasmonic) excitations in solids

“plasmon wave”

“photoelectron”

Attosecond time-resolved photoemission from solids

Attosecond physics at the nanoscale

Zhang, U.T., PRA 84, 063403 (2011)

12Uwe Thumm, KSU

= static asymptotic limit of

dynamical “plasmon response”:

zzviVzvVHvzV zv

z

z

i

imz

r

implasmonplasmonzim4

1),(),(||

2

1),(

0

int

zzV static

im4

1)(

Static and dynamic image potentials

)()(),( || tvzrtr z

surface-plasmon excitation

bulk-plasmon excitation

Zhang, U.T., PRA 84, 063403 (2011)

Attosecond physics at the nanoscale Uwe Thumm, KSU 13

0 , ..10

eV 10,eV 40

L

sX

ua

Streaked XUV photoemission from Al surface

Instant (static) surface charges

Dynamic surface-charge rearrangement

as 100 stadyn

Towards

time-resolved of collective excitations in solids

zzV static

im4

1)(

),( zim vzV

surf.+bulk plasmon excit.

Static and dynamic image potentials

Zhang & U.T., PRA 84 (2011)U.T., Liao, et al., Handbook of Photonics, Vol.1, Chap. XIII (Wiley, 2015)

Attosecond physics at the nanoscale Uwe Thumm, KSU 14

RABBITT spectra from surfaces

incidentattosecondXUV-pulse train

Photoelectron yield:

RABBITT phase shifts: unknown HH phases

Chen,U.T., Murnane, et al., PNAS 114, E5300 (2017)

ωIR

ωIR

ω2n+1= (2n+1)ωIR

ω2n-1

Sideband 2n

Experiment: Tao et al., Science 353,62 (2016)

Ni(111)

(Reconstruction of Attosecond Beating By Interference of Two-photon Transitions)

Attosecond physics at the nanoscale Uwe Thumm, KSU 15

RABBITT spectra from surfaces

RABBITT phase shifts: unknown HH phases

Kasmi, Keller, et al., Optica 4, 2334 (2017)

Attosecond physics at the nanoscale 16Uwe Thumm, KSU

amplitude

probability

Liao, U.T., PRL 112, 023602 (2014)

Time-resolved interferometric photoemission from metal surfaces

Tk ∼ −∞∞dt ψf t 𝐩 ⋅ 𝐀XUV t + τ ψ𝐤(t)

P = 𝐤 ∈1.𝐵𝑍 Tk2

Final state: damped Volkov wave (~SFA)

ψf(𝐫, t)∼ ei [ 𝐤f+ 𝐀IR ] ⋅ 𝐫 + i ϕV(𝐤f,t)

kf,z = 𝑅𝑒 { kf,z } - i / [2 λ(kf)]

ϕV 𝐤f, t =1

2 t∞dτ 𝐤f+ 𝐀IR (τ)

2

damping factor (z<0)

Volkov phase

Attosecond physics at the nanoscale

XUV

IR

bulk vacuum

IR

|ψ𝐤

|ψf

XUV APT

Initial state: tight-binding, DFT,…

ψ𝐤 𝐫, t ∼ e−i E𝐤 t +i 𝐤 ⋅ 𝐫 u𝐤 (r) + refl. wave

u𝐤 (r) = u𝐤 (r + 𝐑n)

Uwe Thumm, KSU 17

e.g. “Chulkov potential” (LDA fit)

Surface electronic structure

ARPES experiment:Roth et al., J. Electron Spectrosc. 208, 2 (2016)

→ Occupied states

Cu(111)Expt.

Cu(100)Expt.

Ambrosio, U.T., PRA 94, 063424 (2016)

Attosecond physics at the nanoscale Uwe Thumm, KSU 18

RABBITT spectra from Cu surfaces XUV-background subtracted

Band structure

• Fresnel reflection matters• IR pulse attenuation affects surface states

less than bulk states

Theory: Ambrosio, U.T., PRA 94, 063424 (2016); PRA 96, 051403 (2017)Expt.: Lucchini, Keller, et al., PRL 115, 137401 (2015)

Cu RABBITT phasesrelative to Cu(111)surface state

Cu(111) RABBITT phases relative to gaseous Ne(15o and 75o incidence)

TB: tight binding modelMC: class. Monte Carlo model

Attosecond physics at the nanoscale Uwe Thumm, KSU 19

RABBITT spectra from Cu(111) surfaces Final-state - solid interaction effects

Theory: Ambrosio, U.T., PRA 96, 051403 (2017) & to be submittedExpt.: Kasmi,…, Keller, et al., Optica 4, 1492 (2017)

Attosecond physics at the nanoscale Uwe Thumm, KSU 20

Final-state resonance in substrate potential:

• enhances SB 20 yield

• significantly increases RABBITT phase shift

L: lower 3d bandU: upper 3d band

L

U

RABBITT spectra from Au(111) surfaces

RABBITT phases relative to Ar gas target

Expt:Locher, Keller et al., Optica 2, 21323(2015)

Theory: Tight binding. Gen. Sturmian basis. Ambrosio, U.T. in prep.

• Ar RABBITT phases calculated by Mauritsson etal., PRA 72, 013401 (2005) subtracted from ourcalculated Au(111) phases.

• Calculated RABBITT spectrum includes a delayindependent IR and XUV background.

Ambrosio, U.T., PRA 97, 043431 (2018)Attosecond physics at the nanoscale Uwe Thumm, KSU 21

Imaging plasmonic fields near Au nano-spheres in streaked photoelectron spectra

3. Probing collective electronic dynamics in nano-particles

Leone, U.T. et al., Nat. Photon. 8,162 (2014)

QM model: Li, Saydanzad, U.T., PRA 95, 043423 (2017)

CTMC model: Saydanzad, Li, U.T., PRA 95, 053406 (2017)

QM model: Li, Saydanzad, U.T., PRL 120, 223903 (2018)

Plasmonic near field emhancement

EIR

Plasmonic field enhancement 𝜼 and phase shift𝝓

-50 0 50 z [nm]

50

0

-50

x [

nm

]

0

1

2

3

4 EIR,inc

D

QM model: Li, Saydanzad, U. T., PRA 94, 0514101(R) (2016)

Plasmonic near-field calculation

• Mie, Ann. Phys. 25, 377 (1908)

• Dielectric response ε(ω) from exp. data:

Palik & Hunter (1985)

EIR, tot = EIR, inc + Eplas ( D, ω )

Attosecond physics at the nanoscale Uwe Thumm, KSU 23

Classical modeling

𝑉(𝑟)

𝑟𝑟 = 𝑎

WV0

te ts tftime

εxuv

εCB

1-Photoelectron excitation 2-Transport to the surface

3-Escape from the surface 4-Propagation to the detector

εF

Fermi level

Excitation Arrival at surface

Detection

2

3

1𝑟0

Detector

4

Attosecond physics at the nanoscale

Probing collective electronic dynamics in nano-particles with streaked photoemission

24Uwe Thumm, KSU

CTMC model: Saydanzad, Li, U.T., PRA 95, 053406 (2017)

QM model: Li, Saydanzad , U.T., PRL 120, 223903 (2018)

Numerical model

Final state Ψ𝐤f 𝐫, t

• Streaking-field dressed “generalized” Volkov state

• Plasmonically enhanced streaking field enters Volkovphase.

r

V

Ψ𝐤 𝐫, t

Ψ𝐤fτ 𝐫, t

ɛF

W

𝐄XUV 𝐫, t

T𝐤 𝐤f, τ = −i dt Ψ𝐤fτ 𝐫, t 𝐀XUV 𝐫, t ∙ 𝐩 Ψ𝐤 𝐫, t

ϕ𝑉 =1

2 𝑡

∞

𝑑𝑡 𝒌𝑓 + 𝑡

∞

𝑑𝑡 𝑬𝐼𝑅,𝑡𝑜𝑡 𝒓, 𝑡

2

Gaussian XUV pulse 𝐄XUV 𝐫, t

• Au nanosphere considered transparent XUV pulse

Initial state Ψ𝐤 𝐫, t

• Bound states in Au conduction band below 𝜀𝐹𝑒𝑟𝑚𝑖

P εf, τ =

𝐤∈occ

T𝐤 𝐤f, τ2

Li, Saydanzad , U.T., PRA 95, 043423 (2017); PRL 120, 223903 (2018)

Effective potential(sph. Square well, DFT, etc)

Attosecond physics at the nanoscale Uwe Thumm, KSU 25

from Palik & Hunter (1985)

ωplas

Retrieving plasmonic enhancements and phase shifts from streaked photoelectron spectra

permittivity x: retrieved EIR, tot

max. polarizability:Re[ε(ωplas)] = -2

Au

Centers of energy

streaked spectrawith/without Eplas

Li, Saydanzad , U.T., PRA 95, 043423 (2017)

EIR, tot = EIR, inc + Eplas ( D, ω )

Attosecond physics at the nanoscale Uwe Thumm, KSU 26

4D-streaked imaging of plasmonic fields

Reconstruction algorithm

𝐄𝐈𝐑, 𝐭𝐨𝐭 𝛉,𝛗, 𝛕 =𝜕

𝜕τ

𝓔𝐟 𝛕; 𝛉,𝛗 − ωX − 3 5 σc − V0

2 𝓔𝐟 𝛕; 𝛉,𝛗

𝓔𝐟 𝛕; 𝛉,𝛗 : Photoelectron spectral center of energy

ωX: XUV central photon energy (50 eV)

σc: Conduction-band width (8 eV)

V0: Conduction-band model potential depth (-13.1 eV)

Li, Saydanzad , U.T., PRL 120, 223903 (2018)

Attosecond physics at the nanoscale Uwe Thumm, KSU 27

All targets• Interpretation of streaking time delays & RABBITT phases

Surfaces/nanoparticlesDependence of photoemission and time delay on • electron propagation/dispersion • accurate final state modeling • IR /XUV skin depth, surface charges, …

Imaging plasmonic near-fields:• exp. validation of spatio-temporal near-field imaging

• plasmon response / collective modes

Field-dressed band-structure • atomic resolution in space & time• towards time-resolved ARPES….

Challenges & opportunities

Attosecond physics at the nanoscale 28Uwe Thumm, KSU