EXPERIMENTELLE PHYSIKEXPERIMENTELLE
PHYSIKVIIII

Unscrambling orbital character and spin:
The importance of the final state
CORPES17
Hiroshima
6. July 2017Friedel Reinert
reinert@physik.uni-wuerzburg.de

Acknowledgments
Würzburg Group: SARPES experiments- Hendrik Bentmannwith Henriette Maaß, Christoph Seibel, Thiago Peixoto
Photoemission theory:- E. Krasovskii (San Sebastian)- J. Braun, H. Ebert, J. Minar (LMU, UWB)
Synchrotron radiation experiments- Kenya Shimada, Taichi Okuda, Masashi Arita (HiSOR)- T. Balasubramanian, M. Leandersson (MAXLAB)MPI Halle, Forschungszentrum Jülich: Momentum Microscope- Christian Tusche

Friedel Reinert

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Motivation: Spin-split electronic structure
Quantum Anomalous Hall effect

Quantum Spin Hall effectRashba effectSpin-Hall effect

2D

Weyl semimetal

Spin-Orbit Coupling (SOC)

spin-polarization of electronicstates→ origin of non-trivial topology

Spin transistor

Topological insulator
Topological Kondo insulator

direct spectroscopy by spinand angle-resolved
photoemission
3D

Friedel Reinert

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ARPES on systems with strong
spin-orbit coupling
Complications by initial state→ linear dichroism

Importance of the final state→ photoelectron polarization

Friedel Reinert

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How to address intrinsic spin properties by photoemission?
Circular dichroism (indirectly)

Scholz et al., Phys. Rev. Lett. 110, 216801 (2013)

H. Ebert→ „final state effect“, dichroism depends on excitation energy
Photoelectron spin polarizatione-hv

Hsieh et al., Nature 460, 1101-1105 (2009)→ also dependence on photoemission process?
Friedel ReinertSARPES & Photoemission Final State

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Spin- and angle-resolved photoelectron spectroscopy
Bi2Te3Sb2Te3e-hv

intrinsic spin?

photoelectron spin

PRL 114 (2015) 066802• electronic structure probed withsimultaneous energy,momentum, and spin sensitivity
kykykxkx
Friedel Reinert• relation between intrinsic andphotoelectron spin texture?
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Light-polarization dependence of photoelectron spin
Fermi surface of TSS in Bi2Te2Se

expected spin texture

hv = 6 eVs-polkz

kykx

kykx

p-polkzkykx

Nature Commun. 7 (2016) 11621

Friedel Reinert

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9

Experiment vs. one-step photoemission theorys-polkz

hv = 6 eV

hv = 6 eV

hv = 6 eV

hv = 6 eV

s-pol

p-pol

kykx

p-polkz

kykx

Calculations by Jürgen Braunand Jan Minar (LMU, UWB)Friedel Reinert

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10

Spin-orbit coupling in Bloch wave functions

EnergyBloch wave:

Wave vector kBloch wave with spin-orbit interaction:

when k inmirror plane:

Henk et al., PRB68 (2003) 165416
Friedel Reinert

keven

odd

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Dipole selection rules and spin-orbit coupling
yeven

Dipole matrix element:

oddx

p-pol

s-polkz

kykx

s-pol
p-polkzkykx

Nature Commun. 7, 11621 (2016)Friedel Reinert

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Dipole selection rules and spin-orbit coupling
yeven

Dipole matrix element:

oddx

p-pol

s-polkz

kykx

s-pol
p-polkz

kykx- photoelectron spin depends on orbital symmetry and experimental
geometry- even the observed spin reversion reflects the intrinsic spin structure→ talk by Koji Miyamoto for d-states of W(110)Nature Commun. 7, 11621 (2016)Friedel Reinert

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Model system: Rashba-split surface states on BiAg2/Ag(111)
1/3 ML Bi on Ag(111)(√3x√3)R30°-reconstruction

Poster by Ryo Noguchi 1-15

C. Ast et al., PRL 98,186807 (2007)

R. Noguchi et al., PRB 95,041111(R) (2017)nearly prefect 2DEG with●large spin-orbit splitting→ spin-polarized bands●occupied states of mainly spz character● unoccupied states of mainly p p characterx y●DFT calculation

pxpyspz

G. Bihlmayer et al., PRB 75, 195414 (2007)
Friedel Reinert

H. Bentmann et al., EPL 87, 37003 (2009)

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Linear dichroism for spin-split states in BiAg2/Ag(111)p-polkz

kykx→ Tx and Tz vary with hv, due tomagnitude?

change of the final statehv
Friedel Reinert

22 eV 26 eV
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Photon energy dependence of spin-polarization

p-polkzkykx→ measured spin-polarization reverses within a few eVof photon energy!

hv|↑>|↓>|↓>|↑>

H. Bentman, FR et al., PRL(2017) acceptedFriedel Reinert

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Photon energy dependence of spin-polarization

p-polkz

ykyevenkxxoddhv• photoelectron spin flips sign with excitation energy• Tz produces spin-↑ and Tx spin-↓ photoelectrons
Friedel Reinert

H. Bentman, FR et al., PRL(2017) accepted
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Ab initio one-step photoemission theoryhv→ hv-dependence
captured by
ab initio theory
E. E. Krasovskii
DIPC San SebastianFriedel Reinert

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Ab initio one-step photoemission theory
Ag(111) band structure above EF
hv

Bragg gap

→ hv-dependence
captured by
ab initio theory
E. E. Krasovskii
DIPC San SebastianFriedel Reinert

TCS
Krasovskii, Schattke, PRB 59 (1999) 15609(R)

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Complex unoccupied band structure: PE Final stateAg(111)

Final-state: density of states●propagating andevanescent waves

gap: only evanescentsolutions→ rapid change of finalstate wave function●Krasovskii, Schattke, PRB 59 (1999) 15609(R)Friedel Reinert

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Topological surface state in Bi2Te3
ΓKmirror planeΓM

Henk et al., PRL108 (2012) 206801• strong hexagonal warping of surfacestate dispersion• in-plane potential landscape• spin-polarization acquires out-of-planecomponent off the mirror planesFriedel ReinertSARPES & Photoemission Final State

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Out-of-plane spin polarization in Bi2Te3
ΓKhν = 23 eV
Mirror planeΓM

Henk et al., PRL108 (2012) 206801

ΓM

ΓK

Unpublished: HiSOR (ESPRESSO), Hiroshima
H. Bentman, FR et al., (2017) unpublishedFriedel Reinert
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Effect of photon-energy on out-of-plane spin polarizationhν = 23 eV
mirror planeΓK→ measured Pz does not reflect intrinsic spinpolarization along z (here), but arises mainly fromthe photoemission process itself

Friedel Reinert

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Photon-energy-dependence of out-of-plane spin polarization
p-polMatrix elements:

kzkykxk along ΓK (no mirror plane)
Photoelectron spin:Friedel Reinert

H. Bentman, FR et al., (2017) unpublished
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Summary
1) SOC couples even and odd WFs
differently to the “intrinsic” spin in2) Experimental geometry (lightpolarization) “selects” WF andtherewith the (photoelectron) spin(→ linear dichroism)3) Different contributions do interferein squared matrix element4) If strong energy dependence of(e.g. near gap), interference terms
might produce changes ofphotoelectron spin by changing hv

Friedel Reinert

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Conclusions
 Photoelectron spin polarization canstrongly depend on experimentalparameters
 Spin density of initial state is
sampled differently depending on
experimental geometry andexcitation energyhv In general: comprehensive data
and/or additional knowledge fromtheory or experiment is required Outlook: soft X-ray SARPES& experimental info about finalstates
Fig. from Jackeli et al., Phys. Rev. Lett. 102, 017205 (2009)Friedel Reinert

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