Probing the Electronic Structure of Complex Systems by State-of-the-Art ARPES Andrea Damascelli

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1 Probing the Electronic Structure of Complex Systems by State-of-the-Art ARPES Andrea Damascelli Department of Physics & Astronomy University of British Columbia Vancouver, B.C.

2 Outline: Part I State-of-the-Art ARPES: the essentials Motivation and potential Formal description One-step vs three-step model The sudden approximation Kinematics of photoemission One-particle spectral function Experimental State-of-art ARPES Surface vs bulk sensitivity Summary and discussion

3 History of Photoemission The Photoelectric Effect First experimental work performed by H. Hertz (1886), W. Hallwachs (1888), von Lenard (1900) Theoretical explanation by Einstein (1905) FIRST EXPERIMENTAL EVIDENCE FOR QUANTIZATION OF LIGHT! Is there anything else we can learn from the photoelectric effect? Insights into the solid-state! Courtesy of Kyle Shen

4 Understanding the Solid State: Electrons in Reciprocal Space Many properties of a solids are determined by electrons near E F (conductivity, magnetoresistance, superconductivity, magnetism) Allowed electronic states Repeated-zone scheme E F Only a narrow energy slice around E F is relevant for these properties (kt=25 mev at room temperature) Second Brillouin zone First Brillouin zone Second Brillouin zone

5 Interaction Effects between Electrons : Many-body Physics Many-body effects are due to the interactions between the electrons and each other, or with other excitations inside the crystal : 1) A many-body problem : intrinsically hard to calculate and understand 2) Responsible for many surprising phenomena : Superconductivity, Magnetism, Density Waves,... Non-Interacting Interacting Courtesy of Kyle Shen

6 Angle-Resolved A Simple Example : Metal Photoemission Surfaces (Cu and Ag) Spectroscopy K = p = E kin E kin, ϑ, ϕ Vacuum E kin K Conservation laws Solid E B k

7 A ARPES: Simple Example One-Step : Metal Surfaces vs Three-Step (Cu and Ag) Model Photoemission Intensity I(k,ω) One-step model

8 A ARPES: Simple Example One-Step : Metal Surfaces vs Three-Step (Cu and Ag) Model Photoemission Intensity I(k,ω) One-step model Three-step model

9 A Simple ARPES: Example The : Metal Sudden Surfaces Approximation (Cu and Ag) Photoemission Intensity I(k,ω) : Sudden approximation : One Slater determinant Excitation in the solid Vacuum Spectrum

10 A Simple ARPES: Example Role : Metal of Surfaces the Crystal (Cu and Ag) Potential Photoemission Intensity I(k,ω) : Sudden approximation : One Slater determinant Excitation in the solid Vacuum Spectrum

11 ARPES: A Simple Inner Example Potential : Metal Surfaces and (Cu Determination and Ag) of k z Free-electron final state because Excitation in the solid Vacuum Spectrum

12 A Simple ARPES: Example FWHM : Metal Surfaces and Inverse (Cu and Ag) Lifetime FWHM of an ARPES peak Hansen et al., PRL 80, 1766 (1998) 1 if 1 2 if 2 if

13 ARPES: Energetics and Kinematics E kin, ϑ, ϕ Energy Conservation E B E kin Momentum Conservation k K E kin ϑ

14 ARPES: Energetics and Kinematics Electrons in Reciprocal Space E kin, ϑ, ϕ k k F E F E B Energy Conservation E B E kin Momentum Conservation k K E kin ϑ K E F E kin

15 ARPES: Interacting Systems A. Damascelli, Z. Hussain, Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003) Photoemission intensity: In general NOT orthogonal

16 ARPES: The One-Particle Spectral Function A. Damascelli, Z. Hussain, Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003) Photoemission intensity: I(k,w)=I 0 M(k,w) 2 f(w) A(k,w) Single-particle spectral function S(k,w) : the self-energy captures the effects of interactions

17 Angle-Resolved Photoemission Spectroscopy Parallel multi-angle recording Improved energy resolution Improved momentum resolution Improved data-acquisition efficiency E (mev) θ past now Momentum Binding Energy

18 SSRL Beamline 5-4 : NIM / Scienta System High resolution E (mev) 2-10 θ 0.2 Ultra-high vacuum (~ torr) High angular precision (+/- 0.1º) Low base temperature ( < 10 K) Wide temperature range ( K) Variable photon energies (12-30 ev) Multiple light sources (He lamp) Control of light polarization Single crystal cleaving tools Sample surface preparation & cleaning Low-Energy Electron Diffraction (LEED)

19 Advantages ARPES: and Limitations Surface of ARPES vs Bulk Sensitivity Mean-free path for excited electrons CeRu 2 Si 2 T K =1000K HeIα 21.2 ev 10 A o CeRu 2 T K =22K Seah, Dench et al., SIA 1, 2 (1979) Sekiyama et al., Nature 403, 396 (2000)

20 Advantages ARPES: and Limitations Surface of ARPES vs Bulk Sensitivity Mean-free path for excited electrons CeRu 2 Si 2 T K =1000K HeIα 21.2 ev 10 A o CeRu 2 T K =22K Seah, Dench et al., SIA 1, 2 (1979) Sekiyama et al., Nature 403, 396 (2000)

21 ARPES on 1D Nanostructures: Spin-Charge Separation? C. Kim et al., PRL 77, 4054 (1996) P. Segovia et al., Nature 402, 504 (1999) Au chains on Si(557) Losio et al., PRL 86, 4632 (2001) SrCuO 2

22 ARPES: Advantages and Limitations Advantages and Limitations of ARPES Advantages Limitations Direct information about the electronic states! Straightforward comparison with theory - little or no modeling. High-resolution information about BOTH energy and momentum Surface-sensitive probe Sensitive to many-body effects Can be applied to small samples (100 µm x 100 µm x 10 nm) Not bulk sensitive Requires clean, atomically flat surfaces in ultra-high vacuum Cannot be studied as a function of pressure or magnetic field Courtesy of Kyle Shen

23 Outline: Part II Electronic structure of complex systems 2H-NbSe 2 - Sr 2 RuO 4 Detecting bands and Fermi surface Bulk & surface electronic structure Nb - Bi 2 Sr 2 CaCu 2 O 8+δ Superconducting gap: s-wave vs. d-wave Bogoliubov quasiparticles in high-t c cuprates Be(0001) - Mo(110) - Bi 2 Sr 2 CaCu 2 O 8+δ Many-body effects in the quasiparticle dispersion Conclusions and discussion

24 2H-NbSe 2 : Normal State Electronic Structure Corcoran et al.,jpcm 6, 4479 (1994) A B C Damascelli et al. (2000) Γ Μ Κ 6 Γ

25 2D perovskite Sr 2 RuO 4 : basic properties Unconventional superconductivity Maeno et al., Nature 372, 532 (1994) SrO RuO 2 SrO Pairing mechanism? Order parameter? FM-AF fluctuations? Rice & Sigrist, JPCM 7, L643 (1995) Nakatsuji & Maeno, PRL 84, 2666 (2000) Ca 2-x Sr x RuO 4 Lattice-magnetism interplay Orbital degrees of freedom Sr 2 RuO 4 : 2D Fermi Liquid (ρ c /ρ ab =850) Ca 2 RuO 4 : insulating Anti-FerroMagnet SrRuO 3 : metallic FerroMagnet

26 Low-Energy Electronic structure of Sr 2 RuO 4 Ru 4+ 4d 4 e g z y z y z y S=1 t 2g x xz yz xy x x Band structure calculation: 3t 2g bands crossing E F 3 sheets of FS{ α (hole-like) β and γ (electron-like) M α γ β Γ A. Liebsch et al, PRL 84, 1591 (2000) X M I.I. Mazin et al, PRL 79, 733 (1997)

27 Fermi Surface Topology of Sr 2 RuO 4 Early ARPES results gave a different topology de Haas-van Alphen LDA ARPES α γ β M Γ A.P. Mackenzie et al., PRL 76, 3786 (1996) C. Bergemann et al., PRL 84, 2662 (2000) X I.I. Mazin et al., PRL 79, 733 (1997) T.Yokoya et al., PRB 54, (1996) D.H. Lu et al., PRL 76, 4845 (1996) ARPES: additional information Reliability of ARPES?? dhva: limited set of systems

28 Fermi Surface Topology of Sr Surface of Sr 2 RuO 4 2 RuO 4 M ARPES : present day X ARPES Spectra X Intensity at E F M X Intensity (a.u.) Γ M Γ A. Damascelli et al., PRL 85, 5194 (2000) M Γ Binding Energy (ev)

29 Fermi Surface Topology of Sr Surface of Sr 2 RuO 4 2 RuO 4 LEED Pattern ARPES Spectra X Intensity at E F M X Intensity (a.u.) Γ M A. Damascelli et al., PRL 85, 5194 (2000) Γ Binding Energy (ev) Surface instability Band folding

30 Surface reconstruction of cleaved Sr 2 RuO 4 LEED STM a-b plane Cleavage plane surface bulk R. Matzdorf et al., Science 289, 746 (2000) Rotation of the RuO 6 octahedra around the c axis (9 )

31 Surface electronic structure of Sr 2 RuO 4 How On to gain samples unambiguous cleaved at information 180 K the surface-related features are on the bulk electronic structure? suppressed E F mapping ±10 mev M X Cold cleave T=10 K Hot cleave T=180 K Γ M Binding energy (mev) Binding energy (mev) A. Damascelli et al., PRL 85, 5194 (2000); K.M. Shen, A. Damascelli, et al., PRB 64, (R) (2001)

32 Bulk electronic structure of Sr 2 RuO 4 What do we learn about the bulk electronic structure? γ α β X Fermi Surface Fermi velocity Effective mass I.I. Mazin et al., PRL 79, 733 (1997) Γ Γ β γ X α M X M γ Γ M β Γ SB M Binding Energy (mev) Binding Energy (mev) A. Damascelli et al., PRL 85, 5194 (2000) Sr 2 RuO 4 cleaved at 180 K T= 10 K hν=28 ev

33 Dispersion of the bulk electronic bands U=1eV v= E/ k band v F / v F exp =3.2 Experiment compares well with LDA+U calculations A. Damascelli et al., PRL 85, 5194 (2000) A. Liebsch & A. Lichtenstein, PRL 84, 1591 (2000)

34 Superconductivity Superconductivity Courtesy of Kyle Shen

35 Classic Low-temperature Superconductors Metallic Density of States Superconductivity can only be seen on low energy scales and needs high resolution! Superconductivity Superconducting Density of States 2-electron bound state k Cooper Pair -k spin-singlet pairing

36 Classic Low-temperature Superconductors Metallic Density of States Superconductivity can only be seen on low energy scales and needs high resolution! A. Chainani et al., PRL 85 (2000) Superconducting Density of States

37 High-Temperature Superconductors: Bi2212 Γ M B B A M Y (π, 0) s-wave Photoemission Intensity Bi2212 Tc = 78K K K A A B d-wave Energy Relative to the Fermi Level (ev) Courtesy of Kyle Shen

38 High-T c Superconductors: s-wave vs. d-wave gap Binding Energy (mev) (π,π) Ding et al. PRB 54, R9678 (1996) B Γ Binding Energy (mev) Courtesy of F. Ronning

39 High-T c Superconductors: Bogoliubov QP in Bi2223 T>T c T<T c Matsui et al., PRL 90, (2003)

40 Many-Body effects: Electron-Phonon Coupling Single-particle spectral function Be(0001) Mo(110) Collective mode Electronic band Eschrig, Norman, PRB 67, (2003) Hengsberger et al., PRL 83, 592 (1999) Valla et al., PRL 83, 2085 (1999)

41 Many-Body effects in the High-T C Cuprates Valla et al., Science 285, 2110 (1999) Bi2212 Mechanism for High-T C Magnetic fluctuations? Electron-phonon coupling?

42 Many Body effects in the Quasiparticle Dispersion Lanzara et al., Nature 412, 510 Binding Energy Electron Momentum Mechanism for High-T C Magnetic fluctuations? Electron-phonon coupling?

43 Conclusions ARPES results from complex systems Bands and FS in unprecedented detail Fermi velocity and effective mass Superconducting (d-wave) gap Many-body effects in the QP dispersion Nanostructured materials (surface FM) ARPES is Feedback a powerful to microscopic tool for the models study of the electronic Quantify the structure spin/charge of complex correlation systems effects For a review article see: A. Damascelli, Z. Hussain, and Z.-X Shen, Rev. Mod. Phys. 75, 473 (2003) For additional material see:

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