Lecture: Introduction to ARPES. Xingjiang Zhou

Transcription

1 2013/01/21-23 Hongkong Lecture: Introduction to ARPES The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Xingjiang Zhou National Lab for Superconductivity Institute of Physics Chinese Academy of Sciences Beijing , China

2 High-Tc Has Changed Landscape of Condensed Matter Physics ARPES Optical Transport Nature 412(2001)510 Neutron Science 300(2003)1410 High Tc Superconductivity Nature 406(2000)486 STM Nature375(1995)561 High Magnetic Field The Nobel Prize in Physics in 1987 X-Ray Scattering Nature 415(2002)412 High Pressure Nature 424 (2003)912 Science 288(2000)1811 Nature 365(1993)323

3 Experimental Tools for Superconductivity DOE Report (2006) ARPES

4 ARPES on High Temperature Cuprate Superconductors d-wave Superconducting gap ARPES on SuperconducBng gap Pseudogap ARPES on Pseudogap Many-Body Effects ARPES on Kink Γ B A M (π, 0) d- wave- like symmetry M Y Photoemission Intensity Bi2212 Tc = 78K K K A B Energy Relative to the Fermi Level (ev) Z.- X. Shen et al., Phys. Rev.Le1.70(1993)1553. Loeser et al., Science 273(1996)325. Ding et al., Nature 382(1996) 51. A. Lanzara et al., Nature 412(2001)510. X. J. Zhou et al., Nature 423(2003)398.

5 ARPES on Topological Insulators Bi 2 Se 3 Bi 2 Te 3 Y. Xia et al., Nature Phys. 5(2009)398. Y. L. Chen et al., Science 325 (2009)178.

6 ARPES on Various Materials C 60 Diamond Nanotube Quantum Well Science 300(2003)303 Nature 438(2005)647 Nature 426(2003)540 Nature 398(1999)132 Quasicrystal MagneBc Materials CDW Nature 406(2000)602 Nature 438(2005)474 Phys. Rev. Le1. 93(2004)126405

7 Content Ø What is ARPES? Brief history, ARPES process, ARPES setup (Light sources, electron analyzer), ARPES resolutions, Matrix element effect Ø What can ARPES do? Fermi surface mapping, Gap measurement Many-body effects Ø Latest and future development of ARPES (Laser ARPES, spin-resolved, time-resolved, spatially-resolved)

8 Brief History of ARPES

9 Principle of Photoemission Photoelectric Effect Discovery 1887 German Physicist: Hertz Photoelectric Effect Explanation 1905) The Nobel Prize in Physics 1921 Albert Einstein ( ) Heinrich Rudolf Hertz ( ) For his services to Theoretical Physics, and especially for his discovery of the law of The Photoelectric Effect"

10 Nobel Prizes in Photoemission Spectroscopy Karl Manne Georg Siegbahn ( ) The Nobel Prize in Physics 1924 for his discoveries and research in the field of X- ray spectroscopy " The X- ray spectra and the structure of the atoms Kai M. Siegbahn ( ) The Nobel Prize in Physics 1981 for his contribubon to the development of high- resolubon electron spectroscopy " Electron Spectroscopy for Atoms, Molecules and Condensed Ma1er

11 Classifications of Photoemission Techniques Photoemission Angle- Integraed Angle- Resolved Spin-integrated E E, k Spin-resolved E, s E, s, k

12 Angle-Resolved Photoemission Spectroscopy (ARPES) Light Source e - Z θ Electron Detector Photoemitted electrons in Vacuum along different angles E kin, K Energy Conservation: E B = hν -E kin -Φ Momentum Conservation: K = k + G X φ Sample Y Electronic States in Solid: Ψ(E, k, s) E-Energy k-momentum; s-spin.

13 First Angle-Resolved Photoemission Experiment of Band Mapping Neville V. Smith ( ) N. V. Smith, M.M. Traum and F.J. DiSalvo Solid State Communications 15, 211 (1974)

14 Angle-Resolved Photoemission Spectroscopy (ARPES) Light Source θ e - Z Electron Detector φ Y X Sample

15 Photoemission Process

16 ARPES Band Mapping and Fermi Surface Energy Distribution Curve (EDC)

17 ARPES Band Mapping and Fermi Surface Energy Distribution Curve (EDC)

18 ARPES Band Mapping and Fermi Surface Energy Distribution Curve (EDC) k F

19 ARPES Band Mapping and Fermi Surface Energy Distribution Curve (EDC) k F

20 Power of ARPES: Direct Measurement of Fundamental Parameters E-k relation Velocity: v=de/dk Effective mass: 1/m* ~ d 2 E/dk 2 Scattering rate (τ): EDC Linewidth EDC lineshape Superconducting gap: EDC position Pseudogap: EDC position Fermi surface Carrier density: FS volume Nesting vector: FS topology

21 Challenge: At which point the sudden approximation breaks down and how?

22 Angle-Resolved Photoemission Spectroscopy (ARPES) -- Direct Comparison between Theory and Experiment I(k,w)=I 0 M(k,w) 2 f(w) A(k,w) Under the impulse approximation, photoemission measurement invloves only single-particle spectral function A( k, ω) 1 π [ ω E Im ( k, ω) = 0 2 Re ( k, ω)] + [Im ( k, ω)] 2 k Fermi Surface Quasiparticle Dynamics ReS(k,w): dispersion ImS(k,w): scattering rate Theories Physical Properties

23 ARPES: A Bridge between Theory and Experiment Conventinal Fermi Liquid: ImΣ = -βω 2 ReΣ =αω Marginal Fermi Liquid: ImΣ = -π/2cx ReΣ =Cωln(x/ωc) where x=max( ω,t) Electron-Phonon Coupling System ImΣ = π ReΣ 0 = 0 2 dωα ( ω) F k k 2 dωα ( ω) k F k ( ω)[2n B ( ω)ln ( ω) + n ω+ u ω u F ( ω + u) + n F ( ω u)]

24 ARPES Experimental Setup

25 ARPES Endstation on BL10.0.1, ALS, LBNL Manipulator Prep Chamber Scienta Analyzer Beam in June, 1999 Sample Transfer Characterization ARPES Chamber Chamber

26 Some Remarks about ARPES Ø ARPES is a surface-sensitive technique, ultra-high vacuum is necessary; Ø ARPES uses electron emission angle to determine the momentum magnetic field is not welcome; Ø Electrons have to travel to analyzer directly ARPES is not compatible with high-pressure, ultra-low temperature yet.

27 ARPES Light Sources 1. Synchrotron Light Sources; 2. Gas Discharge Lamp; 3. UV and VUV lasers.

28 What is Synchrotron? Principle: Charged particles with high energy (near speed of light) gives light when changing directions.

29 Synchrotron Source for ARPES: BL at ALS, Berkeley Hig h Flux Photons/Se c l/mm 925 l/mm 2100 l/mm Ø Wide Energy Range: ev; Ø High Energy Resolution; (<5meV between 20-50eV) Ø High Flux Photon Energ y (ev)

30 Electron Energy Analyzer

31 ARPES--Improved Resolution Brings New Discoveries 3rd Generation Synchrotron Previous Now Energy Resolution (mev) Angle Resolution (degree) ~2 <1 0.1 Ag(111) Surface State ALS Electron Energy Analyzer Scienta G. Nicolay et al., Phys. Rev. B 63(2001)

32 Evolution of Energy Analyzers: from 0D to 1D Angular Detection Before Scienta ~1997 费米面 Fermi Surface Hemispherical Analyzer 费米面 Fermi Surface Ø Energy Resolu: <1meV Ø Angular Resolu: 0.1~0.4 Degree Ø Angle Coverage: 1D: +-15 degrees Angle Detection: 0D Point Angle Detection: 1D Line

33 Better Resolution Reveals Electron Kinkiness in Cuprates Angular Resolution: 2 degrees Angular Resolution: 0.3 degree Dessau et al., PRL (1995).

34 Better Resolution Reveals Electron Kinkiness in Cuprates Angular Resolution: 2 degrees Angular Resolution: 0.3 degree Dessau et al., PRL (1995).

35 Related Issues in Photoemission

36 Surface vs Bulk Property Measurements

37 Matrix Element Effect in Photoemission I = A(k,ω) x M(k,hv) 2 x F(ω) Measured Signal Single-particle spectral function Intrinsic property of materials Fermi-Dirac Distribution Matrix Element Depending on measurement conditions Ø Photon energy; Ø Photon polarization; Ø Momentum.

38 Bilayer Splitting in Bi 2 Sr 2 CaCu 2 O 8+δ Bilayer band splitting Anti-bonding & Bonding Coupling FS with bilayer splitting (π,π) Bi 2 Sr 2 CaCu 2 O 8+δ Bi2212 Tc=90K Γ A. I. Liechtenstein et al., PRB 54, (1996)

39 Calculations of Matrix Element Effect Calculated Measured P. V. Bogdanov et al. Phys. Rev. B 64, (2001) D. L. Feng et al., PRL 86 (2001) Y. D. Chuang et al., PRL 87 (2001) A. Bansil et al., Phys. Rev. Lett. 83(1999) Challenge: How to calculate Matrix Element Effect in correlated systems?

40 Light Polarization on Matrix Element Effect To disentangle different orbitals

41 Related Issues in Photoemission Photoemission Measured (Basically) Occupied States

42 Fermi-Dirac Distribution Function at Different Temperatures I = A(k,ω) x M(k,hv) 2 x F(ω) 1 f(x)=1/(exp(x/kt))+1) Fermi Distribution Function Temperature 300K 200K 100K 50K 10K 1K E - E F (ev)

43 ARPES Measurement of Electronic States above Fermi Level 300 K, Original Divided by Fermi Function E - E F (ev) -0.1 E - E F (ev) Momentum Momentum 0.7

44 Data Analysis in ARPES Energy Gap

45 ARPES on Superconducting Gap of Cuprates Γ A M (π, 0) d-wave Energy Gap B M Y Photoemission Intensity Bi2212 Tc = 78K K K A B Energy Relative to the Fermi Level (ev) Z.-X. Shen et al., Phys. Rev. Lett. 70(1993)1553. H. Ding et al., Phys. Rev. B 54 (1996)9678.

46 ARPES Observation of Pseudogap Bi2212 UD85K D. S. Marshall et al., Phys. Rev. Lett. 76 (1996) 4841; A. G. Loeser et al., Science 273 (1996) 325; H. Ding et al., Nature (London) 382 (1996) 51.

47 Determination of Energy Gaps EDC Symmetrization FeSe D. F. Liu, X. J. Zhou et al., Nature Communications 3 (2012) 931.

48 How to Measure Energy Gap EDC Symmetrization I(k,ω)= I 0 (k,ν,a) A(k,ω) f(ω) f ( ω) = 1 ω exp( ) k T B + 1 I(k,-ω)= I 0 (k,ν,a) A(k,-ω) f(-ω) f ( ω) = 1 ω exp( ) k T B + 1 If A(k,ω)= A(k,-ω), Then I=I(k,ω)+I(k,-ω)= I 0 (k,ν,a) A(k,ω) Fermi distribution function is conveniently removed!

49 ARPES on Energy Gap--Single Layer FeSe D. F. Liu, X. J. Zhou et al., Nature Communications 3 (2012) 931.

50 Superconducting Gap 1. Gap opens along the entire Fermi surface; 2. Gap opening has a particle-hole symmetry. For superconducting gap, in fact, only one point at k F satisfies A(k,ω)=A(k,-ω)

51 ARPES as a powerful tool for many-body effects

52 Power of ARPES A Probe for Many-Body Effects Under the sudden approximabon, photoemission measures single- par.cle spectral func.on Ak (, ω) 1 ImΣ = π [ hω ] + [ E k ReΣ I mσ] Electron self- energy: Σ= ReΣ + i ImΣ Many-Body Effects: Interaction of electrons with other entities such as other electrons, phonons, magnons and etc.

53 Energy Distribution Curve(EDC) vs Momentum Distribution Curve (MDC)

54 EDC Dispersion It Is Difficult to Fit EDCs EDCs

55 MDC Dispersion: It Is Easy to Fit MDCs MDCs

56 Extract Electron Self-Energy from Dispersion and MDC Width Spectral Function: A( k, ω) 1 = π ( ω ν k 1 = π ( k 0 ImΣ ReΣ) ImΣ/ v ( ω ReΣ)/ v ) 2 + (ImΣ) (ImΣ / v 0 ) 2 (1) Lorentzian Lineshape: Lx ( ) = Compare Equ. (1) and (2): 2 H ( Γ /2) ( x ) ( /2) 2 2 k + Γ (2) 0 k = ( E Re Σ)/ v 0 0 Γ /2= Im Σ/ v 0 Re = E k v Therefore 0 0 Im = ( Γ/ 2)* v 0

57 Dispersion and MDC Width -- Fitting MDCs Dispersion from MDC position k 0 (E) MDC Width Γ(E) Lorentzian Fitting: Peak position: k 0 (E) Peak width: Γ(E) ReΣ = E k v 0 0 ImΣ = ( Γ/2)* v 0

58 Manifestation of Many-Body Effects: Band Renormalization Be(0001) Surface State ReΣ ImΣ Ashcrod- Mermin, Solid State Physics Hengsberger et al., PRL 83(1999)592. S. Lashell et al., PRB 61(2000)2371. S. J. Tang et al., Phys. Stat. Solidi. 241(2004)2345.

59 Many-Body Effects in High Temperature Superconductors X. J. Zhou, Z. X Shen et al., Nature 423, 398 (2003).

60 Latest Development Laser ARPES

61 Light Sources for Photoemission Spectroscopy l Synchrotron Radiation l Gas Discharge Lamp He I, hv=21.2 ev He II, hv=40.8 ev l VUV Laser hv=6.994 ev hv θ Z Electron Energy Analyzer e - φ Y VUV--- VacuumUltra-Violet hv>6.5 ev X Sample

62 VUV Laser ARPES System at IOP Sample Transfer Manipulator VUV Laser System Prep Chamber Measurement Chamber (Started development in early 2004, commissioned by the end of 2006) Guodong Liu, X. J. Zhou et al., Rev. Sci. Instrum. 79 (2008)

63 Generation of VUV Laser (hv=6.994 ev) OpBcal Vacuum Chamber To Sample 177.3nm (6.994eV) KBBF- PCT 354.7nm 3.496eV Nd:YVO 4 laser Vanguard q Wavelength 354.7nm (3.496eV) q RepeBBon Rate : 80MHz q Pulsewidth: 10 ps q Output Power: 4W q Pulse Energy : 50nJ

64 KBe 2 BO 3 F 2 (KBBF): New Non-Linear Optical Crystal LBO CBO KDP KABO BBO CLBO KBBF eV 4.54eV 4.81eV 5.50eV 6.05eV 6.20eV 7.70eV Second Harmonic 倍频波长 Wavelength (nm) (nm) C. T. Chen,Z. Y. Xu et al., Chin. Phys. Lett. 18(8), 1081 (2001). J. Appl. Phys., Vol. 74, No. 11, 1 December 1993; J. Appl. Phys. 77 (6), 15 March 1995 Appl. Phys. Lett. 68 (21), 20 May 1996

65 KBe2BO3F2 (KBBF): New Non-Linear Optical Crystal C. T. Chen Z. Y. Xu et al., Chin. Phys. Lett. 18(8), 1081 (2001). Nature Report, February, 2009

66 Advantages and Disadvantages of VUV Laser ARPES Light Source VUV Laser Synchrotron Energy Resolution (mev) ~15 Momentum Resolution (Å -1 ) (6.994eV) (21.1eV) Photon Flux(Photons/s) ~ Electron Escape Depth (Å) 30~100 5~10 Photon Energy Tunability Limited Tunable k-space Coverage Small Large Laser and Synchrotron are complementary.

67 VUV Laser Photoemission Lab at IOP Spin-Resolved ARPES system 2-D Momentum ARPES system Laser ARPES system (Tunable laser, 5.90~7.09eV)

68 Angle-Resolved Photoemission Spectroscopy (ARPES) Light Source e - Z θ Electron Detector Photoemitted electrons in Vacuum along different angles E kin, K Energy Conservation: E B = hν -E kin -Φ Momentum Conservation: K = k + G X φ Sample Y Electronic States in Solid: Ψ(E, k, s) E-Energy k-momentum; s-spin.

69 Principle of Spin-Resolved ARPES Electron Energy Analyzer

70 Mott Spin Detector Electron Beam Electron Detector Heavy Metal Target The efficiency of Mott Spin Detector is extremely low ~ 10-4

71 Synchrotron Radiation-Based Spin ARPES ΔE Energy Resolution ΔE is inversely proportional to Light intensity In order to get decent signal intensity: (1). Sacrifice of energy resolution to get high intensity; (2). Angle-integrated measurements.

72 Direct Evidence for a Half-Metallic Ferromagnet La 0.7 Sr 0.3 MnO 3 National Synchrotron Light Source (NSLS) Brookhaven National Lab 1.Energy Resolution: 200 mev 2.Angle-Integrated. J. H. Park et al., Nature 392 (1998) 794.

73 Spin-Resolved ARPES on Topological Insulators ARPES Spin-Resolved E b (ev) ky(a -1 ) D. Hsieh et al., Nature 460 (2009)1101 Δk ΔE Δk Momentum Resolution ΔE Energy Resolution~80meV Done at Swiss Light Source

74 Advantages of Laser in Spin-Resolved Photoemission Synchrotron Radiation Energy resolution ΔE coupled with photon flux VUV Laser Energy Resolution ΔE decoupled with photon flux ΔE Best energy resolution: ~50-100meV (1).Narrow linewidth (0.26meV); (2).Extremely high photon flux (10 15 photons/s).

75 VUV Laser Spin-Resolved ARPES ARPES (E, k) à Spin-Resolved ARPES (E, k, s)

76 Laser ARPES Based on Time-of-Flight Analyzer Time of Flight Electron Energy Analyzer

77 Evolution of Energy Analyzers: from 0D to 1D Angular Detection Before Scienta ~1997 费米面 Fermi Surface Hemispherical Analyzer 费米面 Fermi Surface Ø Energy Resolu: <1meV Ø Angular Resolu: 0.1~0.4 Degree Ø Angle Coverage: 1D: +-15 degrees Angle Detection: 0D Point Angle Detection: 1D Line

78 Time of Flight Analyzer: From 1D to 2D Angular Detection Hemi-Spherical Analyzer Time-of-Flight Analyzer Ø Energy Res.: better than 1meV Ø Angular Res: 0.1~0.4 Degree Ø Angle Range: 1D: +-15 Deg. Ø Energy Res.: ~0.15meV Ø Angular Res.: 0.08 Degree Ø Angle Range: 2D:+-15Deg. 费米面 费米面 Angle Detection: 1D Line Angle Detection 2D Plane Efficiency of Angle Detection Improved by 250 times

79 Other Developments and Future Developments Ø Ultra-Low Temperature ARPES; He 3 pumping, Sample temperature<1 K; Ø Laser ARPES with Higher Photon Energy; Ø Time-Resolved ARPES; Ø Spatially-Resolved ARPES.

80 Summary In the past two decades, ARPES has continuously experienced dramatic improvements; This improvement still keeps going; Every time there is a significant improvement on resolution, there are new findings.

81 Thanks