High temperature superconductivity - insights from Angle Resolved Photoemission Spectroscopy Adam Kaminski Ames Laboratory and Iowa State University Funding: Ames Laboratory - US Department of Energy
Ames Laboratory Spectroscopy Group: Takeshi Kondo - postdoctoral researcher Ari Palczewski - Ph. D. student James Koll - undergraduate assistant Collaborators: Jörg Schmalian - ISU Rustem Khassanov - University of Zürich, Switzerland Janusz Karpinski - ETH, Switzerland Joel Mesot - PSI, Switzerland Takafumi Sato - Tohoku University, Japan Takashi Takahashi - Tohoku University, Japan Helene Raffy - Universite Paris-Sud, France Kazuo Kadowaki - University of Tsukuba, Japan
Outline: - condensed matter physics - is there anything left to understand? - properties of conventional and high temperature superconductors - introduction to Angle Resolved Photoemission Spectroscopy - electronic properties of high temperature superconductors - new results
condensed matter physics - is there anything left to understand? all physics covered by electrodynamics + quantum mechanics... but complexity and new phenomena arise from large numbers of interacting particles US penny: 3.1 grams of copper, 2.9x10 22 electrons a DVD has 4x10 10 bits so to store information only about spin for each electron we need: 7.25 x 10 11 DVD s, but this is clearly not enough to do any meaningful calculations fortunately electrons in copper are weakly interacting and can be described by Landau Fermi Liquid model (1:1 correspondence with free electron gas), but in many systems the interactions are strong and current state of the art calculations can deal with... 7x7 lattice
Superconductivity Discovered in 1911 by Kamerlinght Onnes first in mercury, then many other metals and alloys Complete theory (BCS) due to Bardeen, Cooper and Schrieffer in 1957 resistance [Ohm] temperature [K]
Superconductivity pairing + condensation pair of two electron is a boson bosons can condense creating superfluid
In the metals electrical resitance arises due to scattering of the conduction electrons from defects E
In BCS the attractive pairing interaction between electrons arises from interaction with the lattice vibrations (phonons)
In the superconducting state current is being carried by superfluid - condensate of very large number of electron pairs
High temperature superconductors Discovered in 1986 by Bednorz and Müller. c BiO BiO Observed so far only in materials that contain copper oxide. Superconducting transition temperature (Tc) up to 130K. a b SrO CuO Ca CuO Pairing mechanism - unknown unit cell SrO BiO T 3.17Å BiO SrO CuO Ca CuO SrO BiO Bi 2 Sr 2 CaCu 2 O 8+x T N AFM T* pseudogap SC ~ 0.15 T c metal carrier concentration
ARPES experiment z analyzer θ detector φ a or b sample
High resolution UV beamline at Synchrotron Radiation Center, Wisconsin e - 800 MeV ring at undulator Synchrotron Radiation Center sample grating hv electron analyzer
Electron analyzer photoelectrons sample lens 2D detector hemispherical analyzer
... high precision lab-based ARPES system Energy resolution: ~1.2 mev Angular resolution: 0.1 deg. UV source: 10 13 photons/sec.
From atoms to solids: two isolated atoms two atom molecule solid Kittel - Solid state physics
Dispersion relation - energy bands metal insulator Kittel - Solid state physics
ARPES experiment z analyzer We need: θ φ detector a or b binding energy - E b initial momentum - k i sample E b = E - hv + W k i =k f = 2mE/h 2 sinθ k i =0 for quasi 2D samples
typical photoemission spectrum from Bi2212 C 1s Bi 4f 5/2 & 4f 7/2 Normalized intensity Sr3p1/2,Sr3p3/2 Theta=5 deg, hv=500 ev T=300K T=40K Sr3d3/2,Sr3d5/2 Theta=5 deg, hv=500 ev Normalized intensity Normalized intensity Ca2p1/2, Ca2p3/2 hv=500 ev Emission angle: 0 deg 10 deg 20 deg 30 deg 40 deg 50 deg -285-280 -275-270 -265-260 Energy [ev] Normalized intensity -140-138 -136-134 -132-130 -128 Energy [ev] T=300K T=40K -355-350 -345-340 Energy [ev] Bi 5f 1/2, 5f 3/2 conduction band valence band -400-300 -200-100 0 Energy [ev]
Valence and conduction bands - simplest example: Au 5d poly Au 150x10 3 Intensity [counts/5min] 100 50 valence band conduction band 0-8 -6-4 -2 0 Energy [ev] Normalized intensity T=100K T=350K -0.5-0.4-0.3-0.2-0.1 0.0 0.1 0.2 Energy [ev]
Electronic structure E ARPES spectra "E f " E b (k 1 ) hν E vac hν W E f k 2 k 1 k f k
Typical modern ARPES data: E=const Momentum Distribution Curve (MDC) ARPES Intensity 0.5 0.4 0.3 k (A -1 ) k=const Energy Distribution Curve (EDC) E k ARPES Intensity I= i A p f 2 A(k, ) f( ) symmetry of electronic structure and interactions -0.3-0.2-0.1 0.0 Energy [ev] A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)
EDC MDC Intensity plot 0.1 0.0-0.1 Energy [ev] -0.2-0.3-0.4-0.5 momentum -0.6-0.4-0.2 0.0 0.2 Energy [mev] -0.6-0.5-0.4-0.3 ky [A -1 ]
Eli Rotenberg, Advanced Light Source
Superconducting gap E T<Tc T>Tc µ 2! k f k J. C. Campuzano et al., Phys. Rev. B 53, 14737 (1996) C. G. Olson, D. W. Lynch et al., Science 245, 731-733 (1989)
1 Y X Fermi surface M 0 (0,0) (π,0) M node d-wave order parameter -1-1 X M 0 k x [ π /a] Y 1 anti-node H. Ding et al., Phys. Rev. B 54, 9678 (1996)
Laboratory system: Scienta analyzer and He Lamp 5.0 mev Normalized intensity Superconducting state LuNi2B2C (Tc=16K) T=9.5K -15-10 -5 0 5 10 Energy [mev] -100-80 -60-40 -20 0 20 40 Energy [mev]
Text S. Souma et al., Nature, 423, 65 (2003)
Collective modes e k-q,ω-ω k,ω e q,ω
Ashcroft and Mermin Solid State Physics Interaction of electrons with a phonon:
Renormalization effects along nodal direction T. Valla et al., Science 24, 2110 (1999) P.V. Bogdanov et al., Phys. Rev. Lett. 85, 2581 (2001) A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)
Interaction of the electrons with a collective mode dispersion in normal and superconducting state 0.00-0.05 Mode energy 1-0.10 Μ 0-0.15 N A -0.20 Γ Node Μ k T=40K T=140K Antinode 40 ased on the dispersion we can conclude that the interaction with the collective mode occurs strength of coupling Fermi velocity in the normal state nly in the superconducting state, its energy is constant throughout the Brillouin 2.0 zone and its 30 trength increases significantly towards in the the SC antinode. state These properties are consistent with the 1.5 esonant mode observed by Inelastic Neutron Scattering (INS) experiments. A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001) V h /V l 20 10 0 0.5 0.6 0.7 k x (π/a) 0.8 0.9 1.0 v F [ev Ang] 1.0 0.5 0.0 0.5 0.6-1 -1 0.7 k x [π/a] 0.8 0 k x [ π /a] 0.9 1.0 1
EDC s in the superconducting state k=(1,0) k=(.730,0) k=(.640,0) k=(.590,0) k=(.550,0) k=(.450,0) k=(1,.365) k=(.730,.365) -0.3-0.2-0.1 0.0 Antinode -0.3-0.2-0.1 0.0 k=(.640,.365) k=(.590,.365) -0.3-0.2-0.1 0.0-0.3-0.2-0.1 0.0 Binding Energy (ev) k=(.550,.365) -0.3-0.2-0.1 0.0 k=(.450,.365) -0.3-0.2-0.1 0.0 Node A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)
Collective mode score card Properties of the bosonic mode magnetic compatibility phonons 1) isotropic energy +Ω yes yes 2) momentum anisotropy yes yes, recently 3) temperature dependence yes not obvious 4) doping dependence yes not obvious
Autocorrelated (AC) ARPES - new tool in studies of scattering processes Scattering in traditional STM Cu on Cu(111) Ag on Ag(111) SPECS website
FT STM -12 mev Fourier transform J. E. Hoffman et al, Science 295, 466 (2002) J. E. Hoffman et al, Science 297, 1148 (2002) K. McElroy et al, Nature 422, 592 (2004) L. Capriotti et al, PRB 68, 014508 (2003) R. S. Markiewicz et al, PRB 69, 214517 (2004)
AutoCorrelated (AC) ARPES - ARPES data and q-space 1.0 ARPES intensity map -12 mev 1.0 q-space map 0.5 q 2 q 1 q 7 0.5 k x [π/a] 0.0 q 3 q 6 q x [π/a] 0.0 q 2 q 1 q 7 q 5-0.5 q 4-0.5 q 3 q 6 q 5-1.0-1.0 q 4-1.0-0.5 0.0 k x [π/a] 0.5 1.0-1.0-0.5 0.0 q x [π/a] 0.5 1.0 S(q,! =! 0 ) = " k x,k y I(k,!) I(k + q,!)
-12 mev ARPES intensity maps
-12 mev q-space
Comparison of FT STM and AC ARPES q 1 q 1 q 3 K. McElroy et al, Nature 422, 592 (2004) q 3 U. Chatterjee et al, Phys. Rev. Lett. (submitted)
Conclusions: - ARPES is an excellent probe to study electronic properties of strongly correlated systems such as heavy fermion systems and high temperature superconductors - the only relevant feature in electronic structure for high temperature superconductivity is a hole pocket Fermi surface centered at k =k =1 x y - bridging the results from ARPES and FT STM will lead to better understanding of low energy excitations and possibly high temperature superconductivity