experiment, phenomenology, and theory David Pines @90 and SCES @60, October 18, 2014 Jörg Schmalian Institute for Theory of Condensed Matter (TKM) Institute for Solid State Physics (IFP) Karlsruhe Institute of Technology KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association www.kit.edu When is a material strongly correlated?  large interactions  low density  large quantum fluctuations  competing ground states I shall not today attempt further to define the kinds of material, but I know it when I see it. (Potter Stewart) it. Deutsche Bücherei Leipzig Chapter 8 : Polaron Problem … 8.5 Effective Mass complex interactions can be incorporated in a mass renormalization R. P Reynman Phys. Rev. 97, 660 (1955) effective mass concept is robust even for very strong coupling Why did I decided to work on strongly correlated electron systems? complex interactions can be incorporated in a mass renormalization T. D. Lee, F. E. Low, and D. Pines, Phys. Rev. 90, 297 (1953) variational wave function of the polaron problem  entanglement of electron and lattice Pioneering contributions to strongly correlated electron physics 60+ε years ago! Collective excitations, quasi-particles complexity of the many body problem  weakly coupled quasi-particles experiment  Drude-Sommerfeld phenomenology of metals phenomenology  Einstein-Debye phenomenology of lattice vibrations  Landau phenomenology of Fermi liquids … theory  Bohm-Pines theory of collective excitations  Fröhlich / Bardeen / Lee-Low-Pines / Feynman approach to electron phonon coupling  Abrikosov-Gor’kov-Dzyaloshinskii foundation of Fermi liquid theory  Tomonaga-Luttinger approach to 1-d systems  Spin waves (Anderson, Tjablikov…) … The success of the quasi-particle approach Plasma resonance in EELS of metals Wikipedia.org Magnon Fractionalization in the Quantum Spin Ladder B. Thielemann et al, PRL 102 (2009) Effective electron-electron interaction Effective interaction mediated by phonons Fröhlich, Bardeen attractive at low energies L. D. Landau “one cannot repeal Coulomb’s law” Effective electron-electron interaction Bardeen, Pines Phys. Rev. 99, 1140 (1955) screening due to electrons and phonons retarded nature of the phonon-exchange  net interaction remains attractive Other ways to evade the Coulomb interaction T. Tzen Ong, P. Coleman, J. Schmalian, arXiv:1410.3554 S+- -pairing state: I=2 angular momentum + J=2 d-wave state  I+J=0 pairing state Octett pairing state  I+J=4 in KFe2As2 Efficiently evades local Coulomb repulsion for single FS-sheets Okazaki et al. Science 337 (2012), Tafti et al. Nature Physics 9 (2013) The non-trivial ways theories emerge J. Schmalian in: Bardeen Cooper and Schrieffer: 50 YEARS, edited by Leon N Cooper and Dmitri Feldman World Scientific Pub Co (2011) H   standard model of CMP (1927)  2 i 2 2 mi i theory of s.c. (1957)    r1  rN   2  ij qi q j ri  r j  1 N! P P'    1   rP   rP'   P,P' i i i 1922 theory of molecular conduction chains • ideal metals are perfect conductors • finite  due to impurities • molecular conduction chains Albert Einstein (1879-1955) 1922 theory of molecular conduction chains Albert Einstein (1879-1955) superconductor: frictionless motion of electrons coherent motion of outer electrons to neighboring atoms superconductivity  chemical bonding prediction: falsified: No superconductivity between two chemically different materials! super-current between lead and tin (H. K. Onnes) 1922 theory of molecular conduction chains Albert Einstein (1879-1955) “With our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas.” 1932 Niels Bohr (1885-1962)) Ralph Kronig (1905-1995) superconductivity results from the coherent quantum motion of a lattice of electrons 1932 • classical electrons freeze as T0 (Ekin~kB T)  crystallize Ralph Kronig (1905-1995) high frequency vibrations  M ion melec lattice  lattice  rigid electron crystal problem: the periodic crystal potential will pin the crystal 1932 electrons do crystallize at low density Wigner crystal (E. P. Wigner 1934) Ralph Kronig (1905-1995) N. Drummond et al. Phys. Rev. B 69, 085116 (2004) Eugene P. Wigner (1902-1995) 1933 Lev D. Landau (1908-1968) Felix Bloch (1905-1983) Theories for ground states with finite current! (An approach inspired by the theory of ferromagnetism) 1933 • demonstrates (correctly) that electrons in a superconductor are coupled to the rest of the system • superconductors are no perfect conductors, as it seems unlikely that all couplings are suddenly switched off below Tc Lev D. Landau (1908-1968) • a superconductor is a state with j0 F  F  j  0   m2 j 2  n2 j 4 m T Tc in the ground state 1933 • Bloch and Landau independently develop similar ideas • Bloch formulates two theorems for superconductivity Felix Bloch (1905-1983) 1933 Bloch’s first theorem The state of lowest electronic free energy of an interacting electron systems corresponds to a zero net current! • Suppose  is the ground state w.f. with finite total momentum P0 in the ground state  current j  eP0 / m Felix Bloch (1905-1983) i    exp  P   rn  n   • consider another wave function • it holds for : T V H V   V   T    T   Nm P0  P  ... • the system can always reduce its energy i.e. ground state!  is not the D. Bohm, Phys. Rev. 75, 502(1949) 1933 Bloch’s second theorem Every theory of superconductivity can be disproved! Felix Bloch (1905-1983) 1934 • metastable current configurations due to local minima in the electron dispersion • superconductivity: non-equilibrium effect December 1934: Ehrenfest  Gorter + Casimir showed that S.C. is an equilibrium effect 1941 Large unit cell distortions lattice distortion: 106 atoms / unit cell John Bardeen (1908-1991) J. Bardeen, Phys. Rev. 59, 928 (1941). 1941 Large unit cell distortions lattice distortion: 106 atoms / unit cell momentum space  k  106 bands 10 4 bands between E F  k BTc John Bardeen (1908-1991)  / L  /L k • some bands have small mass  diamagnetic • a fraction 10-6 of the electrons is superconducting Prediction: good superconductors are poor metals (strong lattice coupling needed) J. Bardeen, Phys. Rev. 59, 928 (1941). 1947-48 • key: to derive the tiny energy gain k BTc  Ekin , ECoul • Coulomb energy  bound state at the Fermi level  gap Werner Heisenberg (1901-1976) ’’…the perfect conductivity rather than the diamagnetism is the primary feature of the phenomenon” 1948 F. London, Phys. Rev. 74, 562 (1948). • demonstrates that a superconductor is not a perfect conductor ( is inconsistent with the Meissner effect)   • argues that Heisenberg missed the leading term in his theory: Fritz London (1900-1954) the Heisenberg exchange energy, J! • proposes that supercond. is due to J Quasi-particles are no magic bullets This is an example where the harmonic approximation becomes questionable: By ModernistCuisine https://www.youtube.com/watch?v=4n5AfHYST6E Quasi-particles are no magic bullets Quasiparticle weight versus incoherent background single hole in an AF backbround mean-field theory of the Mott transition C. L. Kane P. A. Lee and N. Read, PRB 39 (1989) A. V. Chubukov+ D. K. Morr PRB 57 (1998) A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, RMP 68 (1996) low - temperature physics: governed by coherent quasi-particles high energy / temperature: governed by incoherent background But what happens as we go from high to low energy scales? heavy fermions effective mass: Mohammad Hamidian/Davis Lab phenomenology Knight shift anomaly N. J. Curro, B.-L. Young, J. Schmalian, D. Pines, Phys. Rev. B 70, 235117 (2004) 4 Kcf (%) 2.0 K (%) 3 c ab 1.5 1.0 0.5 0.0 0 2 effective magnetic field at a nucleus 20 40 60 80 T (K) 1 0 0 2 4 6 8 -3 χ (x10 10 12 14 emu/mol) FIG. 1: The In(1) Knight shift in CeCoIn5 versus the bulk susceptibility1 . The solid lines are fits to the high temperature data. Inset: KHE versus T , and a fit to Eq. (8). Knight shift and susceptibility are not proportional to each other usual expectation Knight shift anomaly Kcf (%) 0.6 63 0.4 K (%) 3 c ab 1.5 63 Kcf (%) 2.0 K (%) 4 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 0 c ab 100 200 300 T (K) 0.2 1.0 0.5 0.0 0 2 0.0 20 40 60 80 T (K) -0.2 0 2 4 6 -3 χ (x10 10 FIG. 8: The Cu Knight shift in CeCu2 Si2 versus the bulk susceptibility4 . The solid lines are fits to the high temperature data. Inset: KHE versus T , and a fit to Eq. (8). 1 0 8 emu/mol) 0 2 4 6 8 -3 χ (x10 10 12 14 emu/mol) 1.4 0.00 Kcf (%) FIG. 1: The In(1) Knight shift in CeCoIn5 versus the bulk susceptibility1 . The solid lines are fits to the high temperature data. Inset: KHE versus T , and a fit to Eq. (8). 29 1.2 -0.10 -0.20 -0.30 0 0.8 100 200 300 T (K) 29 K (%) 1.0 0.6 Knight shift and susceptibility 0.4 0.2 0.0 are not proportional to each other ab c 0 2 4 6 -3 χ (x10 8 10 emu/mol) FIG. 9: The Si Knight shift in CeCu2 Si2 versus the bulk susceptibility4 . The solid lines are fits to the high temperature data. Inset: KHE versus T , and a fit to Eq. (8). Knight shift anomaly conduction electron spin f-electron spin susceptibilities nuclear spin Knight shift anomaly conduction electron spin f-electron spin susceptibilities nuclear spin different susceptibilities have distinct T-dependence Knight shift anomaly Knight shift susceptibility Emergence of the low-T coherent heavy fermion is gradual transition between incoherent + coherent regimes via spin entanglement Theory of the Knight shift anomaly Quantum Monte Carlo calculation of the periodic Anderson lattice M. Jiang, N. J. Curro, R. T. Scalettar, arXiv:1403.7537 phenomenology helped asking the right questions phenomenology NMR in cuprates overdamped paramagnons as collective modes theory ( Subir’s talk) inspired extensive theory activities of the spin-fermion model Ar. Abanov, A. V. Chubukov, J. Schmalian (2003) M. A. Metlitski, S. Sachdev, PRB (2010) K. B. Efetov, H. Meier, and C. Pépin Nature Phys. (2013) A. M. Tsvelik, A. V. Chubukov, PRB (2014) S. Sachdev, R. La Placa, PRL 2013 C. Pépin, et al. arXiv:1408.5908 inspired search for d-wave pairing P. Monthoux A. Balatsky D. Pines (1991) P. Monthoux, D. Pines (1992) D. A. Wollman et al PRL (1993) C.C.Tsuei, J.R. Kirtley et al. Phys. Rev. Lett. (1994). L. H. Greene et al. Physica (2000). conclusion strongly correlated electron systems are full of surprises = it is very hard to make predictions experiment phenomenology models / theory Averaged annual sun shine in Germany Averaged annual sun shine in Germany