Quantum Criticality, high Tc superconductivity and the AdS/CFT - PowerPoint PPT Presentation

Quantum Criticality, high Tc superconductivity and the AdS/CFT correspondence. Jan Zaanen QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. 1

String theory: what is it really good for? - Hadron (nuclear) physics: quark-gluon plasma in RIHC. - Quantum matter: quantum criticality in heavy fermion systems, high Tc superconductors, … Started in 2001, got on steam in 2007. QuickTime™ and a decompressor are needed to see this picture. Son Hartnoll Herzog Kovtun McGreevy Liu Schalm 2

Quantum critical matter Quark gluon plasma Iron High Tc Heavy fermions superconductors (?) superconductors Quantum critical Quantum critical 3

High-Tc Has Changed Landscape of Condensed Matter Physics Magneto-optics High-resolution ARPES Transport-Nernst effect Spin-polarized Neutron STM High Tc Superconductivity Inelastic X-Ray Scattering Angle-resolved MR/Heat Capacity

? QuickTime™ and a decompressor are needed to see this picture. Photoemission spectrum

Holography and quantum matter “ Planckian dissipation ” : quantum critical matter at high temperature, perfect fluids and the linear resistivity (Son, Policastro, … , Sachdev) . Reissner Nordstrom black hole: “ critical Fermi-liquids ” , like high Tc ’ s normal state (Hong Liu, John McGreevy) . Dirac hair/electron star: Fermi-liquids emerging from a non Fermi liquid (critical) ultraviolet, like overdoped high Tc (Schalm, Cubrovic, Hartnoll) . Scalar hair: holographic superconductivity, a new mechanism for superconductivity at a high temperature (Gubser, Hartnoll … ) . 6

Plan 1. Crash course: quantum critical electron matter in solids. 2. Crash course: the AdS/CFT correspondence. 3. Holographic quantum matter: Planckian dissipation, marginal/critical Fermi-liquids, Fermi liquids and superconductors. 7

Twenty five years ago … Mueller Bednorz Ceramic CuO ’ s, likeYBa2Cu3O7 Superconductivity jumps to ‘ high ’ temperatures 8

Graveyard of Theories Mueller Schrieffer Mott Laughlin Abrikosov Anderson Leggett De Gennes Bednorz QuickTime™ and a decompressor are needed to see this picture. Lee Wilczek Ginzburg Yang 9

The quantum in the kitchen: Landau ’ s miracle Kinetic energy Electrons are waves Fermi Pauli exclusion principle: every energy state occupied by one electron Unreasonable: electrons strongly interact !! Fermi momenta k=1/wavelength Landau ’ s Fermi-liquid: the highly collective low energy quantum excitations are like electrons that do not interact. Fermi surface of copper 10

BCS theory: fermions turning into bosons Fermi-liquid fundamentally unstable to attractive interactions. Bardeen Cooper Schrieffer Quasiparticles pair and Bose condense:   vac .  c  k    BCS   k u k  v k c k  Ground state Conventional superconductors (Tc < 40K): “ pairing glue ” = exchange of quantized lattice vibrations (phonons) ฀ 11

Fermion sign problem Imaginary time path-integral formulation Boltzmannons or Bosons: Fermions:  integrand non-negative  negative Boltzmann weights  probability of equivalent classical  non probablistic: NP-hard system: (crosslinked) ringpolymers problem (Troyer, Wiese)!!!

Phase diagram high Tc superconductors The clash: the quantum … which is good for critical metal superconductivity! The quantized The quantum fog traffic jam (Fermi gas) returns QuickTime™ and a decompressor are needed to see this picture. 13

Divine resistivity 14

Fractal Cauliflower (romanesco)

Quantum critical cauliflower

Quantum critical cauliflower

Quantum critical cauliflower

Quantum critical cauliflower

Quantum criticality or ‘ conformal fields ’ 20

Quantum critical hydrodynamics: Planckian relaxation time  Relaxation time : time it takes to convert work in entropy.        p Viscosity: s    p k B T ฀ Entropy density: T   s  T   k B ?? 1 ฀ “ Planckian viscosity ” ฀  ฀ Planckian relaxation time = the shortest possible     k B T ฀ relaxation time under equilibrium conditions that can ฀ only be reached when the quantum dynamics is scale invariant !! 21 ฀

Critical Cuprates are Planckian Dissipators van der Marel, JZ, … Nature 2003: Optical conductivity QC cuprates Frequency less than temperature: 2  r  pr  1 (  , T )  1  r  A k B T 2 , 4  1   2  r ]  const .(1  A 2 [   k B T ] 2 ) [ k B T  1 ฀ A= 0.7 : the normal state of optimallly doped cuprates is a Planckian dissipator ! ฀ 22

Divine resistivity ?! 23

Quantum Phase transitions Quantum scale invariance emerges naturally at a zero temperature continuous phase transition driven by quantum fluctuations: JZ, Science 319, 1205 (2008) 24

Phase diagram high Tc superconductors The clash: the quantum … which is good for critical metal superconductivity! The quantized The quantum fog traffic jam (Fermi gas) returns QuickTime™ and a decompressor are needed to see this picture. 25

Fermionic quantum phase transitions in the heavy fermion metals JZ, Science 319, 1205 (2008) QP effective mass ‘ bad m *  1 actors ’ E F E F  0  m *   Coleman Paschen et al., Nature (2004) Rutgers ฀

Critical Fermi surfaces in heavy fermion systems Blue = Fermi liquid Yellow= quantum critical regime Antiferromagnetic order FL Fermi surface FL Fermi surface Coexisting critical Fermi surfaces ?

Hertz-Millis and Chubukov ’ s “ critical glue ” Bosonic (magnetic, etc.) order parameter drives the quantum phase transition Electrons: fermion gas = heat bath damping bosonic critical fluctuations Bosonic critical fluctuations ‘ back react ’ as pairing glue on the electrons Supercon ductivity Fermi liquid E.g.: Moon, Chubukov, J. Low Temp. Phys. 161, 263 (2010) 28

“ Strong coupling ” Migdal- Eliashberg theory Attractive interaction due to “ glue boson ” , two parameters:   V / E F Coupling strength:  boson Migdal parameter: E F ฀ Migdal-Eliashberg: dress boson and fermion propagators up to all orders  B / E F ignoring vertex corrections which are O( ). ฀ ฀ 29

Computing the pair susceptibility: full Eliashberg 30

Watching electrons: QuickTime™ and a decompressor are needed to see this picture. photoemission Kinetic energy Electron spectral function: probability to create or annihilate an electron at a given momentum and energy. Fermi energy Fermi momenta Fermi k=1/wavelength energy energy Fermi surface of copper 31 k=1/wavelength

Fermi-liquid phenomenology Bare single fermion propagator ‘ enumerates the fixed point ’ :   Z 1    G , k                      2 k m i E v k k 2 0 F R F     , k      Im G (  , k )  A  , k Spectral function: 2 2 m  2       2     k  k F   , k     , k   The Fermi liquid ‘ lawyer list ’ : - At T= 0 the spectral weight is zero at the Fermi-energy except for the ฀    Z  k  k F   quasiparticle peak at the Fermi surface: A E F , k 2       E F       , k - Analytical structure of the self-energy:                        , k E , k E k k    ฀ F F F F k      T 2  E k k F F   E F , k F , T   - Temperature dependence: ฀ 32 ฀

ARPES: Observing Fermi liquids ‘ MDC ’ at E F in conventional Fermi-liquids: sharp Quasiparticle ‘ poles ’ 2D metal (NbSe 2 ) 33

Cuprates: “ Marginal ” or “ Critical ” Fermi liquids Fermi ‘ arcs ’ (underdoped) EDC lineshape: ‘ branch cut ’ (conformal), closing to Fermi-surfaces width propotional to energy (optimally-, overdoped). 34

Varma ’ s Marginal Fermi liquid phenomenology. Fermi- gas interacting by second order perturbation theory with ‘ singular heat bath ’ : Im P ( q ,  )  N (0)  for |  |  T T ,   , for |  |  T  N (0) sign  QuickTime™ and a decompressor are needed to see this picture. Directly observed in e.g. Raman ?? 1 ฀ G ( k ,  )  Single electron response (photoemission):     ( k ,  )   v F k  k F   2     i  g    /  c    ( k ,  )   ln max |  |, T 2 max |  |, T        c   ฀ 1     max |  |, T Single particle life time is coincident (?!) with the transport life time => linear resistivity. ฀ 35 ฀