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Transcript of Happy Birthday Eugene! - Lehman College ... Happy Birthday Eugene! Wishing you great beach-soccer...

  • Happy Birthday Eugene!

    Wishing you great beach-soccer games with good friends till 120 !

  • Field-induced Quantum Critical Route to a Fermi Liquid in High-Tc Superconductors

    CUNY March 13, 2009

    L. Krusin-Elbaum IBM T.J. Watson Research Center, Yorktown Heights, New York

    Strange metal

    � Antecedent states of matter that become unstable in favor of high Tc – commonly referred as the `normal state’

    � Key to the origins of high Tc

  • Phase diagram

    Pseudogap phenomenon: friend or foe?

    In the `foeIn the `foe’’ views views �� QCPQCP

    • d-density wave (staggered flux state: Laughlin, Chakravarty, Lee, etc.)

    • Loop-current order (broken time-reversal symmetry: C. Varma)

    • Mixed order parameters (dx2-y2+idxy, dx2-y2+is, etc.)

    • RVB: Strange metal beyond the pseudogap energy scale � no need for QCP (P.W. Anderson)

    Strange metalAF

    PG

    `Normal’ state �� Many states, many transitions

    CUNY March 13, 2009

  • Latest: Some evidence for the time-reversal symmetry breaking in the PG phase

    �Novel magnetic order in the pseudogap phase of YBa2Cu3O6+x and HgBa2CuO4+δ Bourges et al., PRL 96, 197001 (2006); condmat/arXiv:0805.2959 (2008), also Mook et al, 2008.

    neutrons

    Polar Kerr effect

    �Spontaneous Kerr rotation in zero field near PG in YBa2Cu3O6+x Kapitulnik et al., PRL 100, 127002 (2008) CUNY

    March 13, 2009

  • •Quantum vortex liquid in La2-xSrxCuO4 L. Li et al., Nature Phys. 3, 311 (2007).

    The Debate: A Friend, Perhaps?

    Vortices and pseudogap •Nernst effect in La2-xSrxCuO4

    Z. A. Xu et al., Nature 406, 486 (2000).

    •THz conductivity in Bi2Sr2CaCu2O8+y J. Corson et al., Nature 398, 221 (1999).

    �Vortex-like excitations (superconducting fluctuations) exist above Tc.

    �Pseudogap - an ultimate upper limit to the vortex state?

    @ 60 T and above?

    CUNY March 13, 2009

  • Phase diagram deduced from ARPES & transport Bi-2212

    A. Kaminski, S. Rosenkranz, H. M. Fretwell, Z. Z. Li, H. Raffy, M. Randeria, M. R. Norman, and J. C. Campuzano, Phys. Rev. Lett. 90, 207003 (2003)

    �coherent metal phase @ low-T & high hole doping p � two well defined spectral peaks in ARPES (due to

    coherent bilayer splitting, superlinear ρ �incoherent metal phase @ high-T & low p � linear ρ, single broad feature in ARPES

    crossover @ Tx CUNY March 13, 2009

  • � Ultrahigh magnetic fields to kill superconductivity and to examine ‘normal’ state far on the overdoped side of the dome

    We have our big hammer:

    Searching for: � Transformation into a conventional metal � Quantum (or not) phase transition(s) between `normal’ states of matter antecedent to high-Tc

    CUNY March 13, 2009

  • Pseudogap Closed by Zeeman Splitting

    � The right-hand-side translates onto the Zeeman energy scale on the left-hand- side as (gµB/kB)H. � Hpg and T* obtained separately in the same crystals in the overdoped regime, give a scaling gµBHpg = kBT* with g = 2.0 (inset).

    T. Shibauchi, L. Krusin-Elbaum, M. Li, M.P. Maley, and P.H. Kes, Phys. Rev. Lett. 86, 5763 (2001)

    200

    150

    100

    50

    0

    µ 0 H

    pg (

    T )

    2001000 T* (K)

    gµBHpg = kBT*

    700

    600

    500

    400

    300

    200

    100

    0

    T o

    r (g

    µ B /k

    B )H

    ( K

    )

    0.250.200.150.10 p

    500

    400

    300

    200

    100

    0

    µ 0 H

    (T )

    Hpg

    Tc

    T* Hsc

    •Pseudogap closing field Hpg decreases with doping

    •Zeeman scaling gµBHpg = kBT* holds → suggesting spin-singlet correlations in forming the pseudogap

    •Peak field scales with Tc(p)

    CUNY March 13, 2009

    Tc vs doping `dome’ � Tc/Tcmax = 1-82.6 (p-0.16)2

  • c-axis resistivity ρc: a powerful probe of the pseudogap •Intrinsic tunneling junctions along the c axis (layered structure with large anisotropy)

    • ρc probes the low-energy DOS in the bulk

    •Recovery of the DOS by magnetic field → negative interlayer magnetoresistance (MR)

    •Pseudogap closing field Hpg = H* can be evaluated

    T. Shibauchi et al., Phys. Rev. Lett. 86, 5763 (2001); Phys. Rev. B 67, 064514 (2003).

    L. Krusin-Elbaum, T. Shibauchi, C. H. Mielke, Phys. Rev. Lett. 92, 097005 (2004).

    T. Watanabe et al., Phys. Rev. Lett. 84, 5848 (2000).

    Bi2Sr2CaCu2O8+y

    T* from the deviation from the T-linear metallic dependence consistent with the tunneling spectra and the static susceptibility.

    T = 110 K

    ρc sensitive to the (π,0) points (`hot spots’) of the Fermi surface, where the pseudogap first opens up

    CUNY March 13, 2009

  • 2.5

    2.0

    1.5

    1.0

    0.5

    0.0

    ρ c (

    Ω c

    m )

    6050403020100

    µ0H (T)

    2.5 K

    20 K

    3.5 K

    50 K

    40 K

    30 K

    10 K 7.5 K

    5 K

    4.2 K

    H0ρ

    Hsc

    2.0

    1.5

    1.0

    0.5

    0.0

    0.1 1 10 100

    40 K

    ρc n

    Hpg H0ρ

    Hsc

    1.34

    1.32

    1.30

    1.28

    1.26

    1.24

    1.22

    1.20

    ρ c (

    Ω c

    m )

    120110100908070

    T (K)

    T*T*T*

    0 T 30 T

    58.5 T

    OD (Tc = 67 K)

    0.4

    0.3

    0.2

    0.1

    0.0

    ∆ ρ c

    ( Ω

    c m

    )

    100806040200 µ0H (T)

    T (K) 62.2 70.4 81.8 95.4

    Hpg

    b

    4

    3

    2

    1

    0

    ρ c (

    Ω c

    m )

    25020015010050

    T (K)

    -10

    -8

    -6

    -4

    -2

    0

    M R

    @ 31.2 T

    (% )T*

    OD (Tc = 78 K)

    0 T

    ∆ρc a

    T. Shibauchi et al., Phys. Rev. B 67, 064514 (2003).

    ρc(H,T) in Bi2Sr2CaCu2O8+y crystals

    T. Shibauchi, L. Krusin-Elbaum, M. Li, M.P. Maley, and P.H. Kes, PRL 86, 5763 (2001).

    CUNY March 13, 2009

  • Field anisotropy of pseudogap closing field

    L. Krusin-Elbaum, T. Shibauchi, C. H. Mielke, Phys. Rev. Lett. 92, 097005 (2004).

    Hpgab / Hpgc = 1.35 ± 0.1 Anisotropy of g-factor [T. Watanabe et al., Phys. Rev. Lett. 84, 5848 (2000)]

    gc /gab = 1.3

    (χc(T) ~ 1.6 χab(T)) Zeeman scaling

    gcµBHpgc = gabµBHpgab ~ kBT* Triplet excitation @high H overcomes spin-singlet correlations responsible for the gap in the spin spectrum and orbital contribution is very small.

    χc/χab=(gc /gab)2

    CUNY March 13, 2009

  • M. R. Norman et al., Adv. Phys. 54, 715 (2005).

    Phase diagram

    CUNY March 13, 2009

  • Y. Kubo et al., Phys. Rev. B 43, 7875 (1991).

    D. N. Basov and T. Timusk, Rev. Mod. Phys. 77, 721 (2005).

    ρ(T)=ρ(0)+AT2

    Fermi liquid metal

    ρ(T) ~ Tn 1�n�2

    Non-Fermi liquid

    polycrystals

    Phase diagram

    Heavily overdoped Tl2Ba2CuO6+x

    -How n-FL state transforms into FL state ? -Magnetic field effect?

    M. R. Norman et al., Adv. Phys. 54, 715 (2005).

    CUNY March 13, 2009

  • Can We Get to a Coventional Fermi Liquid by Applying Magnetic Field?

  • 0.040

    0.035

    0.030

    0.025

    0.020

    0.015

    ρ c (

    Ω c

    m )

    6004002000

    T 1.3

    (K 1.3

    )

    µ0H = 0 T

    0.04

    0.03

    0.02

    0.01

    0.00

    ρ c (

    Ω c

    m )

    100806040200 T (K)

    µ0H = 0 T

    Tl2Ba2CuO6 (Tc~15 K)

    ρc = ρc0 + A0T

    2 +CT

    �At zero field, ρc(T)-ρc0 ~ Tn n=1.3

    or ρc(T)= ρc0 + A0T2+CT

    Non-Fermi liquid (strange metal)

    c-axis longitudinal magneto-transport (less afflicted with orbital contributions)

    M. Abdel-Jawad et al., Nat. Phys. 2, 821 (2006).

    ρab(T) = ρab0 + AT2+CT

    CUNY March 13, 2009

  • 0.040

    0.035

    0.030

    0.025

    0.020

    0.015

    ρ c (

    Ω c

    m )

    6004002000

    T 1.3

    (K 1.3

    )

    µ0H = 0 T

    0.04

    0.03

    0.02

    0.01

    0.00

    ρ c (

    Ω c

    m )

    100806040200 T (K)

    µ0H = 0 T

    Tl2Ba2CuO6 (Tc~15 K)

    ρc = ρc0 + A0T

    2 +CT

    M. Abdel-Jawad et al., Nat. Phys. 2, 821 (2006).

    ρab(T) = ρab0 + AT2+CT

    ~T2 ~T

    isotropic anisotropic

    1/τ

    At zero field,c-axis longitudinal magneto-transport (less afflicted with orbital contributions)

    1/ζcτ

    T & momentum dependence of transport scattering rate τ

    2 channels: �conventional (� T2) �anisotropic (� T) , same symmetry as d-gapCUNYMarch 13, 2009

  • 0.04

    0.03

    0.02

    0.01

    0.00

    ρ c (

    Ω c

    m )

    100806040200 T (K)

    µ0H = 0 T

    Tl2Ba2CuO6 (Tc~15 K)

    µ0H = 45 T

    ρc = ρc(0) + A(45 T)T