No Slide Title

Document Sample
No Slide Title Powered By Docstoc
					        Vorticity and Phase Coherence
         in Cuprate Superconductors
   Yayu Wang, Lu Li, J. Checkelsky, N.P.O. Princeton Univ.
              M. J. Naughton, Boston College
                   S. Uchida, Univ. Tokyo
S. Ono, S. Komiya, Yoichi Ando, CRI, Elec. Power Inst., Tokyo
            Genda Gu, Brookhaven National Lab

          1.   Vortex Nernst effect
          2.   Loss of long-range phase coherence
          3.   The Upper Critical Field
          4.   High-temperature Diamagnetism




                                                Taipeh, June 2006
        Phase diagram of Cuprates


        Mott insulator
                                                s = 1/2   hole



                         T*
T         pseudogap


                          Tc           Fermi
                                       liquid   LSCO = La2-xSrxCuO4
    AF                        dSC               Bi 2212 = Bi2Sr2CaCu2O8

    0       0.05                    0.25        Bi 2201 = Bi2-yLaySr2CuO6

                     doping x
Condensate described by a complex macroscopic wave function

       Y(r) = Y1 + iY2 = |Y(r)| exp[iq(r)]
                  F



                                                F




                              y2
      y1
      amplitude fluctuation
                                                            y2
                                   y1   phase fluctuation

      Anderson-Higgs mechanism:           Phase stiffness
      singular phase fluc. (excitation of vortices)
Phase rigidity ruined by mobile defects
Long-range phase coherence requires uniform q
                                               “kilometer of dirty lead wire”



    q                  q                q                 q

        Hr  1        d 3r r S (q )
                                    2
                                            phase rigidity measured by rs
                 2
          Phase coherence destroyed by vortex motion



                 q
                                                  q


          Kosterlitz Thouless transition in 2D films (1982)
              Vortices, fundamental excitation of type-II SC


    Vortex in Niobium                           Vortex in cuprates

                                                                       CuO2 layers
                     b(r)
Normal core                        superfluid
                                   electrons
                                                        Js             2D vortex pancake

H
                      Js


                                                                 x

                x
                                   coherence length x

                            b(r)                             |Y|  D



                                                             London length l
upper critical field
    Mean-field phase diagram
                                                       Cuprate phase diagram
         2H-NbSe2
4T                                             100 T
                                normal
                                                                    Hc2
                             liquid

H                   Hm H
                                 Hc2
                                                             vortex
          vortex solid
                                                             liquid
                                                       Hm
         Hc1

     0                   T               Tc0                Tc
                                                  vortex    100 K
                                         7K       solid
         Meissner state
      The Josephson Effect, phase-slippage and Nernst signal



                                      Passage of a vortex
                                      Phase diff. f jumps by 2



                   vortex                          
                                        2eVJ   f
                                 2
Phase difference




                                                       
                    f                  2eVJ  2  nV

                            VJ            Integrate VJ to give dc signal
                                          prop. to nv

                                 t
          Nernst experiment




                                          ey




                                                Hm
                                                            H

Vortices move in a temperature gradient        Nernst signal
Phase slip generates Josephson voltage
                                               ey = Ey /|   T|
        2eVJ = 2h nV
        EJ = B x v
   Nernst effect in underdoped Bi-2212 (Tc = 50 K)




Vortex signal persists to 70 K above Tc.
                                  Wang, Li, Ong PRB 2006

Vortex-Nernst signal in Bi 2201
Nernst curves in Bi 2201             Yayu Wang,Lu Li,NPO PRB 2006




                           optimal                underdoped
  overdoped




                                Nernst signal

                                eN = Ey /|   T|
             Kosterlitz-Thouless transition
      Spontaneous vortices destroy superfluidity in 2D films
      Change in free energy DF to create a vortex

      DF = DU – TDS = (ec – kBT) log (R/a)2

DF < 0 if T > TKT = ec/kB       vortices appear spontaneously



                 rs               D




         0               TKT          TcMF
           3D version of KT transition in cuprates?
                                     Nernst
                                     region




•Loss of phase coherence determines Tc
•Condensate amplitude persists T>Tc
• Vorticity and diamagnetism in Nernst region
 In hole-doped cuprates


1.   Existence of vortex Nernst signal above Tc

2.   Confined to superconducting “dome”

3.   Upper critical field Hc2 versus T is anomalous

4.   Loss of long-range phase coherence at Tc
     by spontaneous vortex creation (not gap closing)

5.   Pseudogap intimately related to vortex liquid state


     More direct (thermodynamic) evidence?
Diamagnetic currents in vortex liquid




Supercurrents follow contours of condensate

      Js = -(eh/m)    x |Y|2 z
Cantilever torque magnetometry

Torque on magnetic moment: t = m × B




                       crystal

                        B                  t
                   f                       ×
                                       m




Deflection of cantilever: t = k f
              Micro-fabricated single crystal silicon cantilever
                              magnetometer


                                                                   H




•   Si single-crystal cantilever

•   Capacitive detection of deflection
•   Sensitivity: ~ 5 × 10-9 emu at 10 tesla
    ~100 times more sensitive than commercial SQUID
Underdoped
             Wang et al.
Bi 2212
             Cond-mat/05




             Tc
Paramagnetic background in Bi 2212 and LSCO
       Magnetization curves in underdoped Bi 2212
                                                    Wang et al.
                                                    Cond-mat/05



          Tc




Separatrix Ts
               F



                                                 F




                           y2

   y1
   amplitude fluctuation
                                                            y2

                                   y1   phase fluctuation


Anderson-Higgs mechanism:            Phase stiffness
singular phase fluc. (excitation of vortices)
At high T, M scales with Nernst signal eN
M(T,H) matches eN in both H and T above Tc
    Magnetization in Abrikosov state


M
    Hc1                                  Hc2     H




                              M = - [Hc2 – H] / b(2k2 –1)
          M~ -lnH


      In cuprates, k = 100-150, Hc2 ~ 50-150 T

      M < 1000 A/m (10 G)

      Area = Condensation energy U
Wang et al.
Cond-mat/05
    Mean-field phase diagram
                                                       Cuprate phase diagram
         2H-NbSe2
4T                                             100 T
                                normal
                                                                    Hc2
                             liquid

H                   Hm H
                                 Hc2
                                                             vortex
          vortex solid
                                                             liquid
                                                       Hm
         Hc1

     0                   T               Tc0                Tc
                                                  vortex    100 K
                                         7K       solid
         Meissner state
Hole-doped optimal   Electron-doped optimal




    Tc                                   Tc
Phase fluctuation in cuprate phase diagram



                                             spin pairing
                                             (NMR relaxation,
                                  T*         Bulk suscept.)
                    pseudogap
Temperature T




                         Tonset             Onset of charge pairing
                                            Vortex-Nernst signal
                                            Enhanced diamagnetism
                                            Kinetic inductance
                        vortex liquid

                                  Tc        superfluidity
                                            long-range phase coherence
                                            Meissner eff.

                0               x (holes)
In hole-doped cuprates

1. Large region in phase diagram above Tc dome
with enhanced Nernst signal

2. Associated with vortex excitations

3. Confirmed by torque magnetometry

4. Transition at Tc is 3D version of KT transition
   (loss of phase coherence)

5. Upper critical field behavior confirms conclusion
End
                      Cooper pairing in cuprates

                                      d-wave symmetry
                                                                  +
                                                              -       -
      x    coherence length
                                                                  +

                                                         D(q )  D 0 cos 2q

             Upper critical field            f0
                                     H c2 
                                            2x 2

          cuprates                  Nb3Sn      MgB2                   NbSe2
           18                        29             57                90
                                                                                o
                                                                            x (A)

Hc2       100 Tesla                  40             10                4 Tesla
  Contrast with Gaussian (amplitude) fluctuations

                      In low Tc superconductors,
                      Evanescent droplets of
                      superfluid radius x
                      exist above Tc
              x
                       At Tc, (Schmidt, Prange „69)
                          M‟ = 21/2(kBTc / f03/2) B1/2



This is 30-50 times smaller than observed in Bi 2212
“Fluctuation diamagnetism” distinct from Gaussian fluc.
                                           Wang et al. PRL 2005



                                 1. Robustness
                                  Survives to H > 45 T.
                                  Strongly enhanced by field.
                                  (Gaussian fluc. easily suppr. in H).


                                 2. Scaling with Nernst
                                  Above Tc, magnetization M
                                  scales as eN vs. H and T.



                                 3. Upper critical field
                                 Behavior of Hc2(T) not mean-field.
 Signature features of cuprate superconductivity


1. Strong Correlation                                   +
                                                    -       -
2. Quasi-2D anisotropy                                  +
3. d-wave pairing, very short x

4. Spin gap, spin-pairing at T*

5. Strong fluctuations, vorticity

6. Loss of phase coherence at Tc
                                         Hc2

                                     vortex
                                     liquid

                                    Hm
                                               Tc
     Comparison between x = 0.055 and 0.060
     Sharp change in ground state          Lu Li et al., unpubl.




Pinning current reduced by a factor of ~100 in ground state
Two distinct field scales
In ground state, have 2 field scales

1) Hm(0) ~ 6 T
         Dictates phase coherence, flux expulsion

2) Hc2(0) ~ 50 T
          Depairing field. Scale of condensate suppression




                                                             M (A/m)
               Magnetization in lightly doped La2-xSrxCuO4
Lu Li et al., unpubl.                                 SC dome
                  0.03          0.04     0.05          0.06

                               4.2 K
                 5K
                                         5K



                                                     30 K

                        35 K      35 K        30 K




                                                      4.2 K
                                  dissipative,
                                  vortices mobile




                                   Long-range
                                   phase coherence




               Sharp transition in Tc vs x (QCT?)
Vortex-liquid boundary linear in x as x   0?
The case against inhomogeneous superconductivity
(granular Al)




   1.   LaSrCuO transition at T = 0 much too sharp

   2.   Direct evidence for competition between d-wave SC
        and emergent spin order

   3.   In LSCO, Hc2(0) varies with x
   Competing ground states
Abrupt transition between different ground states
   at xc = 0.055

1. Phase-coherent ground state (x > 0.055)
   Cooling establishes vortex-solid phase; sharp melting field

2. Unusual spin-ordered state (x < 0.055)

    i) Strong competition between diamagnetic state
         and paramagnetic spin ordering

    ii) Diamagnetic fluctuations extend to x = 0.03

    iii) Pair condensate robust to high fields (Hc2~ 20-40 T)

    iv) Cooling to 0.5 K tips balance against phase coherence.
Field sensitivity of Gaussian fluctuations
                                             Gollub, Beasley,
                                             Tinkham et al.
                                             PRB (1973)
Vortex signal above Tc0 in under- and over-doped Bi 2212
                                          Wang et al. PRB (2001)
     Abrikosov vortices near Hc2


          x




      Upper critical field Hc2 = f0/2x2
Condensate destroyed when cores touch at Hc2
Anomalous high-temp. diamagnetic state

1.    Vortex-liquid state defined by large Nernst signal and
     diamagnetism

2.   M(T,H) closely matched to eN(T,H) at high T (b is 103 - 104 times
     larger than in ferromagnets).

3.   M vs. H curves show Hc2 stays v. large as T Tc.

4.   Magnetization evidence that transition is by loss of phase
     coherence instead of vanishing of gap

5.   Nonlinear weak-field diamagnetism above Tc to Tonset.

6.   NOT seen in electron doped NdCeCuO (tied to pseudogap
     physics)
Nernst contour-map in underdoped, optimal and overdoped LSCO
                     Tc
                                 110K




• In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K
• diamagnetic signal closely tracks the Nernst effect
PbIn, Tc = 7.2 K (Vidal, PRB ‟73)                      Bi 2201 (Tc = 28 K, Hc2 ~ 48 T)
                                                      2.0


      T=1.5K                                                                          T=8K
                                                      1.5




                                      e y ( m V/K )
                                                      1.0
           ey

      Hd                                              0.5
                                                                                           Hc2
                      Hc2

                                                      0.0
                                                            0   10   20      30       40   50    60
0.3                 1.0                                                   m 0 H (T)
           H/Hc2

                • Upper critical Field Hc2 given by ey                    0.
                                                                               Wang et al. Science (2003)
                • Hole cuprates --- Need intense fields.
Vortex-Nernst signal in Bi 2201
     NbSe2               NdCeCuO              Hole-doped cuprates



      Hc2                                                     Hc2
                              Hc2

                         vortex                      vortex
                         liquid                      liquid


        Hm
                           Hm                   Hm

               Tc0                     Tc0                      Tc0

                     Expanded vortex liquid   Vortex liquid dominant.
Conventional SC
                     Amplitude vanishes at    Loss of phase coherence
Amplitude vanishes
                     Tc0                      at Tc0 (zero-field melting)
at Tc0 (BCS)
          Phase diagram of type-II superconductor

            2H-NbSe2                                          cuprates

4T
                                normal                        ?
                                                                         ?
                             liquid

H                   Hm                         H          vortex
                                                          liquid
                                 Hc2
          vortex solid
                                                     vortex
         Hc1                                         solid         Hm
                                               Hc1
     0                   T               Tc0         0              T    Tc0
               Meissner state
               Superconductivity in low-Tc superconductors (MF)

     Cooper pairs with coherence length x

                                                                  Quasi-particles


                  x
                                                                      Energy gap D

    Pairs obey macroscopic wave function

       ˆ
       Y (r )  | Y | e i q ( r )           Phase

amplitude
            |Y| D



                                                    Gap D
   Phase q important in Josephson effect
                                                            Temp. T       Tc
      Torque magnetometry                    c, z
                                                             H
  Van Vleck (orbital) moment mp
                                                 q
                                            mp
        t = mp x B + MV x B

                      2D supercurrent               M

      t/V = ccHx Bz – caHz Bx + M Bx
                                                     t

       Meff = t / VBx = Dcp Hz + M(Hz)                       mp



                                                                  H
Exquisite sensitivity to 2D supercurrents
                                                         M
                                  Wang et al., unpublished
Hc2(0) vs x matches Tonset vs x
Overdoped LaSrCuO x = 0.20




                             H*




                              Hm


                                   Tco
                             M vs H below Tc
                                               Full Flux Exclusion
         Strong Curvature!
                                        Hc1




-M



     H
Strong curvature persists above Tc
M non-analytic in weak field



          M ~ H1/d
       Susceptibility and Correlation Length


     Strongly H-dependent
     Susceptibility c = M/H




Fit to
Kosterlitz Thouless theory


   c = -(kBT/2df02) xKT2

    xKT = a exp(b/t1/2)
   Non-analytic magnetization above Tc


      M ~ H1/d

Fractional-exponent
region
 Plot of Hm, H*, Hc2 vs. T


• Hm and H* similar to
hole-doped

• However, Hc2 is
conventional

• Vortex-Nernst signal
vanishes just above Hc2
line
                                                                                                                            Wang et al. Science (2003)

                         overdoped                                          optimum                                                underdoped
               3.5
                         OD-Bi2212 ( T c =65K)                    3.5     OPT-Bi2212 ( T c =90K)                      3.0       UD-Bi2212 ( T c =50K)     40K
               3.0                                                                          75
                                  45
                            50                                    3.0                                       70K
                                                                                                                      2.5                                 45
               2.5                40
                                        55                        2.5                                                                                     50
                                             35
                                                                                                            80        2.0
               2.0
e y ( m V/K)




                                                                                                                                                          55
                                 60                               2.0
                                                        30                            90
               1.5                                                                                          85        1.5                                 60
                                                                  1.5

               1.0               65                            25 1.0                                                 1.0                                 65
                                                                                   95

               0.5                                                                                                                                        70
                                  70                              0.5
                                                                                   100                                0.5                       75
                                             75                20                                                                               80
                                                               80                           105
               0.0                                             85 0.0                                                                           90
                                                                                            110                                                 100
                                                               90                                                     0.0
                     0      5     10      15       20   25   30       0      5   10        15     20   25        30         0      5   10      15   20   25     30
                                       m 0 H (T)                                      m 0 H (T)                                             m 0 H (T)




                                                    Field scale increases as x decreases
Optimal, untwinned BZO-grown YBCO
Nernst effect in LSCO-0.12             Xu et al. Nature (2000)
                                       Wang et al. PRB (2001)




  vortex Nernst signal onset from T = 120 K, ~ 90K above Tc`1
Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50).
Onset temperatures much higher than Tc0 (18 K, 26 K).
Resistivity is a bad diagnostic for
field suppression of pairing
amplitude

 Plot of r and ey versus T at fixed H
 (33 T).

 Vortex signal is large for T < 26 K,
 but r is close to normal value rN
 above 15 K.
                    Resistivity Folly
                                                      Bardeen Stephen law (not seen)               Ong Wang, M2S-RIO, Physica C (2004)

                                                                                  1.0
                                N d CCO ( T c =24.5K)
              0.8                                                                           LSCO (0.20)
                                                                                  0.8
                        12K
              0.6                                r                                          22K
                                                                                                                  r




                                                                    e y( m V/K)
e y (m V/K)




                                                                                  0.6


              0.4
                                                                                  0.4
                                       ey                                                                    ey
              0.2
                                                                                  0.2
                                                                                                                                 Hc2
                                                Hc2
              0.0                                                                 0.0
                    0   2   4      6        8    10     12   14                         0    5    10   15    20       25   30
                                  m 0 H (T)
                                                                                                       m 0 H (T)


                        Resistivity does not distinguish vortex liquid from normal state
Isolated off-diagonal Peltier current axy versus T in LSCO

Vortex signal onsets at 50 and 100 K for x = 0.05 and 0.07
 Contour plots in
 underdoped YBaCuO6.50
 (main panel) and optimal
 YBCO6.99 (inset).


• Vortex signal extends above
70 K in underdoped YBCO,
to 100 K in optimal YBCO

• High-temp phase merges
continuously with vortex
liquid state




                                Tco
           Nernst effect in optimally doped YBCO




                                       Vortex onset temperature: 107 K
Nernst vs. H in optimally doped YBCO
      Separatrix curve at Ts




Optimum doped              Overdoped
              Vortex Nernst signal

axy = b M

b-1 = 100 K
  BCS transition                 2D Kosterlitz Thouless transition
                                                    n vortex
            D                             D


       r                                 r
        s                                 s



   0               Tc                0        TKT   TMF


  H = ½ rs d3r ( f)2
                                 Phase coherence destroyed at TKT
rs measures phase rigidity       by proliferation of vortices


                High temperature superconductors?
             Strong correlation in CuO2 plane

     Cu2+                   Large U
                                                  charge-transfer
                                                  gap Dpd ~ 2 eV




               metal?                                      best
                                      Mott insulator       evidence
antiferromagnet J~1400 K                                   for large U

                            doping




        H   t  c  is c js  U  ni ni                Hubbard
                i , j ,s                   i
              t = 0.3 eV,    U = 2 eV,    J = 4t2/U = 0.12 eV
Hole-doped optimal   Electron-doped optimal
Overall scale of Nernst signal amplitude

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:4
posted:11/29/2011
language:English
pages:82