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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