Happy Birthday Eugene! - Lehman College ... Happy Birthday Eugene! Wishing you great beach-soccer...
date post
14-Aug-2020Category
Documents
view
2download
0
Embed Size (px)
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