Zeeman and Orbital Limiting Magnetic Fields in Cuprate Superconductors: a Signature of

Separated Spin and Charge Degrees of Freedom

Lia Krusin-Elbaum1,*, Gianni Blatter2, Takasada Shibauchi3

1 IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA2 Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland3 Department of Electronic Science and Engineering, Kyoto University,

Kyoto 606-8501, Japan

1

In cuprates, in a view where pairing correlations onset at the (normal state) pseudogap energy scale T* and acquire global coherence at a lower temperature Tc, the region Tc ☯ T ☯ T* is a vast fluctuation regime. The question remains about the doping dependencies and the connection of the relevant magnetic field scales, the field Hc2 bounding the superconducting response and the pseudogap closing field Hpg. Recent in-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi2Sr2CaCu2O8+y report hugely different limiting magnetic fields. Based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scale T* upon transformation as orbital and spin (Zeeman) critical fields, respectively. The region of superconducting coherence, experimentally tracked through the presence of large interplane Josephsoncurrents, is confined to the `dome' defined by Hsc(p) ~ 1.4Tc(p) that coincides with the usual unique upper critical field Hc2 on the strongly overdoped side. The distinctly different orbital and the Zeeman limiting fields can coexist owing to charge and spin degrees of freedom separated to different parts of the cuprates' strongly anisotropic Fermi surface.

Abstract

2

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?3

Pseudogap in high-Tc superconductors

•STM spectra in Bi2Sr2CaCu2O8+y •Generic phase diagram

Ch. Renner et al., Phys. Rev. Lett. 80, 149 (1998).

J. L. Tallon & J. W. Loram, Physica C 349, 53 (2001).

Tc vs doping `dome’Tc/Tc

max = 1-82.6 (p-0.16)2

Tc

sc fluctuations?spin-gap? d-density wave (QCP) ?

4

High-Field Phase Diagram from Nernst Effect

Y. Wang et al., Phys. Rev. Lett. 88, 257003 (2002).

LSCO

YBCOy = 6.50

Nernst signal

transport line-entropy = eyΦ0/ρ(H)

Upper critical field Hc2?5

Limiting Field from Nernst Effect vs DopingY. Wang et al., Science 299, 86 (2003)

Limiting field Hc2N

relates to the gap T* from ARPES , and from intrinsic tunneling spectroscopy

BSCCO

V. M. Krasnov et al., Phys. Rev. Lett. 86, 2657 (2001)

scaling

convert Hc2N to

length scales

ξ0 = (Φ0/2π Hc2N)1/2

ξp = ħvF/α∆

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Field Dependence of the c-axis Resistivity ρc (H) in Bi2Sr2CaCu2O 8+y

Below H0θ ρc(H) is zero, characteristic of pinned vortex solid

H0θ is a harbinger of a vortex liquid state (we used 0.01 ρn

c criterion) where pancake vortices with the attached Josephson strings are sufficiently mobile to cause dissipative phase slips between the sc layers [Morozov et al., PRL 84, 1784 (2000)]

At the peak at Hsc ( Hc2) quasiparticle tunneling takes over that of Cooper pairs

Hpg closes the pseudogap

H||c

H||ab

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Field-Anisotropy in the Superconducting State in Bi2Sr2CaCu2O 8+y

anisotropy large &T-dependent

In quasi-2D, the angle-dependent critical field derived within the Lawrence-Doniach model,

H(θ)sin θ + ε H2(θ) = Hc2c,

is controlled by the Hc2c (T).

ε e2 ld2/6ħc is ~ 6.8 x 10-3 T -1

for Bi-2201, which is nearly twice our estimate for Bi-2212 with p = 0.225. Here, ld is the effective thickness of superconducting layers.

~ -0.27 T/K

~ -3 T/K

Anisotropy ratio γ ∝ (1-T/Tc)-1/2

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Peak Field and the Coherence Length ξ

c-axis conductivity a two-channel tunneling process

peak field Hsc is ~ T-exponential

LSCO magnetic data from H.H. Wen et al., (2003)

L. Krusin-Elbaum et al., Phys. Rev. B (2004)

BSCCO

coherence `dome’defined by Hsc ~ 1.4 Tc

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Pseudogap Closed by Zeeman Splitting

200

150

100

50

0µ 0

Hpg

(T

)200150100500

T* (K)

gµBHpg = kBT*

700

600

500

400

300

200

100

0

T o

r (g

µ B/k

B)H

(K

)

0.250.200.150.10p

500

400

300

200

100

0

µ0 H

(T)

Hpg

Tc

T*Hsc

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 gµBHp g = 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)

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Anisotropy of Hpg

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

Hpgab / Hpg

c = 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 = gabμBHpg

ab ~ kBT*

The paramagnetic limit for isotropic s-wave pairing in the absence of spin-orbit scattering is Hp(T=0) = 1.84 Tc(H=0), and for anisotropic singlet pairing by Hp = 1.58 Tc. By taking T* =TMF0 ~ 100 K this would correspond to 184 T and 158 T respectively, both way above our values of Hpg. 11

How the orbital and Zeeman limiting fields relate

pairing correlations quenched for a0 < ξ*Nernst orbital field Nc2

N

magnetic length

pair correl. length

quadratic in T*

Note: in BCS, Hc2* conventional Hc2

α0.6

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Velocities of Electrons as a Function of Doping in Various Cuprates

(a) The low-energy Fermi velocity (vF) obtained by linearly fitting the dispersion between 0 and -0.05 eV. The dashed line represents an average over all the measured values.

(b) The high-energy velocity (vHE) obtained by linearly fitting the dispersion between the energy range of -0.1 and -0.2 eV. These velocity values are averaged over many different measurements.

The arrow in the inset of (b) shows the (0,0)-(π,π) nodal direction in the first Brillouin zone in the reciprocal space.

X.J. Zhou et al., Nature 423, 398 (2003)

13 Conversion: 1 eV = 2.418x104 m/sec

Evaluating Hc2N (T~ 0 K)

Both LSCO and BSLCO are plotted. We take BSCCO to follow this`universal' curve.

By simple matching of Hc2N to Hsc(0) in OD

regime for p~ 0.2 , where Hsc(0) ~ usual Hc2.

From `universal’ Hc2N(T)/Hc2

N (0) vs T/TonsetN

implicit in the data of Y. Wang et al.

LSCO data on Hc2N(T) @ p = 0.2 vs T/Tonset

N is extrapolated to T = 0.

From `universal’ curve Hc2

N(T)/Hc2N (0) vs T/Tonset

N

one can readout values of Hc2

N (0) for different doping levels p.

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How One Can Dispose of the Same Correlation Energy Twice?

1. via orbital route Hc2N

2. via Zeeman (spin) route Hpg

Resolution: Separated spin and charge degrees of freedom residing in different regions ofstrongly anisotropic (truncated) Fermi surface

Starting point quantum spin-singlet liquid forming at T*. Upon doping, the spin-liquid becomes energetically favorable, charge and spin degrees of freedom separateand holes are expected to condense on the spin-liquid background, turning phase coherent at a lower energy Tc.

Common feature: breakup of the Fermi surface (FS) into regions describing spin-singlet pairs and charged holes:

the spin-pairing opens up gaps near the (0, π) points (the FS corners) − the corresponding pseudogap energy T*establishes correlations on the scale ξ* ~ vF/T*.

upon doping, a truncated Fermi surface appears around the (π, π) diagonals. When charges pair up, they draw correlations from the spin-singlet background, hence spin-singlet pairing at the FS corners and hole-pairing at the diagonals derive from the same energy scale T*.

Pairing energy need not match the underlying energy scale T* of the spin liquid, but STM of the vortex cores do show that this is indeed the case in the UD cuprates.

In the described scenario at large doping the separation is ill defined once the spin- and charge degrees of freedom merge into Fermi-liquid type quasiparticles.

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Recent in-plane thermal (Nernst) and interlayer (tunneling)transport experiments in Bi2Sr2CaCu2O8+y hightemperature superconductors report hugely different limitingmagnetic fields.

Based on pairing (and the uncertainty principle)combined with the definitions of the Zeeman energy and themagnetic length, we show that

in the underdoped regime both fieldsconvert to the same (normal state) pseudogap energy scale T*upon transformation as orbital and spin (Zeeman) critical fields,respectively.

in the overdoped regime both fieldsappear to coincide with the usual upper critical field Hc2.

We reconcile these seemingly disparate findingsinvoking separated spin and charge degrees of freedom residing indifferent regions of a truncated Fermi surface.

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Synopsis