To submit a proposal for magnet time, www.magnet.fsu.edu

Nature 424, 912 (2003)Signature of Optimal Doping in Hall-effect Measurements on a High-Temperature Superconductor

010203040

T [K

]

p (hole concentration per Cu)0.160.100

Metal

Bi2Sr2-xLaxCuO 6+ δ

Strong Insulator

Phys. Rev. Lett. 85, 638 (2000)Metal-to-Insulator Crossover in the Low-TemperatureNormal State of Bi2Sr2–xLaxCuO6+δ

Phys Rev Lett 77, 5417 (1996) Insulator-to-metal crossover in the normal state of La2-xSrxCuO4 near optimum doping

010203040

T [K

]

0.160 0.055Metal

StrongInsulator Log-T Insulator

La2-xSr xCuO4

p (hole concentration per Cu)

The Abnormal Normal State of the High-Tc SuperconductorsUsing 60 teslas ...

...to suppress the superconducting state

...(undress the electrons)……to reveal the low-temperature

normal-state phase diagram

National High Magnetic Field Laboratory

Florida State University

33T Florida Bitter Magnet

45T Hybrid Magnet

65T Pulse Magnet15mm bore

Los Alamos National Laboratory

Advanced MagneticResonance Imagingand Spectroscopy Facility

University of Florida

11.4T MRI Magnet400mm warm bore

High B/T Facility17T, 6wks at 1mK

In-house Scientists:Luis Balicas (Magnetism and Transport)Lloyd Engel (Microwave conductivity)Scott Hannahs (Transport, Data Acquisition)Phil Kuhns (Condensed Matter NMR)Tim Murphy (Low Temp. Physics)Eric Palm (Low Temperature Physics)

Arneil Reyes (Condensed Matter NMR)Dmitri Smirnov (FIR & Raman Spectroscopy)Alexei Souslov (Ultrasound Spectroscopy)Stan Tozer (High Pressure)Yong-Jie Wang (Far Infrared Spectroscopy)Xing Wei (Visible Optical Spectroscopy)Sergei Zvyagin (Sub/Millimeter Wave Spectroscopy)

NHMFL –DC Facility

Imaging the Vortex Lattice in High Tc Superconductor

V. Mitrovic, et al. Nature (2001)

Aharonov Bohm Phase in Carbon Nanotubes

S. Zaric, et al. Science (2004)

In-house Scientists:Scott Crooker (Visible, IR, THz Spectroscopy)Marcelo Jaime (Thermodynamics, esp. Specific Heat)Neil Harrison (Thermodynamics, esp. Magnetization)Fedor Balakirev (Magneto-transport)John Singleton (Magnetization, GHz spectroscopy)Charles Mielke (RF Transport & Head of Users Program)Albert Migliori (Thermodynamics, Ultrasound Spectroscopy)Dwight Rickel (Optical Spectroscopy)Jason Lashley (Thermodynamics, esp. Specific Heat)

NHMFL –Pulsed Facility

Six fully-multiplexed magnet cells host 150-200 visiting scientists a year,

20% travel from overseas to use unique pulsed field capabilities

Magnetic Field Driven Phase Transitions and Quantum Criticality

Jaime, et al, PRL 89 (2002) 287201Harrison, et al, PRL 90 (2003) 096402 Kim, et al, PRL 91 (2003) 256401

Preliminary, unpublished data removed by request of author.

High B/T Facility

In-house Scientists:Jian-Sheng Xia (Low T Physics)Dwight Adams (Low T Physics)Yoonseok Lee (Cond. Matt. Physics)

NHMFL - UF Facilities

•High Field:B = 15.5/17 T– 4.2/2.2 K

•Ultra-Low Temperatures5 mole PrNi5 nuclear demag refrigeratorTmin< 0.5mK, 8nW cooling powerMaintains 1mK for > 6 wks

AMRIS Facility

Rxx (Ω

)2+3/8

7/38/3

7/3

8/3

12/514/5

Need for High B/T• Small energy gap of FQHE states• Small energy differences among

competing quantum phases• Quantum phase transitions

Nuclear MagneticOrdering

Hybrid Insert InnovationsMid-plane disks

use elongated hole to maximize hoop strength.

End disks use elliptical holes to increase bending stiffness.

Mid-Plane / End TurnFlorida Bitter Plates

Cu/Nb3Sn composite strands around Cu cores inside

10mm x 12mm steel conduit45T NHMFL hybrid magnet

Superconducting Magnet Development

900 MHz NMR magnet• 21.1 teslas• 105mm warm bore• 1 ppb homogeneity

High Tc Insert Coil• 1999…3T…16mm bore

in 19T background field• 2003…5T…38mm bore

in 20T background field

NHMFL: Justin Schwartz, Huub Weijers, Ulf TrociewitzIndustrial Collaborator: Ken Marken, Oxford Instruments

A-section(double pancake)

B-section(double pancake)

C-section(layer wound)

Sectionsconnected in series

Terminals

1 mm gapbetween sections

for LHe flow

Bi2212 conductorco-wound with

oxide coated ss-tape

Coil stacks andjoints gluedwith epoxy

100 YEARS OF NON-DESTRUCTIVE MAGNETSM

AG

NE

TIC

FIE

LD

(t

esla

s)

YEAR

2003: 25T in 38mm boreusing 5T high-Tc insert(world record)

2004: 900 MHz (21.1T) NMR magnet(competitive in peak field,uniquely large 105mm warm bore)

1996: 33T DC Resistive Magnet (world record)

1999: 80T Short-Pulse Magnet (ties the world record)

2006 - 100T Multi-shot Pulsed Magnet

1998: 60T Controlled-Pulse Magnet(world record) (rebuild in 2004)

1999: 45T DC Hybrid Magnet(world record)

State-of-the-Art Fermi Surface Studies Sample-Tilting in the Hybrid… or deHaas-vanAlphen Oscillations

in Pulsed Magnetic Fields

30 35 40 45 50 55 60-10

-5

0

5

10

dHvA in Ce0.6La0.4B6si

gnal

(a.u

.)

B (T)

Goodrich et al, PRL (2001), for example

sampledetection coil

compensation

1mm diametMost suitable for:

Heavy mass systemsDisordered systems

Most suitable forlow-dimensional systems

Hussey et al, Nature (2003)“Full Three-Dimensional Mapping of the Fermi Surface in a High-Tc Superconductor: Tl2Ba2CuO6+δ (Tc = 20K)”

0

0.01

0.02

0.03

0.04

0.05

0.06

-90 0 90

ρ c (Ωcm

)

θ (degrees)

H//ab H//c H//ab

0

0.05

0.1

0.15

0 100 200 300

ρ c (Ωcm

)

T (K)

φ

0o

20o

28o

36o

44o

Tl2Ba

2CuO

6+δ

T = 4.2KH = 45 T

Test for interlayer coherence in a quasi-two-dimensional superconductor

Quasi-2D Fermi Surface ofκ-(BEDT-TTF)2Cu(NCS)2. The lines indicate quasiparticle orbits on the Fermi Surface due to the in-plane magnetic field B. Note the closed orbits about the "belly" of the Fermi Surface.

John Singleton, P. A. Goddard, A. Ardavan, N. Harrison, S. J. Blundell, J. A. Schlueter, and A. M. KiniPhys. Rev. Lett. 88, 037001 (2002) “Test for interlayer coherence in a quasi-two-dimensional superconductor”

BaCuSi2O6: An ancient pigmentA quasi-2D magnetic insulatorGapped spin dimer ground state

2 cm

Magnetic fields drive a phase transitionto a gas of bosonic spin triplet excitations (triplons)

Nature 424, 912 (2003)Signature of Optimal Doping in Hall-effect Measurements on a High-Temperature Superconductor

010203040

T [K

]

p (hole concentration per Cu)0.160.100

Metal

Bi2Sr2-xLaxCuO 6+ δ

Strong Insulator

Phys. Rev. Lett. 85, 638 (2000)Metal-to-Insulator Crossover in the Low-TemperatureNormal State of Bi2Sr2–xLaxCuO6+δ

Phys Rev Lett 77, 5417 (1996) Insulator-to-metal crossover in the normal state of La2-xSrxCuO4 near optimum doping

010203040

T [K

]

0.160 0.055Metal

StrongInsulator Log-T Insulator

La2-xSr xCuO4

p (hole concentration per Cu)

The Abnormal Normal State of the High-Tc SuperconductorsUsing 60 teslas ...

...to suppress the superconducting state

...(undress the electrons)……to reveal the low-temperature

normal-state phase diagram

The Abnormal Normal State of the High-Tc SuperconductorsUsing 60 teslas ...

...to suppress the superconducting state

...(undress the electrons)……to reveal the low-temperature

normal-state phase diagram

The Cast of Characters

Joze Bevk, Al PassnerBell Laboratories

Fedor Balakirev, Jon Betts, Neil Harrison, Kee Hoon Kim, Albert MiglioriNational Magnetic Field Laboratory at Los Alamos

BSLCOYoichi Ando, Shimpei Ono, S. Komiya, Kouji Segawa

CRIEPI, Tokyo LSCOKohji Kishio, Masayuki Okuya, Tsuyoshi Kimura,

Jun-ichi Shimoyama, University of TokyoLSCO and Ladder CompoundShin-ichi Uchida, Naoki Motoyama, Kenji Tamasaku,

Noriya Ichikawa, Hiroshi Eisaki, University of TokyoTl-2201Andre Tyler, Andy Mackenzie

Cambridge University and University of St. Andrews Bi-2201Nan Lin Wang, Christoph Geibel, Frank SteglichTH Darmstadt and Max Planck Institute, Dresden

Bi2Sr2-xLaxCuO6+δ

PHASE TRANSITION LINE

PHASE C(superconductivity)

PHASE A(magnetism)

PHASE B(ordinary metal)

MAGNETIC FIELD or PRESSUREor DOPING (carrier concentration)

TEMPER

ATU

RE

STRANGE BEHAVIOR

G. R. Stewart, Rev. Mod. Phys. 73, 797 (2001)

A. Suslov et al., Phys. Rev. B68, 20406-1-4 (2003).P. Chandra et al., Nature 417, 831 (2002).M. Jaime et al., PRL 89, 287201 (2002).N. Harrison et al., PRL 90, 096402 (2003).K.H. Kim et al., PRL to be published (2004).

Tuning to Quantum Critical Pointsusing Pressure or Magnetic Field

The Abnormal Normal State of the High-Tc Superconductors

pseudogap

Anderson, Science 256, 1526 (1992) and Research News, Science 278, 1879 (1997)

Using 60 teslas....to suppress the superconducting state and reveal the normal-state phase diagram

Challenges in Producing High Magnetic Fields

Pressure Under Water 12 feet Ears 6 pounds per square inch

2000 feet Submarine 1000 psi12,000 feet Ocean Floor 6000 psi

Pressure inside NHMFL Pulsed Magnets 800,000 gauss Pulsed Magnet 200,000 psi

(which equals 1.4GPa or 130 kg per square millimeter)(which is more pressure than most materials can handle)

Strong Electromagnets

Generate BIG Forces

The Niobium ribbons work(sort of)

like steel bars in cement…

…except the nano-compositeis stronger than either constituent

20% Niobium Dropletsin 80% Copper Matrix

The diameterof a Human hair

20 times larger magnification

Pulse 915July 28,2000

Analysis of Debrisuntil January 2001

9:15:01 am

9:15:00 am

Until You Spread Your Wings,You’ll Have No Idea How Far You Can Walk.

The Abnormal Normal State of the High-Tc Superconductors

pseudogap

Anderson, Science 256, 1526 (1992) and Research News, Science 278, 1879 (1997)

Using 60 teslas....to suppress the superconducting state and reveal the normal-state phase diagram

PRL 77, 5417 (1996)

0

0.5

1

1.5

0 50 100 150 200 250 300

ρab

[mΩ

cm]

T [K]

x = 0.84

0.76

0.73

0.66

0.39

0.23

Und

erdo

ped

Opt

imum

Ove

rdop

ed

PRL 85, 638 (2000)

BSLCO single crystalsab - plane

La1.92 Sr0.08 CuO4

PRL 75, 4662 (1995)

0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

BSLCO

Bi-2201 kFl =1 @ 3.1 mΩ

0.39

0.66

0.73

0.76

BSLCO y=0.84

ρab

BSL

CO (m

Ω c

m)

DocumentsData

La2-xSrxCuO4 and Bi2Sr2-yLayCuO6+δ In-Plane Resistivity

T(K)

Logarithmic Divergence of the In-Plane Resistivityof Underdoped Bi2Sr2-xLaxCuO6+δ

0.1 1 10 100

1

0.9

0.8

underdoped BSLCO

kFl =1 @ 3.1 mΩ-cm

2

BSLCO y=0.84

ρab

BSL

CO (m

Ω c

m)

Bi2Sr1.16La0.84CuO6+δ In-Plane Resistivity

T(K)

Bi2Sr2-xLaxCuO6+δ

Bi2Sr2-xLaxCuO6+δ

Phys. Rev. Lett. 85, 638 (2000)Metal-to-Insulator Crossover in the Low-TemperatureNormal State of Bi2Sr2–xLaxCuO6+δ

Logarithmically Divergent Resistivity in Underdoped Cuprates

0.2

0.3

0.4

1 10

r ab[m

Wcm

]

T [K]

x = 0.73

x = 0.66

kFl =15

0.1 1 10 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

BSLCO

Bi-2201 kFl =1 @ 3.1 mΩ

0.39

0.66

0.73

0.76

BSLCO y=0.84

ρab

BSL

CO (m

Ω c

m)

DocumentsData

La2-xSrxCuO4 and Bi2Sr2-yLayCuO6+δ In-Plane Resistivity

T(K)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

LSCO

0.22

0.17

0.15

LSCOx=0.08

LSCO kFl =1 @ 1.6 mΩ

ρab

LSC

O (m

Ω c

m)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

LSCO

0.22

0.17

0.15

LSCOx=0.08

LSCO kFl =1 @ 1.6 mΩ

ρab

LSC

O (m

Ω c

m)

kFl ~ 15

Similarities between the Insulator-to-Metal crossover in BSLCO and LSCO:--- occurs under the superconducting ‘dome’--- occurs at the same normalized resistivity, at kFl ~15.--- the Insulator exhibits Log-T divergence.

ρab /cο = h/(e2kFl)

QUANTUM CRITICAL POINTin the HIGH-Tc CUPRATES ?

--- In the quantum critical region, temperature is the only energy scale controlling the physics.

--- Strong critical fluctuations can mediate singular interactions between quasiparticles.

--- These singular interactions can provide both a strong pairing mechanism and a source of non-Fermi liquid behavior.

--- The observed linear-T resistivity is attributed to Quantum Critical Behavior

from “Universal Quantum-Critical Dynamics of Two-Dimensional Antiferromagnets”Subir Sachdev and Jinwu Ye, PRL 69 (1992) 2411

Ref [4] is Chakravarty, Halperin and Nelson, PRL 60 (1988) 1057; PR B39 (1989) 2344

0

10

20

30

40

T [K

]

0.160 0.055

Metal StrongInsulator Log-T Insulator

La2-xSrxCuO4

Searching for evidence of a quantum critical point in the resistivity

Sharp Insulator-to-Metal Crossover---at optimum doping

Evidence of a Quantum Critical Point ?---at optimum doping---where linear-T resistivity

has been attributed to critical behavior

Y. Ando et al., Physica C341, 1913(2000)

Tc

0.84

0.23 = x0.390.490.510.73

Carrier Concentration

SC

Hall Effect in Bi2Sr2-xLaxCuO6+d

La doping

- Unusual Temperature-dependence of Hall coefficient not understood

?

- What happens below Tc ?

Tc

0.10

Hole Concentration, p

0.18 = p0.160.150.14

0.12

Bi2Sr2-xLaxCuO6+dLa x=0.49Tc =33K

Low Temperature Normal State Hall Effect

Hall Resistivity

0 20 400

50

100

150

1.3K20K25K30K

35K40K50K

ρ ab(µ

Ω c

m)

B(T)

In-plane Resistivity

Bi2Sr2-xLaxCuO6+dLa x=0.49Tc =33K

High-field Hall voltage is linear in field

0 10 20 30 40 50 60

0

0

0

0

0

0

2

4

6

8

10

1.3K

H(T)

5K

20K

30K

40K

ρxy

(µΩ

-cm

)

50K

Y. Ando et al.cond-mat/0004134 (2000)

BSLCO Hall Effect in DC Magnet

0

1

2

3

4

5

6

7

RH(e

/NV c

ell)

Tc

0.84

Carrier Concentration

0.230.390.49

0.510.73

Low-T Hall Effect in BSLCO(two years to develop technique)

37/44

0 20 40 60 80 1000

1

2

3

4

5

6

7

8

RH(e

/NV ce

ll)

T(K)

La=.84 La=.73 La=.51 La=.49 La=.39 La=.23

Calculated Evolution of Hall Coefficient (= 1/Hall density)

upon Doping

Shastry, Shraiman, SinghPRL 70, 2004 (1993)

Measured Evolution of Hall Density upon Doping

We may understand the high-temperaturebehavior of the Hall number from the t-J model…

…but not the peak that develops…

…at temperatures below Tc…and centered on optimum doping

0.10 0.12 0.14 0.16 0.180.0

0.2

0.4

0.6

0.8

1.0

1.2

n H

ALL

, nor

mal

ized

per

Cu

p, hole doping

Peak or Jump near Optimal Doping

Low-TemperatureHall Number

in Bi2Sr2-xLaxCuO6+d

Onset of carriers yields onset of superconducting phase

Hall Number is correlated with Tc

0.10 0.12 0.14 0.16 0.180.0

0.2

0.4

0.6

0.8

1.0

1.2

0

5

10

15

20

25

30

35

40

n H

ALL

, nor

mal

ized

per

Cu

p, hole doping T

c(K)

Critical Temperatureand Hall NumberIn BSLCO

In the underdoped regime…n Hall shows remarkably linear

correlation with Tc

…but not in the overdoped regime…

0.0 0.5 1.00

10

20

30

40c

n HALL

Evidence that the superconducting transition is governed by phase stiffness (superfluid density)

in the underdoped regime

Y. J. Uemura et al., PRL 62, 2317(1989)

0.0 0.5 1.00

10

20

30

40

balakirev_fig3

c

n HALL

TC(K

)

…and so is the Hall number…

Superfluid density in thesuperconducting state corresponds to the Hall density

throughout the underdoped regime

Hall coefficient becomes T-independent at low-T near optimum doping in BSLCO---suggesting a measurement of the Hall number.

Sharp anomaly in doping dependence of the Hall number at optimum doping

---suggesting change in the Fermi Surface

…suggests a Quantum Critical Point governs High-Tc Superconductivity

0.0 0.5 1.00

10

20

30

40

balakirev_fig3

c

n HALL

TC(K

)

Linear relation between Tcand the low-T Hall number

---suggests phase stiffnessgoverns superconducting transitionin the underdoped regime

0 20 40 60 80 1000

1

2

3

4

5 p=0.115

T(K)

p=0.145p=0.14

p=0.13

p=0.12

p=0.15RH(e

/Vce

ll)

To submit a proposal for magnet time, www.magnet.fsu.edu

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