Lecture 6 Superconducting Materials and

Their Structures Low Tc materials and their Alloys

Organic Superconductors

High Tc materials: cuprates, borides , and AsFe superconductors

Tc Shot Up Like a Rock (many cuprates superconduct above 77K)

Record TC versus Year Discovered

0

20

40

60

80

100

120

140

160

180

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Year

TC (

K)

Hg

NbNNb3Ge

La-Ba-Cu-O

La-Sr-Cu-O

YBa2Cu3O7

Bi2Sr2Ca2Cu3O8

Tl-Ba-Ca-Cu-O

HgBa2Ca2Cu2O8

HgBa2Ca2Cu2O8 Pressure

1986

BiSCCO Cu is purple, O is brown

Tl2Ba2Ca2Cu30x

Tl2Ba2Ca2Cu3Ox

Tl2

Tl

TEP for Tl2Ba2Ca2Cu3Ox

Hg1223

Ott, Schilling, et al

Mixed-Phase Hg 1223,1212 Onbasli, Hermann, et al

Current world record

Phase diagram

Cuprate The red circles indicate the onset temperature of the P4=nmm to Cmma phase transition. The black squares and green triangles designate the Ne´ el temperatures of Fe, TN (Fe), and Cerium, TN (Ce), respectively, as determined from neutron measurements

J.Zhao, et.al, Nature Mater. 7, 953(2008)

1. There are 2e- pairs 2. The pairs are d-wave (L=2, S=0) 3. There are “normal” (i.e., 2e-) vortices 4. Quasiparticles exist (but only below Tc)

What We DO Know

d-wave pairing observed by phase sensitive tunneling - van Harlingen, Kirtley & Tsuei Kirtley et al, Nat. Phys. (2006)

Cava et al

G. Bednorz

&

K.A. Müller

(La/Ba)2CuO4 YBa2Cu3O7

C.W. Chu

&

M.K. Wu

MgB2

Superconductivity Tc over time

Akimitsu’s Discovery: 2001

MgB2: an intercalated graphite-like system

• Searching for ferromagnetism,

superconductivity near 40K was discovered

in 2001

• Quickly reproduced and synthesis techniques

were extended by several groups

• Crystal Structure is simple: quasi-2D

• Electronic structure is simple: s-p electrons, intermetallic compound.

CENTRAL QUESTION: What is the origin

of high TC in MgB2?

J. Nagamatsu, et al., Nature (London) 410, 63 (2001)

T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001)

Electronic structure

• Near Fermi level almost B p character, other contributions are very small.

• All bands are highly dispersive (light).

• pz bands are quite isotropic, 3D, cross Ef

px,y bands are 2D, only two (bonding) of them cross Ef.

• 2D character contribute > 30% to N(0).

• pz bands hybridize with the empty Mg s band, increasing the effective ionicity.

• Bands can be perfectly described by tight binding model with

• Hole-type conduction bands like the high-Tc cuprates. (0.28,0.59)

• Multiple gaps.

J. Kortus, et al., Phys. Rev. Lett. 86, 4656 (2001).

J. M. An and W. E. Pickett, Phys. Rev. Lett. 86, 4366 (2001).

T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001).

In-plane boron modes

T. Yildirim, et al., Phys. Rev. Lett. 87, 37001 (2001).

Summary

• covalent bonds become metallic.

• Large deformation potential D=13 eV/A

• 2D (cylinder) Fermi surfaces focus strength.

• Yet structure remains stable: intrinsic covalency.

• Phonon mediated pairing s-wave.

• Mediate el-ph coupling constant ~ 0.8. (Holes in the B-B bonding sigma bands, relative softness of the optical bond-stretching modes.)

• Strongest coupling of the in-plane B motion, which is anharmonic.

• High frequency contributes most to Tc.

• Boron isotope effect gives Delta Tc=1.0 K, which further confirms that boron phonon modes are playing an important role in the superconductivity of MgB2.

FeAs-based SC

Crystal and magnetic Structure of BaFe2As2

Marianne Rotter, et al, PRL 101 107006 (2008)

The structural and electronic properties of the parent compound BaFe2As2 are closely related to LaFeAsO. By hole doping potassium in this barium compound they get a Tc=38K

Crystal Structure of LaOFeAs

Schematic crystal structure of LaOFeAs. Electron carriers generated by F-doping into oxygen sites are injected into FeAs metallic layers as a result of the large energy offset between these two layers. Note that the carrier doping layer is spatially separated from the conduction layer. They got Tc=43k at 4GPa on this F-doped LaOFeAs

Hiroki Takahashi, et al, Nature 06972 (2008)

Fe is sitting on a tetrahedral coordination. And Fe is formally divalent.

Introduction

• Four Chinese groups quickly pushed the critical temperatures higher by replacing the lanthanum with other rare earth elements.

Xianhui Chen reported on the arXiv preprint server (www.arXiv.org) a Tc=43K Four days later, Zhong-Xian Zhao reported on the server that praseodymium oxygen fluorine iron arsenide has a Tc=52K 55 kelvin for the samarium compound grown under pressure

Magnetic Structure

Plainly similar. The old and the new superconductors both contain planes of ions magnetized in opposite directions. In the older ones, electrons hop from copper to copper (arrow). For Fe-based SC, early results shows the As-Fe-As layer is responsible for the superconductivity.

Adrian Cho, Science 320, 870(2008)

Simplified doping dependent phase diagrams of iron-based superconductors for both Ln-1111 and Ba-122 materials. The phases shown are the antiferromagnetic/spin density wave (AF/SDW) phase close to zero doping and the superconducting phase around optimal doping. the superconducting phase is close to or overlapping with the magnetic phase.

Summary

• Compare to cuprate Fe- based SC have a lower Tc up to now

• The magnetic moment in Fe-based SC are aligned with in the FeAs plane. In cuprate, it is up and down.

• For the magnetic ordered state in the cuprate, the AFM phase parent is Mott insulator whose electrons are localized. For the Fe-based superconductors, the AFM phase or SDW phase remains metallic.

• Its Superconductivity is competing with the spin wave density state. SC and SDW may coexist in underdoped samples.

Organic Superconductors

e-

e-

(the electron-phonon case) 1. 1st e- attracts + ions 2. Ions shift position from red to blue 3. 1st e- moves away 4. 2nd e- sees + ion hole and moves to former position of 1st e- Interaction is local in space (s-wave pairs, L=0, S=0) but retarded in time (Tc << Debye frequency)

Everything You Wanted to Know About Pair Formation (But Were Afraid to Ask)

1. Resonating valence bonds 2. Spin fluctuations 3. Stripes 4. Anisotropic phonons 5. Bipolarons 6. Excitons 7. Kinetic Energy lowering 8. d-density wave 9. Charge fluctuations 10. Flux phases 11. Gossamer superconductivity 12. Spin bags 13. SO(5) 14. BCS/BEC crossover 15. Plasmons 16. Spin liquids

Not to Mention Interlayer tunneling Marginal Fermi liquid van Hove singularities Quantum critical points Anyon superconductivity Slave bosons Dynamical mean field theory

Theories Connected with High Tc Superconductivity