Superconductivity – 100 yearsDavid Quesada

School of Science, Technology, and Engineering Management16401 NW 37 Ave., Miami Gardens FL 33054

Heike Kamerlingh Onnes “the gentleman of absolute zero”, discovered Superconductivity on April 1911. Onnes won the Nobel Prize in 1913, just two years after his incredible discovery. Onnes died in 1926.

In 1898 Onnes’ rival, James Dewar, beat him in the race to liquefy hydrogen. Onnes then moved on to a new goal, liquefying helium, and this time, Onnes beat Dewar in the race, producing the first liquid helium in July 1908. Though he only liquefied a tiny amount of helium at that time, the liquefaction of helium made it possible to cool other substances to such low temperatures. Onnes managed to cool the liquid to about one degree above absolute zero, at the time the coldest temperature ever achieved.“The resistance of pure mercury at helium temperatures,” Communications from the Physical Laboratory at Leiden, April 1911. “On the Sudden Change in the Rate at which Resistance of Mercury Disappears.” November 1911. Soon after finding the effect in mercury, Onnes showed that tin and lead also become superconducting at low temperatures. In 1913 Onnes first used the term “supraconductivity,” to describe the effect; later he changed it to “superconductivity.” By 1914 he had found another interesting feature: he started a supercurrent flowing in a lead wire, and a year later, found that it was still flowing, with no noticeable change. Onnes himself had believed that quantum mechanics would explain the effect, but he wasn’t able to produce a theory.

James Clerk Maxwell, Scottish physicist and mathematician father of the theory of electro-magnetic fields, the first unification of two fields in nature

"On Physical Lines of Force," which he published between 1861 and 1862.

1905 – 1915 – Quantum Mechanics

Edwin Schrodinger

Albert Einstein

Niels Bohr

Electromagnetic Properties of Superconductors

Walter Meissner

Fritz London

Superconducting Materials and Theory of Phase Transitions

Quantum Solid State Physics – Applications of Quantum Mechanics

Bose – Einstein Condensation

Bardeen, Cooper, Schrieffer (BCS)

Lev D. Landau and V. Ginzburg

Theories of Superconductivity

A.A. Abrikosov

BCS Theory of Superconductivity

Superconducting Gap in the electronic spectrum – Order parameter.

Brian Josephson

In 1961, Deaver, Fairbank, Doll, and Näbauer showed that a closed superconducting loop will contain integers of flux quantum, which in units of magnetic flux is Φ0≈2.0678×10-15Wb. A Superconducting Quantum Interference Device (SQUID) is a device that can measure the number of these flux quantum that are threading a superconducting loop. Currently SQUID can detect magnetic fields of around 10-15T and they have noise levels as low as 3fT×Hz-1/2.

Macroscopic Wave Function

N.N. BogoliubovQuasi - means

Lev Gorkov

G.M. Eliashberg

How did I get introduced to Physics and Mathematics?

Moscow State University “M.V. Lomonosov”

July 25, 1984 our cohort arrived to Moscow

Dr. and Professor Alla Andreevna Novakova, Solid State Physics Division, School of Physics, Moscow State University Lomonosov

Mossbauer Spectroscopy in Fe-based compounds

Rudolph Mossbauer

High Temperature Superconductivity Breakthrough

Muller and Bednorz, 1987

Paul Chu, 1988

Historical Events while I was studying in Moscow

Chernobyl nuclear accidentApril 26, 1986

Mikhail Gorbachev and Ronald ReaganIn Moscow. He graduated from Moscow State University in 1955 with a degree in law

On May 31, 1988 President Ronald Reagan addressed the students and faculty at Moscow State University (MSU). Although previous presidents desired such an opportunity, no other U.S. president except Richard M. Nixon had stood east of the Berlin Wall and spoken directly to the citizens of the Soviet Union.

Berlin Wall turn down, Nov. 9 1989Challenger disasterJanuary 28, 1986

MS in Physics and Mathematics – Suma Cum LaudeThesis Title: Coulomb’s contribution to the phonon spectrum of compounds of YBCO family.Area: Theoretical Solid State Physics (1984 – 1990)

• “Structural Study of Amorphous Alloy Fe-Si-B-C obtained by detonation technique”(poster presentation), Structural Problems in Amorphous Metallical Alloys, Moscow, 1988.•“Structural Study of Amorphous Alloy Fe-Si-B-C obtained by detonation technique”(oral presentation), Young Scientific Conference: Students and Scientific Progress, Novosibirsk University, April 12-14, 1988.•“Application of Mossbauer spectroscopy in archeology dating” (poster presentation), International Conference LACAME'90, Havana, Cuba, Oct. 29-Nov. 2, 1990.

Effect of Co – gamma radiation dose on ceramic Superconductors and its response in presence of magnetic fields

• γ- Cobalt-60 Radiation Effects in High Temperature Superconductors, Leyva-Fabelo, J.C. Suarez-Sandín, M. Mora-Alfonso, C.M. Cruz-Inclán, D. Quesada-Sáliba, A. Gómez-González, Nucleus 13, 3, (1992).• Ac Magnetic Susceptibility in High Temperature Superconductors irradiated with γ-Rays, A. Leyva, J.C. Suarez, M. Mora, C.M. Cruz and D. Quesada, Phys.Stat.Solidi (a) 134, K 29, (1992).

• Magnetic Field distribution in superconducting grain of spherical shape, D. Quesada, in Proceedings of the Conference: Magnetism, Magnetic Materials and their Applications, Section III (Part 2), Havana, 1991, Ed. by J.L. Sánchez Llamasares and F. Lecabue, IOP Publishers.

• M. Mora, C. Cruz, A. Leyva, J.C. Suarez, D. Quesada, Nucleus 18, 21 (1995).

Typical Crystalline Structures found within Superconductors

School of Physics, University of Havana, Cuba 1992 - 2001

Dr. and Professor Carlos Trallero-Giner, Theoretical Solid State Physics

Effects of low-dimensionality in the electronic spectrum of high Tc

onto superconducting properties.

Band structure modelsBand structure models

Dr. and Professor Rafael Baquero, Solid State Physics Division, CINVESTAV – IPN Mexico DF

-2

0

2

-2

0

2

-2

-1

0

1

2

-2

0

2

-2

0

2

d-wave order parameterNote the different behavior along. Nodal direction (in red) and anti Nodal direction (in blue)

-2

0

2

-2

0

2

-2

-1

0

1

2

-2

0

2

-2

0

2

Anisotropic s-wave order parameter. Note the extended character of nodes for this parameter in contrast to d-wave order parameter

-2

0

2

-2

0

2

-2

-1

0

1

2

-2

0

2

-2

0

2

akaktakakt yxyxk coscos'4)cos(cos2 ++−=ε

Effect of low dimensionality of the electronic spectrum onto superconductivity

0 50 100 150 200 250 3003.0

3.5

4.0

4.5

5.0

5.5

6.0

C e

n ( T

) / T

(

mJ

/ mol

/ K

2 )

T ( K )

0.01 0.02 0.03 0.04 0.05

0.004

0.008

0.012

0.016

k B T

max

εF - ε

c

Electronic specific heat in the normal state. Note the appearance of a peak at Some characteristic temperature T*, determined only by the position of the Van Hove singularity with respect to the Fermi level.

Electronic Topological Electronic Topological Transitions and Van Transitions and Van

Hove singularity Hove singularity

Gap model functionsGap model functions

symmetryiddi

symmetryisdi

symmetrysd

symmetrysextended

symmetrywavedyx

symmetrywavedyx

symmetryscanisotropiyx

symmetrysisotropic

kkk

kkk

kkk

kkk

k

k

k

k

*438

237

236

215

*04

03

02

01

sinsin

)cos(cos

)cos(cos

+∆+∆=∆

+∆+∆=∆+∆+∆=∆

−∆+∆=∆−∆=∆

−−∆=∆−+∆=∆

−∆=∆

The temperature dependence of the gap is in agreement with the BCS behavior

Electronic Specific HeatElectronic Specific HeatNormal state Normal state

Superconducting state Superconducting state

]||

2

1)][(1)[(

2)(

22

2 ∑ ∆−−=

k

kkkk

Bes dT

dTEEfEf

TkTC

∑ −=k

kkkB

es ffTk

TC

22

)](1)[(2

)( εεε

]|)(||)(|

[cos2

|)(||)(||)(| 222

dT

Td

dT

Td

dT

Td

dT

Td

dT

Td

d

ks

k

d

k

s

k

dk

skk

∆∆+∆

∆

+∆

+∆

=∆

ϑ0.2 0.4 0.6 0.8 1.0 1.2 1.4

0

2

4

6

(a)

4

32

1

s-wave

Ces (

T )

/ C

en (

Tc )

T / Tc

0.2 0.4 0.6 0.8 1.0 1.2 1.4

2

4

6

8

d-wave

(b)

32

1

Ces (

T )

/ C

en (

Tc )

Comparative study of the Electronic specific heat in the superconducting state for a mixture of d-wave and isotropic s symmetry.(b)The s-wave gap is determining the Tc, while the second gap (d-wave) increases in value.(b) The d-wave gap drives the Tc, the s-gap appears as a small jump in the background of the d-wave symmetry.

Oracio Navarro, 2001 Hawaii

Yuri Gurevich

Gerardo Gonzalez de la Cruz

Coherence Length

Workshops and Conferences1. “On the Van Hove Scenario” and “Estimation of the Electron-Phonon interaction from GP-DOS measurements in 123 compounds” (oral presentations), Second CINVESTAV Superconductivity Symposium: Manifestation of the Electron-Phonon Interaction in Oxide Superconductors, Tequisquiapan, Querétaro,

México, Nov 2-6, 1992.2. “Are Universal Relations within the van Hove Scenario possible?” (poster presentation), IV International Conference on Nanostructured Materials, Cancún, México, August 27 to September 3, 1995.3. “Thermodynamics of the van Hove BCS model: Mixed gap symmetries” (poster presentation), University of Miami Conference on High Temperature Superconductivity and related topics HTS99, January 7 - 13, 1999 Coral Gables Miami, USA.4. “Implications of the pairing symmetry and the Van Hove singularity for the normal and superconducting properties of cuprates” (poster presentation), 6th International Conference Materials and Mechanism of superconductivity and high temperature superconductors, February 20-25, 2000 Houston Texas, USA.

Publications21.BCS theory in systems with van Hove singularity in the electronic spectrum, D. Quesada, C. Trallero-Giner y R. Baquero, Rev. Mex. Fis. 41, 1397, (1995).2. BCS Universal Ratios within the van Hove Scenario, R. Baquero, D. Quesada and C. Trallero-Giner, Physica C 271, 122, (1996).3. Thermodynamic functions within the van Hove BCS model: symmetry Mixing effects, D. Quesada, R. Peña and C. Trallero-Giner, Physica C 322, 169 (1999).4. Thermodynamics of the van Hove BCS model: Mixed gap symmetries, D. Quesada, R. Peña and C. Trallero-Giner, High Temperature Superconductivity, AIP Conference Proceedings Vol 483, Ed. by S.E. Barnes, J. Ashkenazi, J. Cohn, F. Zuo, AIP Woodbury New York (1999).5. Implications of the pairing symmetry and the van Hove singularity for the normal and superconducting properties of cuprates, D. Quesada and R. Peña, Physica C 341-348, 1683 (2000).6. The Van Hove singularity as a source of anomalies in NIN and NIS tunneling experiments, D. Quesada, Physica C 364-365, 170 (2001).

Graduated from Universidad de La Habana, Cuba 2000, Ph.D. in Physics, Best young scholar research of the year 2000 – School of Physics

Roger Pena-Escobio, BSDrs. Roberto Mulet and Ernesto Altshuler

Alexei Vazquez

From Superconductivity to Complexity and Dynamical Systems

Fermi Liquid ApproachFermi Liquid Approach

Strongly Correlated Systems Strongly Correlated Systems

Free electron picture

Tight binding electrons with singularities in the electronicDensity of States

Interactions andLuttinger theorem

Landau picture of quasi-particles, Electronic Topological Transitions

Nested and AlmostLocalized Fermi liquids

Marginal and AlmostMagnetic Fermi Liquids

Hubbard based models : Single and multi -band models Hubbard based models : Single and multi -band models

Zhang-Rice Anderson

local ization

Local pairs : b i -polarons And spin-bags

Str ipes and Flux phases

Slave-boson ansatz Brickman-Rice point

Gutzwiller ansatz

Phillip Anderson, RVB theory

Angle Resolved Photo-emission Spectroscopy

Superconductivity and Strongly Correlated Electron Systems

Two band model with anisotropic hopping depending only on plane momentum.

2)cos(cos4

)( akakt

kt yxz +−= Eight points in the FBZ where this

hopping element becomes zero

2)cos(cos4

)( akakt

kt yxz −−=

Four points in the FBZ where this hopping element becomes zero

Spectral Function in ARPESSpectral Function in ARPESNormal StateNo interactions included

22)(),(

Γ+−Γ=k

kA

εωωπ

Interactions included

22

21

2

))(())((

)(),(

ωωεωω

ωπkkk

kkA

Σ+Σ−−Σ

=

Superconducting StateNo interactions included(modified BCS spectral function)

22

2

22

2

)()(),(

Γ++Γ

+Γ+−

Γ=

k

k

k

k

E

v

E

ukA

ωωωπ

),(),(),(

),(

21

1

ωωω

ωεω

kikk

kkk

Σ+Σ=Σ

Σ+=

Self-energy modelsSelf-energy models

SF

SF

cMFL

BFL

i

Txxix

Tki

ωω

ωλω

ωπω

ωλω

πωβαωω

||11

2)(

)|,max(|]2

ln[)(

])([)( 22

−+=Σ

≈−=Σ

++=Σ

““The kink”The kink” could be explained by appealing to self- could be explained by appealing to self-energy effects. The self-energy could depend or not energy effects. The self-energy could depend or not on momentum as a necessary condition.on momentum as a necessary condition.

yyyy

xxxx

kk

kk

∂∂

∂Σ∂−

=

∂Σ∂+

∂∂

∂Σ∂−

=∂∂

∂∂

∂Σ∂−

=

∂Σ∂+

∂∂

∂Σ∂−

=∂∂

ε

ω

ε

ω

ω

ε

ω

ε

ω

ω

1

1

1

1

1

1

1

1

1

1

1

1

1

1

No dependence on k in

There is a Renormalization of the quasi-particle energy There is a Renormalization of the quasi-particle energy but but the Fermi surface Topology (critical points) remains the Fermi surface Topology (critical points) remains the same.the same.

x=kxa y=kya

The ARPES experiment and the superconducting gap symmetry: How far can we determine the gap symmetry? D. Quesada, Int. J. Mod. Phys. B 17, 3559 (2003).

Applications of Superconductors

From Superconductivity to Quantum Computers - Qubits

“Dynamics of the Josephson junction immersed in a non linear medium” (poster presentation), Z. Barrientos and D. Quesada, First Ibero-American workshop of Nanostructures and its application for Opto and Microelectronics, November 20-24, 2000 CINVESTAV-DF, Mexico-DF, Mexico.

Bogoliubov and Landau ideas of Spontaneous Symmetry BreakingFrom Superconductivity to Higg’s Boson and Astrophysics

Guth Linde, phase transition ideas applied to symmetry breakingin forces of nature, symmetry breaking of super-forces.

From moving vortices to hurricanes