High-Temperature Superconductors - PowerPoint Presentation

Slide1

High-Temperature Superconductors

Anthony Fiory

1

New Jersey Institute of TechnologyPhysics Department (Ret.)

A collaboration with Dr. Dale R Harshman

The College of William and Mary

Slide2

Outline

Conventional Superconductivity

Electron pairing mediated by

lattice ionsUnconventional SuperconductivityElectron pairing mediated by electronic interactionsFocus PointsSuperconducting Critical Temperature TCUnconventional Electronic Coulomb CouplingExperimental Data2

Slide3

Superconductors

3

High Current in Magnetic Field

Superconducting Circuits

Superconducting Quantum Interference Device

SQUID 

Josephson Junctions

S/N/S

Quantum Al-Superconductor

Processor

“Quantum Supremacy” Google, Nature 2019 Operated at T  0.02 K

IBM

transmon

qubit

Nb

-Ti

conventional

Magnet Cable

ITER Tokomak

Operated at T



4 K

High-T

C

Superconductor

unconventional

Wind Turbine Rotor Tape

Bergen et al. 2019Operated at T  20 K

Slide4

Superconductivity Basics

Macroscopic Quantum State

I

   eℏA V  /t 4

 = n e

i



Resistance

Drop at T

C

Persistent Current

R

 0

Gerrit

Flim

& Heike

Kammerlingh

Onnes

“

Superconductivity” Leiden 26 Oct 1911

Slide5

Meissner Effect

Repel Flux

B

 0Superconductivity Basics 5

High-T

C

Superconductor

Permanent Magnet

High-T

C

– Type II Superconductor

Magnetic Vortices B > 0

Vortices Pinned near Defects

B

 ConstantYBa2Cu3O7 Scanning SQUID Imagery

Wells et al. Nature 2015

VortexCore

Slide6

BCS Theory

Weak Electron-Phonon Coupling

Conventional Superconductors

6

Schrieffer Bardeen Cooper

1957

Electron – Phonon Coupling

Cooper Pairs of Electrons

Time-Retarded Electron-Ion Forces

 = N(0)V  < 1

T

C





Debye

e

1/



Coherence distance

Slide7

7

Strong Electron

–

Phonon Coupling

 > 1

Migdal

1957

Éliashberg

1959

Allen and Dynes

1975

 > 2

T

C

 (

⟨



phonons

⟩

)

1/2

⟨



phonons

⟩

  ⟨ Felectron

-ion ⟩2

2

2

Trends in High T

C

High phonon frequencies



Large electron-phonon coupling



Slide8

8

High T

C

SuperconductorsMüller & Bednorz1986“Possible high

T

c

superconductivity in the

Ba

–La–Cu–O system”

Previous High T

C

Nb

3

Ge TC = 23 KY–Ba–Cu–O TC = 93K Chu et al. 1987

Slide9

Superconductors Grouped by Theoretical Studies

9

Electron-Phonon Theories

T

C

(K)

Elements

Al

1.20

In

3.4

Hg

3.95, 4.15

Pb

7.19

Ta

4.48

V

5.03

Nb

9.26

Compounds

TiN

5.6

ZrN

10

NbTi

10

Nb

3

Sn

18.3

Nb

3

Ge

23.2

MgB

2

39

H

3

S

200

LaH

10

250-260

Electron-Electron Theories

T

C

(K)

Copper

La

1.837

Sr

0.163

CuO

4

38

Bi

2

Sr

2

CaCu

2

O

8

89

YBa

2

Cu

3

O

6.92

93.7

TlBa

2

Ca

2

Cu

3

O

0

133.5

HgBa

2

Ca

2

Cu

3

O

8

145

Ruthenium

Ba

2

YRu

0.9

Cu

0.1

O

6

35

Iron

Ba

0.6

K

0.4

Fe

2

As

2

37

FeSe

0.977

36.5

Nitrogen Halogen

Li

0.2

HfNCl

20

κ–[BEDT-TTF]2Cu[N(CN)2]Br

10.5

Carbon

Cs

3

C

60

35.2,38.2

Gated Bi-Layer Graphene

1.83

Hydrides

at High

Pressure

H

3

S

201

LaH

10

248,262

YH

9

243

Slide10

10

Electronic Charges in High-T

C Superconductors

Anion Doping YBa2Cu3O6.92Valence Substitution La1.837

Sr

0.163

CuO

4

Intercalation

Li

0.2

HfNCl

Stoichiometry FeSe0.977Applied Pressure YBa2Cu4O8 Cs3C60 H3S LaH10Applied Charge Twisted Bi-Layer Graphene

Slide11

Charges in the Layers of YBa

2

Cu3O6+x

Superconductor 11

Layered Crystal Structure

Layered Electronic Charges

Bond Valence Sum Calculations

from Dow

et al

. 2001

Slide12

12

Optimal Superconductors

YBa

2

Cu

3

O

6+x

Optimal Oxygen

Dopings

at x = 0.6 and x = 0.92

Superconducting Transition

Sharp, Narrow Width

Meissner Effect

Flux Repelled  100% Normal-State Resistance Minimal Residual Defects T

C vs Electronic Doping Maximum TC

Local Maximum in TCfrom Jorgensen et al. 1990

CRITERIA

x

0

Slide13

13

Coulomb Coupling Theory

Electronic Charge Separation





Coulomb Interaction

Mediating Charge

Pairing Charge

Pairing Charge

Virtual Photon

Virtual Photon

T

C



Photon

Scattering

Probability  Interaction Energy

Type I

Type II

ℓ

k

B

T

C

= /ℓ

 e2/

Electron-Photon Compton Scattering  = 1.933(6) ƛ

C = 0.007465(22) Å

 < ℓ <



Slide14

14

Superconducting Interaction Charge Density



Participating Charge

A dimensionless fraction

A

Area per formula unit



Number of CuO

2

layers

A



=

2





ℓ

2

= /A

}

YBa

2

Cu

3O6.92Optimization Criterion

Type I Pairing Charges in balance with theType II Mediating Charges

Slide15

15

Charge Allocation Theory

2[x-x

0] = 1.14 Electrons from Optimal CuO0.92 are Shared Equally among the Five Oxide Layers  = 0.228 Optimal

YBa

2

Cu

3

O

6.92

T

C

= 93.7 K

Slide16

16



0  0.228

Scaling  to Other Cuprates fromOptimal

YBa

2

Cu

3

O

6.92

Examples

Mercury Cuprates

CuOx 

HgOx

Y  Ca Bismuth Cuprates CuO

x  (BiO)1or2 Ba

 Sr Y  Y/Ca Thallium Cuprates CuO

x  (TlO)

1or2 Y  Ca

Scaling Derives from Valency, Oxidation State and Electronegativity

Slide17

17

Doping Charge Allocation Theory

La

2xSrxCuO4

Optimal x=0.163 T

C

= 38 K

Doping Species

in Type I, Type II, or Both

Type I

FeSe

0.977

Type II Ba2YRu0.9Cu0.1O6 Both La1.75Ba1.3Ca0.45Cu3O7

Slide18

Coulomb Coupling Theory Parameters

31

Layered High-T

C

Superconductors

Layer Separation

Mean Distance Between

Pairing Charges

Measured

Optimal T

C

(K)

18

Slide19

19

Theory

Measured

Optimal T

C

(K)

k

B

T

C

= e

2

/ℓ

Slide20

20

Gated Twisted Bi-Layer Graphene Device

From Cao

et al.

2016

Two Adjacent Graphene Sheets Twisted at Small Angle

  1

Moiré Super Lattice – Flat Electronic Band

Electronic Doping –

Charging TBL

Graphene

with Gate Voltage

Slide21

21

Gated Twisted Bi-Layer Graphene Device

A Two-Dimensional “High-T

C” Superconductor

Data

From Cao

et al.

2018

Fluctuation

Superconductance

in the Normal State

 =

n

e i

Fluctuation Resistance

in the Superconducting State

Data TC

= 1.83 KTheory TC = 1.94 K

Slide22

22

Cs

3C60

A Fully 3D High-TC SuperconductorMeasured TC = 38.3 KTheory TC = 38.19 K

3 electronic charges from

Cs

atoms are shared between

Cs

3

and

C

60

Pairing Charges on C

60Mediating Charges on CsBody Centered Cubic C60Optimized at 0.93 GPa PressureExperiment by Takabayashi et al. 2009

Slide23

Superconducting Poly Hydrides at High Pressure

H

3

S High Pressure Crystal Structure PredictionsSuperconductivity Predictions TC 191204 K at 200 GPa

Duan

et al.

2104

Synthesis from H

2

S in Diamond Anvil Cell

TC  201 K at  150 GPa Drozdov et al. 2014-2015

Ab

Initio Theory

–

Computational Software Packages Stable High-Pressure Crystals Electronic Structure Phonon Structure Electron-Phonon Coupling Solving Migdal-Éliashberg Equations for TC

23

Slide24

High T

C

in

H3S at High Pressures24Electron-Phonon Theories

Duan

et al

. 2014 (D)

& others

(A,E,F,G,K,

К

,J,P,

S)Coulomb Coupling Theory (H) H3 and S Share their 9 Valence Electrons at Optimal P = 150 GPaH-S Electronic Interaction between Separate Sublattices

S

H



Interlaced Cubic Sublattices

Drozdov

et al

.

Slide25

25

LaH

10

High Pressure Crystal Structure Predictions Phonon Superconductivity Predictions Liu et al. 2017

T

C

286 K (210 GPa)

Peng

et al.

2017

TC 288 K (200 GPa) Synthesis in Diamond Anvil Cell – Resistance Drop Temperatures Drozdov et al. 2019 La+H2 250 K (150 GPa) Somayazulu et al. 2019 La+H3NBH3 260 K (190 GPa)

La fcc

La

H

32

Cage

Hydrogen

Clathrate

Slide26

High T

C

LaH10

26Coulomb Coupling Theory La and H10 Share their 13 Valence ElectronsLa

-

H

Electronic Interaction between

H-cage

and central

La

Slide27

High Pressure Super Hydrides -

Status

Theoretical

Clathrate

Structure

Phonon Theories (2017 – 2019)

Highest

Predicted

T

C

T

C 303 – 326 K Coulomb Coupling – Non-Optimal: Ionic Electron Charge Transfer Y e H10 Experiment Kong et al. 2019

YH10 Not Stabilized

YH9 mixture TC 243 K

YH

10(+)

(−)

27

Theoretical YH9

Slide28

k

B

T

C = e2/ℓ

54 High-T

C

Superconductors

Optimal T

C

2 – 260 K

Accuracy 1.6 K

Relative Accuracy 4.3 %

Coulomb Coupling Theory ResultsPairingChargesMediatingChargesℓ



28

Slide29

29

Acknowledgements

Prof. Dale R. Harshman, The College of William and Mary

Prof. John D. Dow, Arizona State UniversityProf. N. M. Ravindra, New Jersey Institute of TechnologyProf. Sufian Abedrabbo, Khalifa University

and

The College of William and Mary

New Jersey Institute of Technology

The University of Notre Dame

Arizona State University

Physikon

Research

Integron Solutions

and

Khalifa University of Science and Technology