# Presentation: 119294

## Fermion Glue in the Hubbard Model:New Insights into the Cuprate Pairing Mechanism with Advanced Computing 

- Thomas C. Schulthess
**Computer Science and Mathematics Division**
**Center for Nanophase Materials Sciences**

## Outline

- Superconductivity

- A model for high-temperaturesuperconductors

- Algorithm andleadership computing

- New scientific insights

**0.0**

**2.5**

**3.0**

**2.0**

**1.5**

**1.0**

**0.5**

**50**

**40**

**30**

**20**

**10**

**0**

**-10**

**-20**

**-30**

**T/t**

**U = 8t; N****o**** = 4;(n) = 0.85**

**V****d**

**3/2********m**

**1/2********d**

******irr**

**Superconductor**

**Non-super-****conductive metal**

**0 K**

**Tc**

**Temperature**

**Resistance**

## What is superconductivity?

**A macroscopic quantum state with**
**Zero resistance**
**Perfect diamagnetism**
**Applications:**
**MAGLEV, MRI,****power transmission,  generators, motors**
**Only disadvantage:**
**Cooling necessary**
**T****c**** ≈ 150 K in HTSC**
**Ultimate goal:**
**T****c**** ≈ room temperature**

**Superconductor**

**Non-super-****conductive metal**

**0 K**

**T****c**

**Temperature**

**Resistance**

## Discovered byBednorz and Müllerin 1986

**Discovered by****Bednorz and Müller****in 1986**

**Highly anisotropic**
**Superconducting****CuO - planes**

**Liquid****He**

**140**

**100**

**60**

**20**

**T [K]**

**1920**

**1960**

**1980**

**1940**

**2000**

**TIBaCaCuO 1988**

**HgBaCaCuO 1993**

**HgTlBaCuO 1995**

**BiSrCaCuO 1980**

**La****2-x****Ba****x****CuO****4**** 1986**

**Nb=A1=Ge**

**Nb****3****Ge**

**MgB****2**** 2001**

**Nb****3****Su**

**NbN**

**Nb**

**Hg**

**Pb**

**NbC**

**V****3****Si**

**YBa****2****Cu****3****O****7**** 19870**

**High temperature****non-BCS**

**Low temperature BCS**

**Bednorz****and Müller**

**BCS Theory**

- High-temperature superconductors

**Liquid H****2**

## HTSC: 1023 interacting electrons

**HTSC: 10****23**** ****interacting electrons**

**2D Hubbard model****for CuO planes **

**DCA/QMC:****Map Hubbard model onto embedded cluster**

- 2D Hubbard model ofhigh-temperature superconductors

## Algorithm and leadership computing: Fixed startup cost favors fewer,faster processors ➙ Cray X1E

**G**

**Warm up**

**Sample**

**QMC time**

- (N = 4480)

- (4480 x 32)

**Measurement** ➙ **cgemm**

**Warm up**

**G**

**G**

**Warm up**

**G**

**Warm up**

- Algorithm and leadership computing: Fixed startup cost favors fewer,faster processors ➙ Cray X1E

## Superconductivity as a consequence of strong electronic correlations

- (TAM *et al.*, PRL ‘05)

| Nc | Zd | Tc |
| --- | --- | --- |
|  4A | 0 | 0.056 |
|  8A | 1 | -0.006 |
|  12A | 2 | 0.016 |
|  16B | 2 | 0.015 |
|  16A | 3 | 0.025 |
|  20A | 4 | 0.022 |
|  24A | 4 | 0.020 |
|  26A | 4 | 0.023 |

## Pairing interaction:A matter of perspective

- =

- +

- Γpp

- Γph

- +

- Γph

- Γ

- Γ

- Λirr

- Pairing interaction

- Mechanism

**(Pfitzner and Wölfle, PRB 1989; Esirgen and Bickers, PRB 1998)**

**Fully irreducible**

**S = 0**

**S = 1**

**Calulate with DCA/QMC (Maier *****et al*****., PRL 2006)**

- Pairing interaction:A matter of perspective

## Attractive pairing interaction between nearest neighbor singlets
Dynamicsassociated with antiferromagnetic spin fluctuation spectrum
Pairing interaction mediated by antiferromagnetic fluctuations

- Maier *et al.*, PRB 2006
- Maier *et al.*, in preparation

**Attractive pairing interaction between nearest neighbor singlets**
**Dynamics****associated with antiferromagnetic spin fluctuation spectrum**
**Pairing interaction mediated by antiferromagnetic fluctuations**

- Magnetic origin of pairing interaction

## Summary/Conclusions/Outlook

**Superconductivity: A macroscopic quantum effect**
**2D Hubbard model for strongly correlated****high-temperature superconducting cuprates**
**Dynamic cluster quantum Monte Carlo simulations****on Cray X1E**
**Superconductivity as a result of strong correlations**
**Pairing mediated by antiferromagnetic spin fluctuations**
**Simple spin susceptibility representation****of pairing interaction?**
**Verification by neutron scattering experiments?**

## Contacts

- Thomas Maier
- Oak Ridge National Laboratory
- (865) 576-3597
- maierta@ornl.gov

-    Schulthess_Superconductivity_0611

- Paul Kent
- Oak Ridge National Laboratory
- (865) 574-4845
- kentpr@ornl.gov

- Thomas Schulthess
- Oak Ridge National Laboratory
- (865) 574-4344
- schulthesstc@ornl.gov

## The Team

**M. Jarrell **

- University
- of Cincinnati

**D. Scalapino **

- University
- of California

**Paul Kent**
**Thomas Maier**
**Thomas Schulthess**

- Oak RidgeNational Lab