Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction...
Transcript of Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction...
![Page 1: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/1.jpg)
Fermi Surface Reconstruction and the Origin of High Temperature Superconductivity
Mike Norman
Materials Science Division
Argonne National Laboratory &
Center for Emergent Superconductivity
Toulouse – April 5, 2012 Physics 3, 86 (2010)
![Page 2: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/2.jpg)
0
50
100
150
200
250
300
350
0 0.05 0.1 0.15 0.2 0.25 0.3
Tem
pera
ture
(Kel
vin)
Hole Doping (x)
superconductor
pseudogap
Ant
iferr
omag
net
spinglass
"normal" state
FermiLiquid
T*
Tc
TN
Tcoh
(?)
Phase Diagram of the Cuprates
d-wave
![Page 3: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/3.jpg)
1. Spin singlets
2. Pre-formed pairs
3. Spin density wave
4. Charge density wave
5. d density wave
What is the Pseudogap Due to?
6. Orbital currents
7. Flux phase
8. Stripes/nematic
9. Valence bond solid/glass
10. Combination?
![Page 4: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/4.jpg)
Doping a Mott Insulator - x versus 1+x
“Slater” approach - AF order causes small pockets around (π/2, π/2) whose area scales like x, the number of doped holes
Chubukov & Morr Phys. Reports (1997)
![Page 5: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/5.jpg)
Doping a Mott Insulator - x versus 1+x
“uniform” RVB approach large Fermi surface, but spectral weight scales as x
Feng et al., Science (1999)
![Page 6: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/6.jpg)
Doping a Mott Insulator - x versus 1+x
“flux phase” RVB approach small pockets originating from Dirac cones
Lee, Rep. Prog. Phys. (2008)
![Page 7: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/7.jpg)
Doping a Mott Insulator - x versus 1+x
“umklapp” RVB approach large Fermi surface truncated at AF zone boundary
Yang, Rice, Zhang PRB (2006)
![Page 8: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/8.jpg)
Quantum Oscillations (period determines area of extremal orbit)
Physics 3, 86 (2010) (Brad Ramshaw)
![Page 9: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/9.jpg)
Fowler et al., PRL (1992) Kito et al., JPCS (1992) Haanappel et al., JPCS (1993) but see Springford et al., PRL (1992)
Quantum Oscillations (the bad old days)
small Fermi surface!
![Page 10: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/10.jpg)
Angle Resolved Photoemission Spectroscopy (ARPES)
J C Campuzano Z X Shen Peter Johnson Buckley Prize - 2011
![Page 11: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/11.jpg)
Extraction of the Superconducting Energy Gap from Photoemission Ding et al., PRB (1996) following the pioneering work of Shen et al., PRL (1993)
Δk --> cos(kxa) - cos(kya) --> d-wave energy gap
EM
M!
Y
1
15
0
10
20
30
0 20 40 60 80FS angle
115
|!| (
meV
)
Bi2212, Tc=87K
![Page 12: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/12.jpg)
Norman et al., Nature (1998)
T < Tc (d-wave node)
Tc < T < T* (Fermi arc)
T > T* (large Fermi
surface)
Fermi Arcs
![Page 13: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/13.jpg)
Is the T=0 limit of the pseudogap phase a nodal metal?
Kanigel et al., Nat. Phys. (2006)
![Page 14: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/14.jpg)
Doping Dependence of the Gap Anisotropy
optimal insulator
Chatterjee et al., Nat. Phys. (2010)
![Page 15: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/15.jpg)
Chang et al., New J. Phys. (2008)
Pocket in Nd-doped LSCO (x=0.12) (structural?)
![Page 16: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/16.jpg)
Meng et al., Nature (2009)
Pocket in La doped Bi2201 (structural?)
Structural? – yes – King et al., PRL (2011)
![Page 17: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/17.jpg)
Yang et al., Nature (2008)
Pocket in Bi2212?
Tc=91K (optimal doped)
Tc=65K (underdoped)
![Page 18: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/18.jpg)
Yang et al. PRL (2011)
![Page 19: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/19.jpg)
Truncation of QPI at the AF zone boundary
Kohsaka et al., Nature (2008) Lee et al., Science (2009)
![Page 20: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/20.jpg)
Quantum Oscillations make a comeback (2007)
Doiron-Leyraud et al., Nature (2007) (underdoped - small Fermi surface)
Vignolle et al., Nature (2008) (overdoped - large Fermi surface)
![Page 21: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/21.jpg)
Doiron-Leyraud et al. Nature (2007)
The Hall number is negative! (electron pockets?)
![Page 22: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/22.jpg)
LeBoeuf et al., Nature (2007)
Hall number < 0 in YBCO forms a dome around x=1/8
LeBoeuf et al., PRB (2011)
![Page 23: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/23.jpg)
Antiphase Stripes - Tranquada et al. - Nature (1995) Charge peaks at (±2x,0), Spin peaks at (1/2±x,1/2), x~1/8
-0.5
0
0.5
1
-0.5 0 0.5 1
q y (2!/
a)
qx (2!/a)
spin peaks
charge peaks
doped holes
local spins
![Page 24: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/24.jpg)
For magnetic stripes, electron pockets are stable for a range of potentials
e- pocket
Millis & Norman, PRB (2007)
![Page 25: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/25.jpg)
Are electron pockets consistent with photoemission?
www.aps.org (2009)
![Page 26: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/26.jpg)
For charge only stripes, there are no pockets!
Millis & Norman, PRB (2007)
![Page 27: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/27.jpg)
Though strong nematicity can stabilize them
Yao, Lee, & Kivelson, PRB (2011)
e- pocket
![Page 28: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/28.jpg)
Sebastian et al., Nature (2008)
A larger hole Fermi surface (β) from a spin spiral state?
![Page 29: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/29.jpg)
Sebastian et al., PRB (2010)
Small electron (warped cylinder), small hole (unwarped cylinder), and larger hole Fermi surfaces?
![Page 30: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/30.jpg)
Divergence of cyclotron mass near x=0.09 (exciton instability)?
Sebastian et al., PNAS (2010)
![Page 31: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/31.jpg)
Lifshitz Transition (electron pockets touch) near x=0.09?
Norman, Lin, & Millis, PRB (2010)
![Page 32: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/32.jpg)
Electron pocket near the node due to checkerboard charge order?
Harrison & Sebastian, PRL (2011)
![Page 33: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/33.jpg)
Sebastian et al., PRL (2009)
Quenched Zeeman splitting? (no spin zeros)
![Page 34: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/34.jpg)
Full Zeeman splitting?
Ramshaw et al., Nat. Phys. (2011)
![Page 35: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/35.jpg)
Longitudinal (L) SDW versus transverse (T) SDW
Norman & Lin, PRB (2010) following Ramazashvili, PRL (2010)
![Page 36: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/36.jpg)
Quantum oscillations in the specific heat
1. √H dependence all the way into the oscillatory region 2. γ(H=0) = oscillatory part of γ = one pocket/zone/bilayer
Riggs et al., Nature Phys. (2011)
![Page 37: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/37.jpg)
A pocket is found by band theory near the S/Y points for YBCO (Ortho-I and II), but NOT for Y124
Carrington & Yelland, PRB (2007)
![Page 38: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/38.jpg)
Field induced spin density wave in YBCO?
Dai et al., PRB (2001)
Tc=35K
Haug et al., PRL (2009)
Field induced CDW in YBCO?
Wu et al., Nature (2011)
![Page 39: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/39.jpg)
Is the Pseudogap a Nematic Phase?
Vojta, Adv. Phys. (2009)
![Page 40: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/40.jpg)
Nematic Spin Response below T* (a ≠ b)
Hinkov et al., Science (2008)
Tc=35K
![Page 41: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/41.jpg)
Anisotropic Nernst Signal below T* (a ≠ b)
Daou et al., Nature (2010)
![Page 42: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/42.jpg)
Contrasting Low Field/High T (ARPES) & High Field/Low T (dHvA)
Senthil & Lee, PRB (2009); Micklitz & Norman, PRB (2009)
![Page 43: Fermi Surface Reconstruction and the Origin of High Temperature ... · Fermi Surface Reconstruction and the Origin of! High Temperature Superconductivity!! Mike Norman!! Materials](https://reader033.fdocuments.in/reader033/viewer/2022051811/60273038051ec676225803a7/html5/thumbnails/43.jpg)
QUESTIONS
1. What happens for x < 0.09?
2. What happens for x > 0.14?
3. Are the oscillations above the upper critical field?
4. Are electron pockets consistent with ARPES and STM?
5. Is the pseudogap really due to nematic order?
6. What does all of this have to say about the origin of high Tc?
Singleton et al., PRL (2010)