The phase diagrams of the high temperature superconductors HARVARD Talk online:...

The phase diagrams of the

high temperature superconductors

HARVARD

Talk online: sachdev.physics.harvard.edu

Max Metlitski, HarvardMax Metlitski, Harvard

HARVARD

Eun Gook Moon, Harvard

The cuprate superconductors

Ground state has long-range Néel order

Square lattice antiferromagnet

d-wavesuperconductorA

Incommensurate/disordered

antiferromagnetism and charge

Pseudogap

StrangeMetal

Pseudogap

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity,

and change in Fermi surface

StrangeMetal

Iron pnictides: a new class of high temperature superconductors

Ishida, Nakai, and HosonoarXiv:0906.2045v1

S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni,

S. L. Bud'ko, P. C. Canfield, J. Schmalian, R. J. McQueeney, A. I. Goldman,

Physical Review Letters 104, 057006 (2010).

Temperature-doping phase diagram of the iron pnictides:

S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,

H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, 184519 (2010)

Temperature-doping phase diagram of the iron pnictides:

S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido,

H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda, Physical Review B 81, 184519 (2010)

StrangeMetal

N. D. Mathur, F. M. Grosche, S. R. Julian, I. R. Walker, D. M. Freye, R. K. W. Haselwimmer,

and G. G. Lonzarich, Nature 394, 39 (1998)

Lower Tc superconductivity in the heavy fermion compounds

CePd2Si2

Lower Tc superconductivity in the heavy fermion compounds

G. Knebel, D. Aoki, and J. Flouquet, arXiv:0911.5223

Can quantum fluctuations near the loss of antiferromagnetism induce higher temperature superconductivity ?

Questions

If so, why is there no antiferromagnetism in the cuprates near the point where the superconductivity is strongest ?

Questions

What is the physics of the strange metal ?

Questions

1. Loss of antiferromagnetism in an insulator Coupled-dimer antiferromagnets and quantum criticality

2. Onset of antiferromagnetism in a metal From large Fermi surfaces to Fermi pockets

3. Unconventional superconductivity Pairing from antiferromagnetic fluctuations

4. Competing orders Phase diagram in a magnetic field

5. Strongly-coupled quantum criticality in metals Fluctuating antiferromagnetism and Fermi surfaces

Outline

Ground state has long-range Néel order

Weaken some bonds to induce spin entanglement in a new quantum phase

Ground state is a “quantum paramagnet”with spins locked in valence bond singlets

Pressure in TlCuCl3A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).

TlCuCl3

An insulator whose spin susceptibility vanishes exponentially as the temperature T tends to zero.

TlCuCl3

Quantum paramagnet at

ambient pressure

TlCuCl3

Neel order under pressureA. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).

Quantum critical point with non-local entanglement in spin wavefunction

Pressure in TlCuCl3

Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,

Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)

TlCuCl3 with varying pressure

Prediction of quantum field theory

S. Sachdev, arXiv:0901.4103

Pressure in TlCuCl3

CFT3 at T>0

Pressure in TlCuCl3

CFT3 at T>0

Pressure in TlCuCl3

Outline

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity,

and change in Fermi surface

StrangeMetal

Fermi surface+antiferromagnetism

Hole states

occupied

Electron states

occupied

Hole states

occupied

Electron states

occupied

Hole states

occupied

Electron states

occupied

S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, 14874 (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997).

Hole pockets

Electron pockets

Hole-doped cuprates

Hole pockets

Electron pockets

Hole-doped cuprates

Hole pockets

Electron pockets

Hole-doped cuprates

Hole pockets

Electron pockets

Hole-doped cuprates

Fermi surface breaks up at hot spotsinto electron and hole “pockets”

Hole pockets

Electron pockets

Hole-doped cuprates

Fermi surface breaks up at hot spotsinto electron and hole “pockets”

Physical Review B 81, 140505(R) (2010)

Suchitra E. Sebastian, N. Harrison, M. M. Altarawneh, Ruixing Liang, D. A.

Bonn, W. N. Hardy, and G. G. Lonzarich

Evidence for small Fermi pockets

Original observation:N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J.

Levallois, J.-B. Bonnemaison, R.

Liang, D. A. Bonn, W. N. Hardy,

and L. Taillefer, Nature 447, 565 (2007)

Theory of quantum criticality in the cuprates

QuantumCritical

QuantumCriticalStrangeMetal ?

Outline

Physical Review B 34, 8190 (1986)

Spin density wave theory in hole-doped cuprates

Spin-fluctuation exchange theory of d-wave superconductivity in the cuprates

Ar. Abanov, A.V. Chubukov,

and J. Schmalian, Advances in

Physics 52, 119 (2003).

Outline

Competition between superconductivity (SC) and spin-density wave (SDW) order

Phenomenological quantum theory of competing orders

Ar. Abanov, A.V. Chubukov,

and J. Schmalian, Advances in

Physics 52, 119 (2003).

Quantum oscillations

Many experiments

have presented

evidence for the predicted

green quantum

phase transition line

from SC to SC+SDW in a magnetic field

G. Knebel, D. Aoki, and J. Flouquet, arXiv:0911.5223

Similar phase diagram for CeRhIn5

Ishida, Nakai, and HosonoarXiv:0906.2045v1

S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni,

S. L. Bud'ko, P. C. Canfield, J. Schmalian, R. J. McQueeney, A. I. Goldman,

Physical Review Letters 104, 057006 (2010).

Outline

Quantum criticality of the onset of antiferromagnetism in a metal

Metal with “large” Fermi surface s

Metal with electron and hole pockets

Quantum critical theory is strongly-coupled in two (but not higher) spatial dimensions (but not a CFT).

M.A. Metlitski and S. Sachdev, Physical Review B 82, 075128 (2010)

Theory has strong (log-squared) instability already at the Fermi energy to superconductivity with sign-changing pairing amplitude near quantum criticality.

There is non-Fermi liquid behavior at the QCP not only at hotspots, but on entire Fermi surface.

Questions

Questions and answers

Competition between antiferromagnetism and superconductivity has shifted the antiferromagnetic quantum-critical point (QCP), and shrunk the region of antiferromagnetism. This QCP shift is largest in the cuprates

What is the physics of the strange metal ?Proposal: strongly-coupled quantum criticality of fluctuating antiferromagnetism in a metal

Competition between antiferromagnetism and superconductivity has shifted the antiferromagnetic quantum-critical point (QCP), and shrunk the region of antiferromagnetism. This QCP shift is largest in the cuprates

The phase diagrams of the high temperature superconductors HARVARD Talk online:...

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