The quantum phase transitions of metals in two

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The quantum phase transitions of metals in two dimensions Talk online: sachdev. physics. harvard.

The quantum phase transitions of metals in two dimensions Talk online: sachdev. physics. harvard. edu HARVARD

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities in momentum space 2. Fermion pairing in metals with fluctuating spin density waves Non-Fermi liquids and superconductivity in a doped CFT

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities in momentum space 2. Fermion pairing in metals with fluctuating spin density waves Non-Fermi liquids and superconductivity in a doped CFT

Max Metlitski, Harvard Eun Gook Moon, Harvard ar. Xiv: 1001. 1153 HARVARD

Max Metlitski, Harvard Eun Gook Moon, Harvard ar. Xiv: 1001. 1153 HARVARD

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface Strange

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface Strange Metal

C A B D

C A B D

C A B D Strong anisotropy of electronic states between x and y directions:

C A B D Strong anisotropy of electronic states between x and y directions: Electronic “Ising-nematic” order

Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor R. Daou, J.

Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor R. Daou, J. Chang, David Le. Boeuf, Olivier Cyr-Choiniere, Francis Laliberte, Nicolas Doiron-Leyraud, B. J. Ramshaw, Ruixing Liang, D. A. Bonn, W. N. Hardy, and Louis Taillefer Nature, 463, 519 (2010).

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic ordering y x

Quantum criticality of Ising-nematic order

Quantum criticality of Ising-nematic order

Quantum criticality of Ising-nematic ordering TI-n Quantum critical

Quantum criticality of Ising-nematic ordering TI-n Quantum critical

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality D=2+1 Ising

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality D=2+1 Ising criticality ?

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality D=2+1 Ising

Quantum criticality of Ising-nematic ordering TI-n Quantum critical Classical d=2 Ising criticality D=2+1 Ising criticality ?

Quantum criticality of Ising-nematic ordering TI-n Strange Quantum Metal critical?

Quantum criticality of Ising-nematic ordering TI-n Strange Quantum Metal critical?

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Quantum criticality of Pomeranchuk instability

Theory of Ising-nematic transition

Theory of Ising-nematic transition

Theory of Ising-nematic transition

Theory of Ising-nematic transition

“Hot” Fermi surfaces

“Hot” Fermi surfaces

Leading order fermion Green’s function

Leading order fermion Green’s function

Leading order fermion Green’s function

Leading order fermion Green’s function

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities in momentum space 2. Fermion pairing in metals with fluctuating spin density waves Non-Fermi liquids and superconductivity in a doped CFT

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities

Outline 1. Theory of Ising-nematic ordering in a metal Field theories and line singularities in momentum space 2. Fermion pairing in metals with fluctuating spin density waves Non-Fermi liquids and superconductivity in a doped CFT

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface Strange

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface Strange Metal

Fermi surface+antiferromagnetism Hole states occupied Electron states occupied +

Fermi surface+antiferromagnetism Hole states occupied Electron states occupied +

Hole-doped cuprates Hole pockets Electron pockets S. Sachdev, A. V. Chubukov, and A. Sokol,

Hole-doped cuprates Hole pockets Electron pockets 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-doped cuprates Hole pockets Electron pockets S. Sachdev, A. V. Chubukov, and A. Sokol,

Hole-doped cuprates Hole pockets Electron pockets 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-doped cuprates Hole pockets Electron pockets Hot spots S. Sachdev, A. V. Chubukov, and

Hole-doped cuprates Hole pockets Electron pockets Hot spots 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-doped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up at hot

Hole-doped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up at hot spots into electron and hole “pockets” 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-doped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up at hot

Hole-doped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up at hot spots into electron and hole “pockets” 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).

Evidence for small Fermi pockets Fermi liquid behaviour in an underdoped high Tc superconductor

Evidence for small Fermi pockets Fermi liquid behaviour in an underdoped high Tc superconductor Suchitra E. Sebastian, N. Harrison, M. M. Altarawneh, Ruixing Liang, D. A. Bonn, W. N. Hardy, and G. G. Lonzarich ar. Xiv: 0912. 3022

Theory of underdoped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up

Theory of underdoped cuprates Hole pockets Electron pockets Hot spots Fermi surface breaks up at hot spots into electron and hole “pockets” 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).

Theory of underdoped cuprates Hot spots H. J. Schulz, Physical Review Letters 65, 2462

Theory of underdoped cuprates Hot spots H. J. Schulz, Physical Review Letters 65, 2462 (1990) B. I. Shraiman and E. D. Siggia, Physical Review Letters 61, 467 (1988). J. R. Schrieffer, Journal of Superconductivity 17, 539 (2004)

Theory of underdoped cuprates

Theory of underdoped cuprates

Higgs Coulomb

Higgs Coulomb

Higgs Coulomb

Higgs Coulomb

Complete theory

Complete theory

R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke Xu, Phys. Rev. B 78,

R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke Xu, Phys. Rev. B 78, 045110 (2008).

T=0 Phase diagram Higgs Coulomb

T=0 Phase diagram Higgs Coulomb

T=0 Phase diagram d-wave superconductivity

T=0 Phase diagram d-wave superconductivity

T=0 Phase diagram Competition between antiferromagnetism and superconductivity shrinks region of antiferromagnetic order: feedback

T=0 Phase diagram Competition between antiferromagnetism and superconductivity shrinks region of antiferromagnetic order: feedback of “probe fermions” on CFT is important d-wave superconductivity

Theory of quantum criticality in the cuprates * T

Theory of quantum criticality in the cuprates * T

Theory of quantum criticality in the cuprates * T Criticality of the coupled dimer

Theory of quantum criticality in the cuprates * T Criticality of the coupled dimer antiferromagnet at x=xs

Theory of quantum criticality in the cuprates * T Criticality of the topological change

Theory of quantum criticality in the cuprates * T Criticality of the topological change in Fermi surface at x=xm

Theory of quantum criticality in the cuprates * T

Theory of quantum criticality in the cuprates * T

T*

T*

TI-n Onset of superconductivity disrupts SDW order, but VBS/CDW/ Ising-nematic ordering can survive R.

TI-n Onset of superconductivity disrupts SDW order, but VBS/CDW/ Ising-nematic ordering can survive R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke Xu, Physical Review B 78, 045110 (2008). VBS/CDW and/or Ising-nematic order

Similar phase diagram for Ce. Rh. In 5 G. Knebel, D. Aoki, and J.

Similar phase diagram for Ce. Rh. In 5 G. Knebel, D. Aoki, and J. Flouquet, ar. Xiv: 0911. 5223

Similar phase diagram for the pnictides Ishida, Nakai, and Hosono ar. Xiv: 0906. 2045

Similar phase diagram for the pnictides Ishida, Nakai, and Hosono ar. Xiv: 0906. 2045 v 1 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,

Conclusions Theory of Ising-nematic ordering in a twodimensional metal: line singularities in momentum space,

Conclusions Theory of Ising-nematic ordering in a twodimensional metal: line singularities in momentum space, and an emergent dimension: 2+1 dimensional field theories labeled by points on the Fermi surface

Conclusions Gauge theory for pairing of Fermi pockets in a metal with fluctuating spin

Conclusions Gauge theory for pairing of Fermi pockets in a metal with fluctuating spin density wave order: Many qualitative similarities to holographic strange metals and superconductors