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Pairing of critical Fermi-surface states

Pairing of critical Fermi-surface states. Max Metlitski Kavli Institute for Theoretical Physics. XVIIth International Conference on Recent Progress in Many-Body Theories, Rostock, Germany, September 11, 2013. TexPoint fonts used in EMF.

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Pairing of critical Fermi-surface states

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  1. Pairing of critical Fermi-surface states Max Metlitski Kavli Institute for Theoretical Physics XVIIth International Conference on Recent Progress in Many-Body Theories, Rostock, Germany, September 11, 2013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A

  2. Collaborators SubirSachdevSenthilTodadri David Mross (Harvard) (MIT) (MIT Caltech) Erez Berg(Weizmann Inst.) Diego Hofman (Stanford/SLAC) Sean Hartnoll(Stanford) Rahul Nandkishore(Princeton) M.M, S. Sachdev, Phys. Rev. B 82, 075127, 2010M.M., S. Sachdev, Phys. Rev. B 82, 075128, 2010 M.M., D. Mross, S. Sachdev and T. Senthil - forthcoming

  3. Critical Fermi surface states • Are there states with • - a sharp Fermi-surface - no Landau quasiparticles • 1d: Luttinger liquids: • d > 1 ?

  4. Some candidate critical Fermi surface states • Phase transitions in metals • Spinon Fermi-surface state of Mott-insulators • Halperin-Lee-Read state of Quantum Hall system at ν=1/2 Sr3Ru2O7 S.A. Grigera, R. S. Perry, A. J. Schofield et al (2001) Field(T) Watanabe et al (2012) R. Willet et al (1987)

  5. Phase transitions in metals • Order parameter: Non-Fermi-liquid Fermi liquid Fermi liquid • pnictides, electron-doped cuprates, heavy-fermion compounds, organics, Sr3Ru2O7*

  6. “Strange Metal” Resistivity Fermi-liquid: Strange metal: S.Kasahara et al (2010) Nd2-xCexCuO4 Sr3Ru2O7 La2-xSrxCuO4 Field (T) N.P. Fournier, P. Armitage and R.L. Greene (2010) R.A. Cooper et al (2009) S.A. Grigera, R. S. Perry, A. J. Schofield et al (2001)

  7. SC Phase transitions in metals: pairing instability Non-Fermi-liquid Fermi liquid Fermi liquid

  8. Phase transitions in metals (d = 2) ferromagnet: nematic: charge-density wave: spin-density wave:

  9. Ising-Nematic QCP • Breaking of rotational symmetry of the lattice, translational symmetry preserved • Introduce an Ising order parameter: • Transition out of a metallic state (Pomeranchuk instability) under 90 degree rotations,

  10. Theory of phase transitions in metals • Theory of an order parameter interacting with the Fermi surface • Difficult problem, due in part to an absence of a full RG program • Long history: - J. A. Hertz, PRB (1976), A. J. Millis (1993) - Parallel development in the context of spinon Fermi-surface concluded class with is solvable in the limitP. A. Lee, N. Nagaosa (1992), J. Polchinski (1993), B. Altshuler, L. Ioffe, A. Millis (1994) • - Similar conclusion for class with • Ar. Abanov and A. V. Chubkov (2000), Ar. Abanov, A. V. Chubukov, J. Schmalian (2003) - Problemdeclared open again after work of S. S. Lee (2009). • M.M. and S. Sachdev (2010) D. Mross, J. McGreevy, H. Liu and T. Senthil (2010) M.M., D. Mross, S. Sachdev and T. Senthil (to appear)

  11. Theory of the Ising-nematic transition • Theory of the order parameter interacting with the Fermi surface Fermions: Bosons: Interaction:

  12. Theory at RPA level • RPA: • Low energy dynamics controlled by the Landau-damping: J. A. Hertz, PRB (1976)

  13. Feedback on the fermions • Non Fermi-liquid ( ! )! • Reason: singular forward scattering at small angle P. A. Lee, N. Nagaosa (1992); J. Polchinski (1993)

  14. How to scale? Order parameter Fermions R. Shankar K. Wilson

  15. Two-patch regime • Most singular kinematic regime: two-patch J. Polchinski (1993); B. Altshuler, L. Ioffe, A. Millis (1994).

  16. Two-patch theory • For each expand the fermion fields about two opposite points on the Fermi surface, and . • Key assumption: can neglect coupling between patches.

  17. Two-patch scaling Critical Fermi surface Fermi-liquid does not flow J. Polchinski (1993); B. Altshuler, L. Ioffe, A. Millis (1994), S. S. Lee (2008).

  18. Scaling properties • Symmetries constrain the RG properties severely • Only two anomalous dimensions • Bosons: • Fermions: - fermion anomalous dimension - dynamical critical exponent M.M and S. Sachdev (2010)

  19. Problem • No expansion parameter. Theory strongly coupled. • Direct large- expansion fails. • A more sophisticated genus expansion also fails. Unknown if limit exists. • Uncontrolled three loop calculations S. S. Lee (2009) M.M. and S. Sachdev (2010)

  20. Problem • Uncontrolled three loop calculations give • Contrary to the previous belief that no qualitatively new physics beyond one loop. M.M. and S. Sachdev (2010)

  21. How to control the expansion? • Goes back to work on the Halperin-Lee-Read state in QHE • Some control appears when • More control if B. I. Halperin, P. A. Lee, N. Read (1994) C. Nayak and F. Wilczek (1994) - fixed D. Mross, J. McGreevy, H. Liu and T. Senthil (2010) at three loop order.

  22. Pairing of critical Fermi surfaces • A regular Fermi-liquid is unstable to arbitrarily weak attraction in the BCS channel. • How about a critical Fermi surface?

  23. Pairing instability of the nematic transition • Nematic fluctuations lead to attraction in the BCS channel • Fundamental problem: as one approaches the critical point the pairing glue becomes strong, but the quasiparticles are destroyed • Who wins? Non-Fermi-liquid SC Fermi liquid Fermi liquid

  24. Conceptual difficulties with two-patch RG • Low-energy states on the Fermi-surface cannot be integrated out

  25. Conceptual difficulties with two-patch RG • Treatment of the pairing instability requires a marriage of two RG’s: does not flow

  26. D. Son’s RG procedure • Keep interpatch couplings! D. T. Son, Phys. Rev. D 59, 094019 (1999).

  27. Perturbations • Only two types of momentum conserving processes keep fermions on the FS Forward-scattering BCS scattering

  28. Fermi-liquid RG

  29. D. Son’s RG • Generation of inter-patch couplings: • Generates an RG flow:

  30. Pairing: Ising-nematic transition Non-Fermi-liquid SC Fermi liquid Fermi liquid • Always flows to (transition unstable to pairing) • Pairing preempts the Non-Fermi-liquid physics whenever calculation controlled ( )

  31. Pairing: Ising-nematic transition • Always flows to (transition unstable to pairing) • Pairing preempts the Non-Fermi-liquid physics whenever expansion controlled Fermi liquid SC

  32. Conclusion • Progress in understanding phase transitions in metals. • Controlled description of a superconducting instability of the QCP. • Implications for other critical Fermi-surface state (spinon Fermi-surface, Halperin-Lee-Read state of QHE). Thank you!

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