Unusual quantum criticality in metals and insulators T. Senthil (MIT) T. Senthil, ``Critical fermi surfaces and non-fermi liquid metals”, PR B, June 08 T. Senthil, ``Theory of a continuous Mott transition in two dimensions”, PR B, July 08 D. Podolsky, A. Paramekanti, Y.B. Kim, and T. Senthil, ``Mott transition between a spin liquid insulator and a metal in three dimensions”, PRL, May 09 T. Senthil and P. A. Lee, ``Coherence and pairing in a doped Mott insulator: Application to the cuprates”, PRL, Aug 09 Precursors: T. Senthil, Annals of Physics, ’06, T. Senthil. M. Vojta, S. Sachdev, PR B, ‘04 Saturday, October 22, 2011 High Tc cuprates: doped Mott insulators Many interesting phenomena on doping the Mott insulator: Loss of antiferromagnetism High Tc superconductivity Pseudogaps, non-fermi liquid regimes , etc. Stripes, nematics, and other broken symmetries This talk: focus on one (among many) fundamental question. How does a Fermi surface emerge when a Mott insulator changes into a metal? Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Evolution from Mott insulator to overdoped metal : emergence of large Fermi surface with area set by usual Luttinger count. Mott insulator: No Fermi surface Overdoped metal: Large Fermi surface ADMR, quantum oscillations (Hussey), ARPES (Damascelli,….) Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Large gapless Fermi surface present even in optimal doped strange metal albeit without Landau quasiparticles . Mott insulator: No Fermi surface Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Large gapless Fermi surface present also in optimal doped strange metal albeit without Landau quasiparticles . Mott insulator: No Fermi surface In SC state, the d-wave gap is centered on the large Fermi surface down to low doping. Saturday, October 22, 2011 High Tc cuprates: how does a Fermi surface emerge from a doped Mott insulator? Large gapless Fermi surface present also in optimal doped strange metal albeit without Landau quasiparticles . Even in the pseudogap regime the minimum gap features (nodal Fermi arcs, antinodal gaps) in ARPES are located at large Fermi surface! Mott insulator: No Fermi surface In SC state, the d-wave gap is centered on the large Fermi surface down to low doping. Saturday, October 22, 2011 A basic question Quite generally, large Fermi surface visible (at least at short time scales) already in underdoped. How should we understand the emergence of the large Fermi surface in a doped Mott insulator? Saturday, October 22, 2011 Heavy electron critical points Magnetic metal Fermi liquid Pressure/B-field/etc Quantum critical point with striking non-fermi liquid physics The Fermi surface may reconstruct dramatically across the quantum critical point due to loss of Kondo screening. Saturday, October 22, 2011 dHvA in CeRhIn5CeRhIn5 H. Shishido, R. Settai, H. Harima, & Y. Onuki, JPSJ 74, 1103 (2005) Saturday, October 22, 2011 Kondo breakdown and the Mott transition Heavy fermi liquid phase: f-moments part of the Fermi surface due to Kondo screening. ``Kondo breakdown”: Quantum phase transition where f- moments drop out of Fermi surface. Useful point of view: Mott-like transition of the f-band in the presence of itinerant conduction electrons. Basic questions: How does the large Fermi surface die? Role in observed non-fermi liquid physics? Interplay with magnetism? Saturday, October 22, 2011 The fundamental problem: Mott metal- insulator transition Need ways to handle theoretically the Mott transition and its possible quantum criticality. DMFT and extensions: powerful for many questions …..but likely need other methods to confront immediate vicinity of transition directly in two or three dimensions. Saturday, October 22, 2011 Some difculties Saturday, October 22, 2011 Quantum spin liquids to a partial rescue Quantum spin liquid: Mott Mott – no fermi Metal- surface sharp Fermi insulator with no surface magnetism or other t/U symmetry breaking. QCP? Mott transition between a metal and a quantum spin liquid insulator: Study metal-insulator transition without complications of magnetism. Can address issues of loss of Fermi surface, metallic conduction, etc; possibly even second order. Saturday, October 22, 2011 Experimental realization of a weak first (second?) order Mott transition Saturday, October 22, 2011 Two varieties of Mott transitions U/t Mott insulator ``Filling controlled” (similar to cuprates) Fermi liquid μ = chemical potential ``Bandwidth controlled” (relevant to organics, Na4Ir3O8) Both these Mott transitions from a metal can be continuous, and can be handled theoretically when the Mott insulator is a certain gapless quantum spin liquid. Saturday, October 22, 2011 Continuous Mott transitions: How does the Fermi surface die? Old idea: Quasiparticle residue vanishes continuously and everywhere on the Fermi surface (Brinkmann-Rice 1970) Electronic structure right at quantum Mott critical point? Single particle Mott gap E(k) must close at Fermi surface when a continuous Mott transition is approached from insulator => Fermi surface remains sharp though there is no Landau quasiparticle! (Senthil, 2008) Death of Fermi surface: Sharp ``critical Fermi surface” with scale invariant electron spectral function Saturday, October 22, 2011 The bandwidth controlled Mott transition Saturday, October 22, 2011 Structure of critical theory in Saturday, October 22, 2011 Both charge and spin sector theories are well understood enabling a theory of the Mott transition. Saturday, October 22, 2011 Approach from Fermi liquid Saturday, October 22, 2011 Crossover out of criticality: Anderson is diferent (from Higgs) Saturday, October 22, 2011 Finite T crossovers: Marginal Fermi liquids Saturday, October 22, 2011 Same Mott transition in three dimensions Saturday, October 22, 2011 Filling controlled continuous Mott transition in two dimensions U/t Similar theoretical methods useful. Mott Fermi liquid μ = chemical potential NFL2: ``Incoherent Fermi liquid” (IFL) A non-fermi liquid regime with no spin-charge separation, incoherent quasiparticles and a full Fermi surface. Saturday, October 22, 2011 Lessons for spin liquid based theories of the cuprates Old idea: deal with doped cuprate as a doped spin liquid – worry about magnetism later. RVB ``slave boson” theory: represent electron operator as Saturday, October 22, 2011 ``Standard” slave boson RVB theory of doped Mott insulator Above T* - describe as doping a spin liquid Mott insulator with a Saturday, Octoberspinon 22, 2011 Fermi surface True coherence scale: Anderson is diferent Saturday, October 22, 2011 Modified slave boson gauge theory Saturday, October 22, 2011 Underdoped: theory of a pseudogap state Saturday, October 22, 2011 Problems with the theory Saturday, October 22, 2011 Heavy fermions: the Kondo breakdown transition TS, Vojta, Sachdev, 2004 Study destruction of Kondo efect without worrying Coleman et al, 2005 about magnetism: Paul, Pepin, Norman, 2007 Quantum phase transition from a heavy Fermi liquid Pepin, 08 with a large Fermi surface to a small Fermi surface metal where local moments form a spin liquid. Asymptotic low energies: Filling controlled Mott transition of f-band in the presence of a spectator QC metal conduction band Crossover from quantum critical metal Spin liquid QCP Heavy FL to heavy Fermi liquid: metal Intermediate ``Incoherent Fermi Liquid” regime where spin fluctuations remain quantum critical but charge fluctuations behave almost like a Fermi Incoherent liquid. Fermi Liquid Saturday, October 22, 2011 Summary-I • Concrete theory of continuous Mott-like transitions in two dimensions where an entire Fermi surface disappears. - Fermi surface dies by forming a `critical Fermi surface’ at the Mott quantum critical point. - Charge and spin correlations crossover from quantum critical regime to fermi liquid at two diferent energy scales. - Specific predictions for Mott transitions in spin Saturday, October 22, 2011 Summary-II Some successes and difculties in direct application to cuprates/heavy fermions. However these results provide concrete theoretical examples of many interesting phenomena we would like to understand: A strange metal and a pseudogap regime with gapless Fermi arcs in doped Mott insulators, critical destruction of Kondo screening in heavy electron metals, etc. Saturday, October 22, 2011.