COLOR SUPERCONDUCTIVITY Massimo Mannarelli INFN-LNGS [email protected] GGI-Firenze Sept. 2012 venerdì 21 settembre 12 “Compact Stars in the QCD Phase Diagram”, Copenhagen August 2001 venerdì 21 settembre 12 Outline • Motivations • Superconductors • Color Superconductors • Low energy degrees of freedom • Crystalline color superconductors Reviews: hep-ph/0011333, hep-ph/0202037, 0709.4635 Lecture notes by Casalbuoni http://theory.fi.infn.it/casalbuoni/barcellona.pdf venerdì 21 settembre 12 MOTIVATIONS venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ Compact stars venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ Compact stars Warning: QCD is perturbative only at asymptotic energy scales venerdì 21 settembre 12 QCD phase diagram T Quark Gluon Plasma (QGP) Tc Hadronic Color ? Superconductor (CSC) µ Compact stars Warning: QCD is perturbative only at asymptotic energy scales HOT MATTER ENERGY-SCAN EMULATION RHIC RHIC Ultracold fermionic EXPERIMENTS LHC NA61/SHINE@CERN-SPS atoms CBM@FAIR/GSI MPD@NICA/JINR venerdì 21 settembre 12 Compact stars quark⌧hybrid traditional neutron star star N+e N+e+n n,p,e, µ n superfluid hyperon n d u c o c t neutron star with star e r i n p g pion condensate u n, s p,e p , µ r u,d,s o quarks t o , 2SC n , CFL s , H crust Fe color−superconducting 6 3 strange quark matter K 10 g/cm (u,d,s quarks) 11 10 g/cm 3 2SC CFL 14 3 CSL CFL−K + 10 g/cm gCFL 0 CFL−K LOFF 0 Hydrogen/He CFL− atmosphere strange star nucleon star R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 venerdì 21 settembre 12 Compact stars quark⌧hybrid traditional neutron star star N+e “Probes” N+e+n n,p,e, µ n superfluid cooling hyperon n d u c o c t neutron star with star e r i n glitches p g pion condensate u n, s p,e p , µ r instabilities u,d,s o quarks t o n mass-radius , 2SC , CFL s , H crust magnetic field Fe color−superconducting 6 3 strange quark matter K 10 g/cm GW (u,d,s quarks) 11 10 g/cm 3 2SC ...... CFL 14 3 CSL CFL−K + 10 g/cm gCFL 0 CFL−K LOFF 0 Hydrogen/He CFL− atmosphere strange star nucleon star R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 venerdì 21 settembre 12 Compact stars quark⌧hybrid traditional neutron star star N+e “Probes” N+e+n n,p,e, µ n superfluid cooling hyperon n d u c o c t neutron star with star e r i n glitches p g pion condensate u n, s p,e p , µ r instabilities u,d,s o quarks t o n mass-radius , 2SC , CFL s , H crust magnetic field Fe color−superconducting 6 3 strange quark matter K 10 g/cm GW (u,d,s quarks) 11 10 g/cm 3 2SC ...... CFL 14 3 CSL CFL−K + 10 g/cm gCFL 0 CFL−K LOFF 0 Hydrogen/He CFL− atmosphere strange star nucleon star R ~ 10 km F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 Example PSR J1614-2230 mass M ~ 2 M⊙ Demorest et al Nature 467, (2010) 1081 hard to explain with quark matter models Bombaci et al. Phys. Rev. C 85, (2012) 55807 venerdì 21 settembre 12 SUPERCONDUCTORS In 1911, H.K. Onnes, cooling mercury, found almost no resistivity at T = 4.2 K. arbitrary units -D T CV ~ e CV ~T ê R ~ T3 T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Tc venerdì 21 settembre 12 Superconductivity is a quantum phenomenon at the macroscopic scale venerdì 21 settembre 12 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS Bosons occupy the same quantum state: They “like” to move together, no dissipation 4He becomes superfluid at T ≃ 2.17 K, Kapitsa et al (1938) BEC venerdì 21 settembre 12 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum Fermions cannot occupy the same state: They “like” to move together, quantum state. A different theory of no dissipation superfluidity 4He becomes superfluid at 3He becomes superfluid at T ≃ 2.17 K, Kapitsa et al (1938) T ≃ 0.0025 K, Osheroff (1971) BEC BCS venerdì 21 settembre 12 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum Fermions cannot occupy the same state: They “like” to move together, quantum state. A different theory of no dissipation superfluidity 4He becomes superfluid at 3He becomes superfluid at T ≃ 2.17 K, Kapitsa et al (1938) T ≃ 0.0025 K, Osheroff (1971) BEC BCS venerdì 21 settembre 12 Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Bosons occupy the same quantum Fermions cannot occupy the same state: They “like” to move together, quantum state. A different theory of no dissipation superfluidity 4He becomes superfluid at 3He becomes superfluid at T ≃ 2.17 K, Kapitsa et al (1938) T ≃ 0.0025 K, Osheroff (1971) BEC ? BCS venerdì 21 settembre 12 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity “active” Fermi sphere T=0 fermions PF “frozen” fermions venerdì 21 settembre 12 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity “active” Fermi sphere T=0 fermions PF “frozen” fermions Cooper pairing : Any attractive interaction produces correlated pairs of “active” fermions Cooper pairs effectively behave as bosons and condense venerdì 21 settembre 12 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity “active” Fermi sphere T=0 fermions PF “frozen” fermions Cooper pairing : Any attractive interaction produces correlated pairs of “active” fermions Cooper pairs effectively behave as bosons and condense It costs energy to break a Cooper pair E(p)= (✏(p) µ)2 +∆(p, T )2 quasiparticle dispersion law: − p venerdì 21 settembre 12 BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity “active” Fermi sphere T=0 fermions PF “frozen” fermions Cooper pairing : Any attractive interaction produces correlated pairs of “active” fermions Cooper pairs effectively behave as bosons and condense It costs energy to break a Cooper pair E(p)= (✏(p) µ)2 +∆(p, T )2 quasiparticle dispersion law: − p Increasing the temperature the coherence is lost at T 0.3∆ c ' 0 venerdì 21 settembre 12 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = �ϕ. Irrotational: �× v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions) venerdì 21 settembre 12 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = �ϕ. Irrotational: �× v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions) Superfluid Broken global symmetry Transport of the quantum numbers Goldstone boson ϕ of the broken group with (basically) no dissipation v = �ϕ venerdì 21 settembre 12 Superfluid vs Superconductors Definitions Superfluid: frictionless fluid with potential flow v = �ϕ. Irrotational: �× v = 0 Superconductor: perfect diamagnet (Meissner effect) Cooper pairing is at the basis of both phenomena (for fermions) Superfluid Broken global symmetry Transport of the quantum numbers Goldstone boson ϕ of the broken group with (basically) no dissipation v = �ϕ Superconductor Broken gauge symmetry Broken gauge fields with mass, M, Higgs mechanism penetrates for a length λ 1/M / venerdì 21 settembre 12 BCS-BEC crossover v correlation length ⇠ F ⇠ ∆ vs 1/3 average distance n− up down 1/3 ⇠ n− BCS fermi surface phenomenon venerdì 21 settembre 12 BCS-BEC crossover v correlation length ⇠ F ⇠ ∆ vs 1/3 average distance n− up down g weak 1/3 ⇠ n− BCS fermi surface phenomenon strong venerdì 21 settembre 12 BCS-BEC crossover v correlation length ⇠ F ⇠ ∆ vs 1/3 average distance n− up down g weak 1/3 ⇠ n− BCS fermi surface phenomenon 1/3 BCS-BEC crossover ⇠ n− depleting the Fermi sphere ⇠ strong venerdì 21 settembre 12 BCS-BEC crossover v correlation length ⇠ F ⇠ ∆ vs 1/3 average distance n− up down g weak 1/3 ⇠ n− BCS fermi surface phenomenon 1/3 BCS-BEC crossover ⇠ n− depleting the Fermi sphere ⇠ strong BEC 1/3 4 ⇠ n− equivalent to He ⌧ venerdì 21 settembre 12 COLOR SUPERCONDUCTIVITY venerdì 21 settembre 12 A bit of history • Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966) ... • Quark Cooper pairing was proposed by Ivanenko and Kurdgelaidze (1969) • With asymptotic freedom (1973) more robust results by Collins and Perry (1975), Baym and Chin (1976) • Classification of some color superconducting phases: Bailin and Love (1984) venerdì 21 settembre 12 A bit of history • Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966) ... • Quark Cooper pairing was proposed by Ivanenko and Kurdgelaidze (1969) • With asymptotic freedom (1973) more robust results by Collins and Perry (1975), Baym and Chin (1976) • Classification of some color superconducting phases: Bailin and Love (1984) Interesting studies but predicted small energy gaps ~ 10 ÷100 keV negligible phenomenological impact for compact stars venerdì 21 settembre 12 A bit of history • Quark matter inside compact stars, Ivanenko and Kurdgelaidze (1965), Paccini (1966) ..