COLOR SUPERCONDUCTIVITY Massimo Mannarelli INFN-LNGS - PowerPoint PPT Presentation

COLOR SUPERCONDUCTIVITY Massimo Mannarelli INFN-LNGS massimo@lngs.infn.it 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) T c Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12

QCD phase diagram T Quark Gluon Plasma (QGP) T c Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12

QCD phase diagram T Quark Gluon Plasma (QGP) T c Hadronic Color ? Superconductor (CSC) µ venerdì 21 settembre 12

QCD phase diagram T Quark Gluon Plasma (QGP) T c Hadronic Color ? Superconductor (CSC) µ Compact stars venerdì 21 settembre 12

QCD phase diagram T Quark Gluon Plasma (QGP) T c 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) T c Hadronic Color ? Superconductor (CSC) µ Compact stars Warning : QCD is perturbative only at asymptotic energy scales EMULATION HOT MATTER ENERGY-SCAN Ultracold fermionic RHIC RHIC EXPERIMENTS atoms LHC NA61/SHINE@CERN-SPS CBM@FAIR/GSI MPD@NICA/JINR venerdì 21 settembre 12

Compact stars t r ad i t i ona l neu t r on s t a r qua r k − hyb r i d s t a r N + e N + e + n n , p , e , µ n s u hype r on o n d u p c c e t neu t r on s t a r w i t h r i s t a r r e n f l p g u p i on condensa t e i u d n , p , e , µ p s r u,d,s o quarks t � , � , � , � 2SC o n � CFL � s H c r us t F e K � color − superconducting 10 6 g / c m 3 strange quark matter (u,d,s quarks) 10 11 g / c m 3 2SC CFL g / c m 3 10 14 CSL CFL − K + gCFL CFL − K0 LOFF 0 Hydrogen/He � CFL − atmosphere s t r ange s t a r nuc l eon s t a r F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 R ~ 10 km venerdì 21 settembre 12

Compact stars t r ad i t i ona l neu t r on s t a r qua r k − hyb r i d s t a r “Probes” N + e N + e + n cooling n , p , e , µ n glitches s u hype r on o n d u p c c e t neu t r on s t a r w i t h r i s t a r r e n f l p g u p i on condensa t e instabilities i u d n , p , e , µ p s r u,d,s o mass-radius quarks t � , � , � , � 2SC o n � CFL magnetic field � s H c r us t F e GW K � color − superconducting 10 6 g / c m 3 strange quark matter ...... (u,d,s quarks) 10 11 g / c m 3 2SC CFL g / c m 3 10 14 CSL CFL − K + gCFL CFL − K0 LOFF 0 Hydrogen/He � CFL − atmosphere s t r ange s t a r nuc l eon s t a r F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 R ~ 10 km venerdì 21 settembre 12

Compact stars t r ad i t i ona l neu t r on s t a r qua r k − hyb r i d s t a r “Probes” N + e N + e + n cooling n , p , e , µ n glitches s u hype r on o n d u p c c e t neu t r on s t a r w i t h r i s t a r r e n f l p g u p i on condensa t e instabilities i u d n , p , e , µ p s r u,d,s o mass-radius quarks t � , � , � , � 2SC o n � CFL magnetic field � s H c r us t F e GW K � color − superconducting 10 6 g / c m 3 strange quark matter ...... (u,d,s quarks) 10 11 g / c m 3 2SC CFL g / c m 3 10 14 CSL CFL − K + gCFL CFL − K0 LOFF 0 Hydrogen/He � CFL − atmosphere s t r ange s t a r nuc l eon s t a r F. Weber, Prog.Part.Nucl.Phys. 54 (2005) 193 R ~ 10 km 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 C V ~ e -D ê T C V ~ T R ~ T 3 T 0.0 0.5 1.0 1.5 2.0 2.5 3.0 T c 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 4 He 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 Fermions cannot occupy the same Bosons occupy the same quantum quantum state. A different theory of state: They “like” to move together, superfluidity no dissipation 3 He becomes superfluid at 4 He becomes superfluid at T ≃ 0.0025 K, Osheroff (1971) T ≃ 2.17 K, Kapitsa et al (1938) BEC BCS venerdì 21 settembre 12

Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Fermions cannot occupy the same Bosons occupy the same quantum quantum state. A different theory of state: They “like” to move together, superfluidity no dissipation 3 He becomes superfluid at 4 He becomes superfluid at T ≃ 0.0025 K, Osheroff (1971) T ≃ 2.17 K, Kapitsa et al (1938) BEC BCS venerdì 21 settembre 12

Superconductivity is a quantum phenomenon at the macroscopic scale T=0 BOSONS FERMIONS Fermions cannot occupy the same Bosons occupy the same quantum quantum state. A different theory of state: They “like” to move together, superfluidity no dissipation 3 He becomes superfluid at 4 He becomes superfluid at T ≃ 0.0025 K, Osheroff (1971) T ≃ 2.17 K, Kapitsa et al (1938) BEC BCS ? venerdì 21 settembre 12

BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity Fermi sphere “active” T=0 fermions P F “frozen” fermions venerdì 21 settembre 12

BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity Fermi sphere “active” T=0 fermions P F “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 Fermi sphere “active” T=0 fermions P F “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 ( ✏ ( p ) − µ ) 2 + ∆ ( p, T ) 2 p E ( p ) = quasiparticle dispersion law: venerdì 21 settembre 12

BCS Theory Bardeen-Cooper-Schrieffer (BCS) in 1957 proposed a microscopic theory of fermionic superfluidity Fermi sphere “active” T=0 fermions P F “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 ( ✏ ( p ) − µ ) 2 + ∆ ( p, T ) 2 p E ( p ) = quasiparticle dispersion law: Increasing the temperature the coherence is lost at T c ' 0 . 3 ∆ 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 correlation length ξ ∼ v F ∆ vs average distance n − 1 / 3 up down BCS ξ � n − 1 / 3 fermi surface phenomenon venerdì 21 settembre 12

BCS-BEC crossover correlation length ξ ∼ v F ∆ vs average distance n − 1 / 3 up down g weak BCS ξ � n − 1 / 3 fermi surface phenomenon strong venerdì 21 settembre 12

BCS-BEC crossover correlation length ξ ∼ v F ∆ vs average distance n − 1 / 3 up down g weak BCS ξ � n − 1 / 3 fermi surface phenomenon BCS-BEC crossover ξ ∼ n − 1 / 3 depleting the Fermi sphere strong venerdì 21 settembre 12