(Color-)magnetic flux tubes in dense matter

Transcription

1 Seattle, Apr 17, Andreas Schmitt Mathematical Sciences and STAG Research Centre University of Southampton Southampton SO17 1BJ, United Kingdom (Color-)magnetic flux tubes in dense matter A. Haber, A. Schmitt, PRD 95, (2017); EPJ Web Conf. 137, (2017) A. Haber, A. Schmitt, arxiv: [hep-ph] two-component superconductors: unconventional type-i/type-ii behavior (flux tube clusters) flux tubes and domain walls in superconducting quark matter

2 Seattle, Apr 17, Reminder: type-i/type-ii superconductivity flux tube ξ λ condensate magnetic field B Ginzburg-Landau parameter κ = λ ξ radius Η c2 normal type-ii superconductivity for κ > 1/ 2: flux tube lattice for 1 < H < 2 A.A. Abrikosov, Soviet Physics JETP 5, 1174 (1957) flux tubes Η c1 Η c Meissner κ H

3 Seattle, Apr 17, Two-component superconductors Ginzburg-Landau potential for two complex scalar fields with electric charges q 1, q 2 (neutron/proton: q 1 = 2e, q 2 = 0) U = B2 2 + ] [ ( + iq i A)φ i 2 µ 2 i φ i 2 + λ i φ i 4 i=1,2 + 2h φ 1 2 φ 2 2 further extensions: derivative coupling ( entrainment ) M. G. Alford, G. Good, PRB 78, (2008) A. Haber, A. Schmitt, PRD 95, (2017) color superconductor: 3 scalar fields φ 1, φ 2, φ 3 and 3 gauge fields A. Haber, A. Schmitt, arxiv: [hep-ph]

4 Seattle, Apr 17, Two-component superconductors in neutron star cores T c inner crust core core outer crust neutron (singlet) proton H c1 H c2 H c T c neutron (triplet) κ 2 = 1/2 density density density-dependent κ type-i/type-ii transition in the core? effect of coupling to superfluid on type-i/type-ii transition?

5 Seattle, Apr 17, Critical magnetic fields in a two-component system compute flux tube profiles and flux tube interaction attractive long-distance interaction in type-ii regime isolated superconductor superconductor coupled to a superfluid 2 flux tubes 1 κ H H' c2 flux tubes 1 2 H' c1 small- ν approximation (our calculation) 2 flux tubes 1 H' c2 H' c1 complete solution (conjecture) numerical calculation supports conjecture A. Haber, D. Müller, preliminary results first-order phase transition allows for flux tube clusters see also type-1.5 superconductors J. Carlström, J. Garaud, E. Babaev, PRB 84, (2011)

6 Seattle, Apr 17, Quark matter in a magnetic field color-superconducting quark matter in a magnetic field use perturbative results for Ginzburg-Landau parameters µ, λ, h H [μ 2 /λ 1/2 ] unpaired CFL 2SC h/λ= strong coupling constant g d Color-flavor locked (CFL) phase 2SC phase φ 1 = φ 2 = φ3 φ paired: 1 = φ 2= 0 φ unpaired: 3= 0 s d s d d u s d u s u s u u d u s

7 Seattle, Apr 17, Magnetic defects in CFL can be superfluid vortices and magnetic flux tubes at the same time! CFL line defects (n 1, n 2, n 3 ) Γ [π/3µ q ] Φ 3 [π/g] Φ8 [π/ g 8 ] Global vortex (n, n, n) n 0 0 Forbes, Zhitnitsky (2002) Semi-superfluid vortex (0, 0, n) n 3 Balachandran, Digal, Matsuura (2006) Magnetic flux tube T 112 (n, n, 2n) 0 0 2n Iida (2005) Magnetic flux tube T 101 (n, 0, n) 0 n n Haber, Schmitt (2017) winding numbers n 1, n 2, n 3 for three scalar fields baryon circulation Γ n 1 + n 2 + n 3 (color-)magnetic flux Φ 8 n 1 + n 2 2n 3 photon/gluon mixing: Meissner effect for B 8 = B 8 cos θ + B sin θ 0 2n 3

8 Seattle, Apr 17, Flux tube profiles f 1 =f 2 f 3 T f 3 f 2 f 1 T B B B flux tube with unpaired core R R flux tube with 2SC core additional B 3 field (cost in free energy) non-vanishing condensate in core (gain in free energy)

9 Seattle, Apr 17, Phase diagram including flux tubes in neutron stars µ q 400 MeV g 3.5 weak-coupling methods and phenomenological models: T c (10 50) MeV H [μ 2 /λ 1/2 ] NOR 2SC CFL 2 1 (D) 1 (T 1 ) 2 1 (T 112 ) 1 (T 101 ) T c /μ q type-ii regime for sufficiently large T c /µ q type-i/type-ii transition complicated (multi-component structure!)

10 Seattle, Apr 17, Phase diagram including flux tubes in neutron stars µ q 400 MeV g 3.5 weak-coupling methods and phenomenological models: T c (10 50) MeV H [μ 2 /λ 1/2 ] NOR 2SC CFL 2 1 (D) 1 (T 1 ) 2 1 (T 112 ) 1 (T 101 ) T c /μ q CFL flux tubes with 2SC core (T 101 ) preferred critical fields H G H NS, however: creation of flux tubes through cooling into superconducting phase? 2SC domain walls (D) preferred over ordinary 2SC flux tubes (T 1 ) for sufficiently large T c /µ q

11 Seattle, Apr 17, Open questions 1. type-i/type-ii transition in multi-component superconductors Do flux tube clusters exist in (a layer of) a neutron star? Do they affect transport properties/deformability? 2. magnetic flux tubes (and superfluid vortices) in quark matter What happens if CFL matter is rotated and placed into a magnetic field? Are there vortices and flux tubes (misaligned), like in neutron/proton matter? Do flux tubes form in the magnetic field evolution of a neutron star? Does the (color-)flux tube lattice sustain magnetic mountains? ɛ CFL 10 7 vs ɛ proton 10 9 K. Glampedakis, D. I. Jones and L. Samuelsson, PRL 109, (2012)... affect the tidal deformability of the star?