Vortex Solution in Holographic Two-Band Superconductor
-- A model of holographic type 1.5 superconductor ? ? Hai-Qing
Zhang Institute for Theoretical Physics, Utrecht University KITPC,
Beijing 13/07/2015 Cooperators: Jackson M.-S. Wu, Shang-Yu Wu,in
progress What is type 1.5 superconductor? Type I Meissner Normal
Type II Vortex Type 1.5 Semi-Meissner H M- Magnetization H-
External Magnetic Field Features Long-range attractive ,
short-range repulsive
Semi-Meissner: mixtures of Meissner and vortex Non-axialsymmetric
vortex Vortex clusters * Two component Ginzburg-Landau (TCGL)
free-energy functional
Then, they can get , type 1.5 E. Babaev and M.Speight, PRB72,
(2005) J. Carlstrom, E. Babaev, M. Speight, PRL105, (2010);PRB, 83,
(2011) * Numerical Simulation Holographicsetup * Action of the
two-band superconductor
* 4-d AdS-Schwarzchild black hole Note that we are considering one
single vortex solution * Boundary condition (B.C.) near z ~ 0
* Ansatz for vortex * Boundary condition (B.C.) near z ~ 0 velocity
current * B.C. at vortex border =R
* B.C. near horizon At=0, regular b.c. for other fields * B.C. at
vortex core =0 * B.C. at vortex border =R Homogenerous b.c. for At
and i In order to avoid the divergence of the energy with
fractional multiple
quantum flux Other numerical parameters: Numerical Results
Holography CMT M.E.Zhitomirsky, V.H. Dao,
PRB 69, (2004) Free Energy * On-shell action * Counter term *
Regularized free energy * Critical magnetic field Bc1
* For n=1 Parameter Regimes for Type 1.5 SC
* Superconducting density * Magnetic penetration depth
* Coherence length * For =0.05, =0, B=0.0125 In order that We find
e=5q Further directions To estimate Bc2 1. From the M-B plots II.
From the formula The effects of Dependent of temperature
Vortex clusters (dependent of time) Thanks for your attention!
