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, PRB 72,180502 (2005) J. Carlstrom, E. Babaev, M. Speight, PRL105, 067003 (2010); PRB, 83, 174509 (2011)

* Numerical Simulation

Holographic setup

* 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 ρ=R * B.C. near horizon At=0, regular b.c. for other fields * B.C. at vortex core ρ=0 … … * B.C. at vortex border ρ=R Homogenerous b.c. for At and φi

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 69,054508 (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 ε=0.05, η=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 η

Dependent of temperature Vortex clusters (dependent of time)

Thanks for your attention!