1. 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

2. What is type 1.5 superconductor?

3. Type I
Meissner
Normal
Type II
Vortex
Type 1.5
Semi-Meissner H

4. M- Magnetization
H- External Magnetic Field

5. Features Long-range attractive , short-range repulsive
Semi-Meissner: mixtures of Meissner and vortex
Non-axialsymmetric vortex
Vortex clusters

6. * Two component Ginzburg-Landau (TCGL) free-energy functional
Then, they can get
, type 1.5
E. Babaev and M.Speight, PRB 72, (2005)
J. Carlstrom, E. Babaev, M. Speight, PRL105, (2010); PRB, 83, (2011)

7. * Numerical Simulation

10. Holographic setup

11. * Action of the two-band superconductor
* 4-d AdS-Schwarzchild black hole
Note that we are considering one single vortex solution

12. * Boundary condition (B.C.) near z ~ 0
* Ansatz for vortex
* Boundary condition (B.C.) near z ~ 0
velocity
current

13. * 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

14. In order to avoid the divergence of the energy with fractional multiple
quantum flux
Other numerical parameters:

15. Numerical Results Holography CMT M.E.Zhitomirsky, V.H. Dao,
PRB 69, (2004)

17. Free Energy
* On-shell action
* Counter term

18. * Regularized free energy

19. * Critical magnetic field Bc1
* For n=1

21. Parameter Regimes for Type 1.5 SC
* Superconducting density

22. * Magnetic penetration depth
* Coherence length

23. * For ε=0.05, η=0, B=0.0125
In order that
We find
e=5q

24. Further directions

25. To estimate Bc2
1. From the M-B plots
II. From the formula

26. The effects of η

27. Dependent of temperature
Vortex clusters (dependent of time)

28. Thanks for your attention!