1. AC Susceptibility Adrian Crisan National Institute of Materials Physics, Bucharest, Romania

2. AC susceptibility measurements fundamental and 3 rd harmonic Quantum Design PPMS -  (T) at various H DC, h ac (  15 Oe), f (  10 kHz): T c (H) -  ”(h ac ),  3 (h ac ) at various fixed T and H DC and varying f: J c (T,H DC, f), U eff (T,H DC ) T m is the on-set of third harmonic susceptibility  3 (T) [A. C. et al., 2003 Appl. Phys. Lett. 83 506]

4. Critical current density as function of temperature, field, and frequency, using AC susceptibility measurements J C = h*/d  (in A/cm 2 ) h * - position of maximum (in Oe) d – film thickness (in cm)  coefficient slightly dependent on geometry (approx. 0.9) E.H. Brandt, Physical Review B 49/13 (1994) 9024.

5. Anderson-Kim Collective pinning Zeldov

6. EXPERIMENTAL: A.C. et al, SuST 22, 045014, 2009

7. SampleU 0 (77.3 K, 3 T) U 0 (77.3 K, 4 T) U 0 (77.3 K, 5 T) (20Pr/565nmY)x2370.1 K254.6 K151.63 K (15Pr/885nmY)x6NA295.05 K181.06 K (15Pr/843nmY)x3433.5 K310.1 K215.8 K YBCO363.6 K247.2 K150.9 K

8. New (unpublished) results on different samples YBZ0.3 – YBCO doped with 4% wt.BZO, 0.3 µm (Mele) YBZ1 - YBCO doped with 4% wt. BZO, 1.1 µm (Crisan) YBZND1 -YBCO doped with 4% wt. BZO, 1.1 µm, grown on STO decorated with Ag Nano-Dots using 15 laser pulses (15Ag) (Crisan) YBZND2 – bilayer (15Ag/ YBCO doped with 4% wt. BZO, 1.1 µm)X2 YBZNPYO0.4 - YBCO doped with 4% wt.BZO and 2% at. Y 2 O 3

15. Field/ Sample YBZ1YBZND1YBZND2YBZ0.3YBZNPYO0.4 3 T 731 K 4 T 638 K 5 T 432 K 530 K 6 T380 K309 K352 K524 K450 K 7 T286 K 285 K465 K386 K 8 T193 K 212 K389 K333 K

16.  ” is a measure of total dissipation: -linear: Thermal Activated Flux Flow (TAFF) and Flux Flow (FF) -nonlinear:Flux Creep  3 is a measure on nonlinear dissipation (flux-creep) only [P. Fabricatore et al, PRB 50, 3189, 1994] Vortex melting line from ac susceptibility

17. - two-fluid: ab (T)= ab (0)[1–(T/T c ) 4 ] -1/2 -3D XY : ab (T)= ab (0)[1–T/T c ] -1/3 -mean-field: ab (T)= ab (0)[1–T/T c ] -1/2 C  1/4  2, c L = 0.15,  =90 

18. Examples Two-fluid3D XY [A. C. et al., 2003 Appl. Phys. Lett. 83 506] [A. C. et al., 2007 PRB 76 21258]  YBCO = 5.4  Tl:1223 =12.6

19. HgBa 2 Ca n-1 Cu n O y (with n ≥ 6 ) n=9 HgBa 2 O 2 9 13 14 9 8 6 8 9 10 a c -  (z) NhNh O(1) 2- O(2) 2- Z OP (SC) IP (AF) (n-2) OP (SC) [A. C. et al., 2008 PRB 77 144518]

20. Magnetically-coupled pancake vortex molecules composed of two pancakes separated by the thin CRL, strongly coupled by Josephson coupling Two-fluid (1245 and 1234)

21. Ba 2 Ca 3 Cu 4 O 8 (O 1−y F y ) 2 [ F(2y)-0234] Ba 2 Ca n-1 Cu n O 2n+2 (n=3-5), F=0, samples are optimally doped with T c larger than 105 K, but they are very unstable The system becomes stable after substitution of F at the apical O site; underdoped states F(2.0)-0234 is not a Mott insulator, but a SC with T c =58 K Thin CRL (0.74 nm) as compared with other multilayered cuprates Allow the investigation of underdoped region by varying the F doping 2y = 1.3, 1.6, 2.0 (105, 86, 58 K) [D. D. Shivagan,.., A.C., et al., SuST 24, 095002]

22. Penetration depth: 3D XY critical fluctuations model F(1.3)-0234 near-optimally-doped, enough carriers in both OP and IPs, 3D SC, strong Josephson coupling

23. Penetration depth: mean-field model F(1.6)-0234 under-doped; out of the region of critical fluctuations; rearrangement of Fermi surfaces through hybridization between OP and IP bands; OP Fermi surface has a 2D character, IP Fermi surface has a 3D character

24. Penetration depth: two-fluid model F(2.0)-0234 heavily under-doped; formal Cu valence is 2+, should be half-filled Mott insulator; evidence of self-doped thick IPs block, as compared with thin IP block of F(2.0)-0212 that shows 3D-2D cross-over Absence of 3D-2D cross-over is a manifestation of cooperative coupling in CRL and IPs