Vortex phase above the melting line in heavy-ion irradiated Bi 2 Sr 2 CaCu 2 O 8

1. Vortex phase above the melting line in heavy-ion irradiatedBi2Sr2CaCu2O8 Kees van der Beek Laboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau • Sylvain Colson, Panayotis Spathis, Mikhail Indenbom, Irina Abalosheva, Marcin Konczykowski Laboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau, France • Ming Li, Peter Kes Kamerlingh Onnes Laboratorium, Leiden, The Netherlands • Marat Gaifullin, Yuji Matsuda Institute of Solid State Physics, The University of Tokyo, Japan • Satyajit Banerjee, Yuri Myasoedov, Eli Zeldov Weizmann Institut e of Science, Rehovot, Israel • Mariela Menghini, Yanina Fasano, Paco de la Cruz Laboratorio de Bajas Temperaturas, Centro Atomico Bariloche, Argentina

2. 1st Order Transition Vortex matter phase diagram in BSCCO Vortex liquid Vortex solid BFOT = 0.5 (F0/g2s2) (e0s / kBT ) rw =  (un+1-un)2 1/2 = ca0 L.I. Glazman & A.E. Koshelev, Phys. Rev. B 43 , 2835 (1991)

3. First Order Transition 0.55 ≤ a ≤ 0.95 2F0 pB rw2 = [1 - cos (fn-fn+1) ] Josephson Plasma Resonance rw (nm) wpl2 (B,T) = wpl2(0,T)cos(fn-fn+1) T / Tc Brandt and Sonin, PRB 66, 064505 (2002). Koshelev, Maley, Bulaevskii, Physica C 341-348, 1503 (2000). If compressional, shear, or "collective" tilt modes dominate, then un 21/2 , rw decrease as function of B  the vortex line tension limits fluctuations

4. •rw(T,B)always behaves as in the "single vortex limit",i.e. as if the line tension (Josephson) term determines everything A.E. Koshelev, L.N. Bulaevskii, Physica C 341-348 (2000)•The temperature dependence of rw(T,B) in agreement with thermal softening of the line tension ( kmax = p/rw not p/x )R. Goldin, B. Horowitz, PRB 58, 9524 (1999) A.E. Koshelev, V.M. Vinokur, PRB 57, 8026 (1998) • Up to the 1st order transition - at the FOT displacements of order a0 cannot be screened by Josephson coupling • "Melting" does not involve c66 vortexlatticepositional order not required• Robust with respect to pinning (See Satyajit Banerjee session III T7)

5. 1st order transition BFOT = 0.5 (F0/g2s2) (e0s/ kBT ) Vortex matter phase diagram in heavy-ion irradiated BSCCO Vortex liquid Vortex solid  2nd order transition  (un+1-un)2 1/2 = ca0 L.I. Glazman and A.E. Koshelev, Phys. Rev. B 43 , 2835 (1991)

6. Vortex fluctuations in heavy-ion irr. BSCCO - low B T / Tc Quantitavely the same behaviour as in unirradiated crystals S. Colson et al,. Phys. Rev. B 69, R180510(2004)

7. Vortex fluctuations in heavy-ion irr. BSCCO - high B T / Tc • Low T : cosf > value before irradiation but < 1  columnar defects cannot align vortex lines as well as in the vortex solid • High T : IRL corresponds to loss of phase coherence cf. Doyle et al. PRL 77, 1155 (1996).

8. Irreversibility ("Bose-glass") line Loss of phase coherence cf. Doyle et al. PRL 77, 1155 (1996). Does not depend on defect density Does not depend on pinning potential - as shown by C60 irradiation, tracks of 20 nm diameter 4. Vortices still pinned in liquid (Monte Verita 1997)  Delocalization line 5. Exponential line, Power-law IV’s  topological transition Feigel’man Geshkenbein Larkin 1990

9. Conclusions • Josephson Plasma Resonance probes c-axis vortex pancake alignment • Columnar defects enhance IRL only at "low enough" T • High T : vortex fluctuations / FOT as in unirradiated BSCCO T-scale determined by e0s B-scale determined byg (Koshelev PRB 1997) • High B : pancakes never aligned as well as in "vortex solid"  Ghost of FOT • IRL : drop in phase correlations Position determined mainly bye0s (in plane properties) • High density of columnsredistributed pancake vortices

10. • Recap on 1st order transition of the vortex ensemble in Bi2Sr2CaCu2O8+d • Columnar defects created by heavy-ion irradiation • Phase diagram as function of doping • Conclusion