Vortex phase above the melting line in heavy-ion irradiated Bi 2 Sr 2 Ca. Cu 2 O 8 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
Vortex matter phase diagram in BSCCO Vortex liquid Vortex solid • 1 st Order Transition BFOT = 0. 5 (F 0/g 2 s 2) (e 0 s / k. BT ) rw = (un+1 -un)2 1/2 = c a 0 L. I. Glazman & A. E. Koshelev, Phys. Rev. B 43 , 2835 (1991)
First Order Transition wpl 2 (B, T) = wpl 2(0, T) cos(fn-fn+1) rw 2 = rw (nm) Josephson Plasma Resonance 0. 55 ≤ a ≤ 0. 95 2 F 0 [1 - cos (fn-fn+1) ] p. B 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
• 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 1 st order transition - at the FOT displacements of order a 0 cannot be screened by Josephson coupling • "Melting" does not involve c 66 vortex lattice positional order not required • Robust with respect to pinning (See Satyajit Banerjee session III T 7)
Vortex matter phase diagram in heavy-ion irradiated BSCCO Vortex liquid Vortex solid • 1 st order transition 2 nd order transition • BFOT = 0. 5 (F 0/g 2 s 2) (e 0 s / k. BT ) (un+1 -un)2 1/2 = c a 0 L. I. Glazman and A. E. Koshelev, Phys. Rev. B 43 , 2835 (1991)
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, R 180510 (2004)
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).
Irreversibility ("Bose-glass") line 1. 2. 3. 4. 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 C 60 irradiation, tracks of 20 nm diameter 5. 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
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 e 0 s B-scale determined by g (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 by e 0 s (in plane properties) • High density of columns redistributed pancake vortices
• Recap on 1 st order transition of the vortex ensemble in Bi 2 Sr 2 Ca. Cu 2 O 8+ • Columnar defects created by heavy-ion irradiation • Phase diagram as function of doping • Conclusion
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