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Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn 5

Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn 5 Roman Movshovich Andrea Bianchi Los Alamos National Laboratory, MST-10 Cigdem Capan Filip Ronning Pascoal Pagliuso John Sarrao

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Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn 5

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  1. Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn5 • Roman Movshovich • Andrea Bianchi Los Alamos National Laboratory, MST-10 • Cigdem Capan • Filip Ronning • Pascoal Pagliuso • John Sarrao • Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconductivity - competition between superconductivity and Pauli paramagnetism. • CeCoIn5 meets all the requirements: • Very clean heavy-fermion superconductor, most likely d-wave • First order phase transition, phase diagram  strong Pauli limiting • Low temperature anomaly in specific heat  second superconducting phase. FFLO? A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003), R. Movshovich et al., Nature 427, 802 (2004).

  2. Superconductors, Tc up to 2.3 K at ambient pressure Tc < 200 mK P ~ 25 kbar Ce2CoIn8, Ce2RhIn8 under pressure

  3. FFLO state (III) appears if certain conditions are satisfied. • (1) clean superconductor • (2) Pauli limited • (3) PL is strong enough compared to orbital limiting: Maki parameter  is large enough. GG:  > 1.8 • Good candidates: • low dimensional sc (organics) • heavy fermion sc: weak orbital limiting. • CeCoIn5 combines both of these properties From Gruenberg and Gunther, Phys. Rev. Lett. 16, 996 (1966)

  4. Pauli limiting PL is due to the competition between Zeeman energy of electrons’s spins in the normal state and the superconducting condensation energy. PL is mostly pronounced for the singlet superconductivity, with S = 0, since superconducting electrons in a pair with opposite spins can not take advantage of the Zeeman energy. Pauli limiting will have effect of suppressing superconductivity and the superconducting critical field. PL field HP for s-wave BCS singlet superconductor is For CeCoIn5 this formula gives HP= 4.2 T, if we use weak coupling BSC value for 0 = 1.76 Tc and g = 2. Problem: experimental values: Hc2 = 5 T for H || [001] and 12 T for H ||[110]!!!  theoretical estimate of 4.2 T is unphysical since HP can not be less then experimental value Hc2. Solution: g  2, strong coupling.

  5. Superconductivity is suppressed with respect to theoretical prediction of Hc2 without PL  CeCoIn5 is Pauli limited.

  6.   T3 at low temperature  lines of nodes in the energy gap in clean limit, Impurity band width is less than 30 mK  very clean material. Order of magnitude rise in /T  qp mean free path of few m. R. Movshovich et al., PRL 86, 5152 (2001)

  7. Symmetry of the order parameter of CeCoIn5 Pauli limiting  Specific heat Thermal conductivity  NQR  + = d-wave

  8. A. Bianchi et al., PRL 89, 137002 (2002)

  9. A. Bianchi et al., PRL 89, 137002 (2002)

  10. A. Bianchi et al., PRL 89, 137002 (2002)

  11. A. Bianchi et al., PRL 89, 137002 (2002)

  12. H||[100] H||[100] C. Capan et al., submitted to PRB. First order nature of the superconducting phase transition is reflected in a step in thermal conductivity at Tc.

  13. Conditions for formation of the FFLO state: (1) clean superconductor (2) Pauli limited (3) PL is strong wrt orbital limiting: Maki parameter  is large enough. GG:  > 1.8 for CeCoIn5: Experimentally, for H || [001]: Hc2 = 5 T and Hc20=13.2 T & GG gives HP = 5.8 T, α = 3.6, T0=.35Tc

  14. A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003)

  15. A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003)

  16. CeCoIn5,C/T (J/mol K2) A. Bianchi et al., Phys. Rev. Lett. 91, 257001 (2003) H. Adachi and R. Ikeda, Phys. Rev. B 68, 186510 (2003)

  17. Conclusions: • CeCoIn5 is a clean Type II strongly Pauli limited superconductor, as seen from (1) the phase diagram and (2) the change of the superconducting transition to first order at high magnetic fields close to the superconducting critical field Hc2, as predicted by K. Maki in 1960’s. • The second phase transition within the superconducting state in the high field-low temperature part of the phase diagram is consistent with the formation of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state predicted in 1960’s. • Needs: • Theoretical support on the detailed predictions of various properties of the FFLO state to compare with experiments. • Experiments that probe directly the microscopic structure of the FFLO state.

  18. Specific heat C and thermal conductivity  can help to determine the symmetry of the superconducting order parameter. C  exp (-/T)   exp (-/T) C  T2 T in impurity dominated region,   universal limit. T3, clean limit

  19. Cel aT + bT2 at low temperature  lines of nodes in the energy gap R. Movshovich et al., PRL 86, 5152 (2001)

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