1. Inhomogeneous Superconductivity in the Heavy Fermion CeRhIn 5 Tuson Park Department of Physics, Sungkyunkwan University, Suwon 440-746, South Korea IOP Workshop, Nov. 10-12, 2012 成 均 館 ( since 1398)

2. Collaborators H. Q. Yuan: Zhejiang University, China X. Lu, H. Lee, F. Ronning, E. D. Bauer, R. Movshovich, J. L. Sarrao, I. Martin, Z. Zhu, J. D. Thompson: Los Alamos National Lab. E. Park, S. Seo, S. Lee, D. Shin, S. Shin : Sungkyunkwan Univ. V. Sidorov: HPPI, Russia SKKU Z. Fisk: Univ. California - Irvine I. Vekhter: Louisiana State Univ. N. Curro: Univ. California - Davis. R. R. Urbano: UNICAMP.

3. Outline  Quantum criticality and superconductivity  Inhomogeneous SC state in the quantum critical superconductor CeRhIn5 - Phys. Rev. Lett. 108, 077003 (2012)  Disorder, magnetism, and superconductivity: Cd-doped CeMIn 5 (M=Co, Rh, Ir) (unpublished)

4. Phase diagram of unconventional SCs cuprateFe-based pnictides organics heavy fermion CeRhIn 5

5. Non-Fermi liquid at optimal T c cuprateFe pnictides organics heavy fermion CeRhIn 5 Common threads Universial Class of SCs

6. Emergent phases near a quantum critical point P. Coleman & A. J. Schofield, Nature 433 ('05) Quantum phase transition is a transition between ordered and disordered states driven by quantum fluctuations at T = 0 K Ordered state δcδc temperature δ temperature –control parameter (δ) phase diagram Ordered state Fermi liquid Quantum critical matter (NFL) Breakdown of Fermi liquid: Δρ  T n (n <2), C/T  log T 0 /T Continuous source of new emergent states: unconventional superconductivity, metamagnetism (Sr 3 Ru 2 O 7 ), stripes in the cuprates, nematic states in URu 2 Si 2 & Fe-based SCs SC

7. Isothermal measurements of CeRhIn 5 as a fn of pressure:  (P)  (5.2 GPa) Nature 456, 366 (2008) Quantum critical superconductivity in CeRhIn 5 4-fold modulation in field-angle specific heat PRL 101, 177002 (2008) Quantum fluctuations are the origin of the unconventional superconductivity

8. Outline  Quantum criticality and superconductivity  Inhomogeneous SC state in the quantum critical superconductor CeRhIn5 - Phys. Rev. Lett. 108, 077003 (2012)  Disorder, magnetism, and superconductivity: Cd-doped CeMIn 5 (M=Co, Rh, Ir) (unpublished)

9. Q. Li et al., PRL 99, 067001 (2007)  resistive transition far above bulk T c  Broad tail below the Tc onset  temperature for transition in  c <  ab Textured SC in high-Tc cuprates I. Martin & C. Panagopoulos, EPL 92, 67001 (2010) Y. Ando et al., PRL 92, 247004 (2004)

10. Filamentary superconductivity in CeRhIn 5 Filamentary superconductivity due to bad sample quality? Manifestation of a new state of matter in the vicinity of a QCP? T c difference below 1.9 Gpa (Knebel et al., JPCM 16, 8905 (2004))

11. Experiments: simultaneous measurements of heat capacity and resistivity under pressure Hybrid clamp-type pressure cell (up to 3 GPa) with silicone as transmitting medium Plug with samples mounted Pb T c as a meausre of pressure

12. CeRhIn 5 in the coexisting phase TNTN TcTc T on T c onset in the resistivity is different from the bulk T c determined by the heat capacity Phase diagram for better sample with RRR ~ 1000

13. Pressure effects on the T c difference T c difference between resistivity and specific heat only in the coexisting phase TP et al., Phys. Rev. Lett. 108, 077003 (2012) a b c T c difference is not from disorder, but from competing orders

14. Resistivity anisotropy in the SC transition regioin At 1bar, residual resistivity for J//c is larger than J // ab by a factor of 10 Contradicting conventional expectation, however, resistivity drops to zero immediately for J // c, while it has a long tail for J // ab Resistivity anisotropy only in the coexisting phase

15. Textured SC state Broad tail of SC transition in ρ ab is not from heating effects. Additional in-plane anisotropy SC AF SC b c a AF

16. Recent neutron scattering in the coexisting phase of CeRhIn 5 Neutron scattering of CeRhIn 5 at 1.48 GPa - Aso et al., JPSJ 78, 073703 (2009). T c corresponds to the bulk T c, where Q 2 completely replaces Q 1 and coexists with SC state T* corresponds to resistive T c => SC & Q2 coexists, while Q1 disappears below bulk Tc SC & Q2 Q1 SC & Q2 b c a Q1 Q 1 = (0.5, 0.5, 0.326), Q 2 = (0.5, 0.5, 0.391)

17. Summary & Discussion I Discovery of a textured SC phase in the heavy fermion compound CeRhIn 5 : - T c difference - Resistivity anisotropy among different crystalline axes - Coincidence of Q 2 onset with T c onset Presence of competing phase & proximity to a QCP are keys to the textured SC phase Is textuerd SC unique in CeRhIn 5 ? SC & Q2 Q1 SC & Q2 b c a Q1 Q 1 = (0.5, 0.5, 0.326), Q 2 = (0.5, 0.5, 0.391)

18. Q. Li et al., PRL 99, 067001 (2007)  resistive transition far above bulk T c  Broad tail below the Tc onset  temperature for transition in  c <  ab Textured SC in high-Tc cuprates I. Martin & C. Panagopoulos, EPL 92, 67001 (2010)

19. Textured SC in organics (TMTSF) 2 PF 6 pressure Pasquier et al., Physica B 407, 1806 (2012)

20. Textured SC in Fe pnictides Chu et al., Science 329, 824 (2010) Fernandes et al., Phys. Rev. B 81, 140501 (2010) (arXiv:1112.2243v1)

21. Perspective on textured state  Quantum critical SCs seem susceptible to new electronic states  Electrons spontaneously adjust themselves to minimize the stress coming from frustration among competing phases  Is textured SC state universal? Most likely  Add one more common thread to the unconventional SCs  Is it beneficial to superconductivity? Probably not in CeRhIn5

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