1. Breakdown of the Kondo effect at an antiferromagnetic instability Outline HF quantum critical points (QCPs) Kondo breakdown QCP in YbRh 2 Si 2 Superconductivity in YbRh 2 Si 2 ? F. Steglich MPI for Chemical Physics of Solids, 01187 Dresden, Germany Collaboration MPI CPfS: M. Brando, S. Ernst, C. Geibel, S. Hartmann, S. Kirchner, C. Krellner, S. Lausberg, H. Pfau, L. Steinke, O. Stockert, S. Wirth TU Braunschweig: G. Zwicknagl U. Goettingen: P. Gegenwart, TU Vienna: J. Custers, S. Paschen U. Cambridge: S. Friedemann, F.M. Grosche Rice U.: Q. Si Rutgers U.: P. Coleman Zhejiang U.: H.Q. Yuan

2. Two types of QCPs [P. Gegenwart, Q. Si & F.S., Nature Phys. 4, 186 (2008)] SDW QCP (Hertz, Millis, Moriya…) Kondo breakdown at AF QCP (Si et al., Coleman et al., 2001) exemplary material: CeCu 2 Si 2 T K ≈ 15 K YbRh 2 Si 2 T K ≈ 30 K cf. O. Stockert‘s talk

3. Emerging local Kondo screening and spatial coherence in the HF metal YbRh 2 Si 2 [S. Ernst et al., Nature 474, 362 (2011), cf. S. Wirth‘s talk] Hierarchy of energy scales from STS J = 7/2 CEF splitting 17, 25 & 43 meV [INS, O. Stockert et al., Physica B 378, 157 (’06)] single-ion T K T K,high  100 K T K,low  30 K [TEP, U. Koehler et al., Phys. Rev. B 77, 104412 (’08)] Kondo-lattice temperature T L  T K,low

4. YbRh 2 Si 2 : T – B phase diagram [J. Custers et al., Nature 424, 524 (2003); T. Westerkamp, Dissertation, TU Dresden (2008)] S eff = 1/2

5. Crossed-field Hall-effect results [S. Friedemann et al., PNAS 107, 14547 (2010)] R H (B 2 ) = lim ρ H (B 1, B 2 )/B 1 B 1 → 0 solid lines:

6. Fermi surface collapse [S. Friedemann et al., PNAS 107, 14547 (2010)] Crossover position T*(B)Crossover width T*(B) agrees with data from ρ, λ, M (P. Gegenwart et al., Science 315, 969 (2007)) FWHM ~ T ω/T scaling (Q. Si, S. Kirchner)

7. Specific heat of YbRh 2 Si 2 under hydrostatic pressure p ≤ 1.4 GPa [R. Borth, M. Nicklas, unpublished]

8. T N anomaly in C(T)/T in Yb(Rh 1-x Co x ) 2 Si 2 [C. Krellner et al., Phys. Rev. Lett. 102, 196402 (2009); Phys. Stat. Solidi B 247, 734 (2010)] C ± (t) = A ± α -1 │t│ - α + b + E · t; t = (T - T N )/T N ; +: t > 0; -: t < 0 x = 0.38 δT N /T N = 5 ·10 -3 α = 0.38 α = -0.12

9. Specific heat (B = 0) [J. Custers et al., Nature 424, 524 (2003)] ΔC = C – C ph – C Q = γT+βT 3 γ ≈ 1.7 J/K 2 mole Magnon contribution C m ( ~ κ m ) = β T 3