Heavy fermions: superconductivity and its relationship to quantum criticality

Figures & data

Figure 1. Low-temperature properties of polycrystalline CeCu₂Si₂, indicating a bulk superconducting phase transition: (a) Electrical resistivity (main part) and magnetic, low-field ac susceptibility (inset) as a function of temperature. (b) Specific heat as C/T vs. T for two samples (from [8]).

Figure 2. (colour online) Phase diagram of CeCu₂(Si_1 − x Ge _x )₂ showing transition temperatures into the anti-ferromagnetically ordered (T _N, open symbols) and the superconducting state (T _c, closed symbols) vs. relative pressure ∆p = p − p _c(x), which reflects the inverse volume. The p _c(x) values are chosen so that the magnetic transition lines for x = 0.1 (p _c = 1.5 GPa, circles) and x = 0.25 (p _c = 2.5 GPa, squares) coincide. Pure CeCu₂Si₂ is assumed here to have p _c = 0.4 GPa (after [28]).

Figure 3. Kondo temperature T _K on a logarithmic scale as a function of the relative volume change produced by the Y and Ce ions in [(La_1 − z Y _z )_1 − x Ce _x ]Al₂ (from [45]).

Figure 4. (colour online) Phase diagram of Ce_1 − x La _x Ni₂Ge₂. Circles, diamonds and triangles mark the single-ion T _K derived from specific-heat results in both the coherent and local Fermi liquid regimes. Stars mark positions T _max of low-temperature maxima in the thermopower (from [47]).

Figure 5. (colour online) Low-temperature behaviour of Lu_1 − x Yb _x Rh₂Si₂. (a) Thermopower as S vs. T. (b) T _K vs. x at ambient pressure and for YbRh₂Si₂ under pressure (dashed line) (from [49]).

Figure 6. (colour online) Scanning tunnelling spectroscopy of YbRh₂Si₂. Differential conductance g (V, T) at selected temperatures. Spectra at T = 14 K and 30 K are offset for clarity. Arrows mark CF excitations. Dip at zero bias reflects local Kondo resonance. Dashed line at -6 meV indicates a peak due to KL formation (from [50]).

Figure 7. “Doniach phase diagram”: Temperature T versus J (> 0), the Kondo exchange coupling constant. Dotted lines represent J dependence of characteristic energy scales k_B T _K and k_B T _RKKY. Solid line denotes magnetic phase boundary (after [52]).

Figure 8. (colour online) Inelastic neutron scattering of S-type CeCu₂Si₂. (a) Magnetic response S _mag (on an absolute intensity scale) at the AF ordering wave vector in the superconducting and normal states at T = 0.07 K (from [48]). (b) Spin-fluctuation dispersion in the normal state (at B = 0, T > T _c and B = B _c2 = 1.7 T, T << T _c) as well as in the superconducting state (B = 0, T << T _c) (from [60]).

Figure 9. (colour online) Changes of Fermi surface properties across a likely Kondo destroying QCP in CeRhIn₅. Pressure dependencies of the dHvA frequencies (a) and cyclotron mass (b) (after [70]).

Figure 10. (colour online) Temperature-magnetic field phase diagram of YbRh₂Si₂ for B ǁ c (a) and YbRh₂(Si_0.95Ge_0.05)₂ for B ⊥ c (b) (from [72]).

Figure 11. (colour online) Disparate behaviours of Sommerfeld coefficient C _el/T vs. T (a) and electrical resistivity ρ vs. T (b) for YbRh₂(Si_0.95Ge_0.05)₂. Results for pure YbRh₂Si₂ are also shown (from [72]).

Figure 12. (colour online) Fermi surface collapse from isothermal crossover in magneto-transport for YbRh₂Si₂. (a) Position of crossover in temperature-field phase diagram for two different samples from crossed-field and single-field Hall coefficient as well as longitudinal magneto-resistivity. (b) Crossover width (FWHM) as a function of temperature. (c) Schematic illustration of abrupt change in R _H(T) at T = 0 and thermal broadening of this jump at finite temperatures (from [75]).

Figure 13. (colour online) Isotherms of Lorenz ratio L/L₀ vs. B between T = 0.1 K and 0.4 K for YbRh₂Si₂ (from [79]).

Figure 14. (colour online) “Global” (T = 0) phase diagram for Yb(Rh_1 − x M _x )₂Si₂, M = Co, Ir (from [82]).

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