Abstract:
Quantum phase transitions arise in many-body systems due to competing interactions that promote rivaling ground states. Recent years have seen the identification of continuous quantum phase transitions, or quantum critical points, in a host of antiferromagnetic heavy-fermion compounds. Studies of the interplay between the various effects have revealed new classes of quantum critical points, and are uncovering a plethora of new quantum phases. At the same time, quantum criticality has provided fresh insights into the electronic, magnetic, and superconducting properties of the heavy-fermion metals. We review these developments, discuss the open issues, and outline some directions for future research.

Abstract:
A large, strongly temperature-dependent Nernst coefficient, $\nu$, is observed between $T$ = 2 K and 300 K for CeCu$_2$Si$_2$ and Ce$_{0.8}$La$_{0.2}$Cu$_2$Si$_2$. The enhanced $\nu(T)$ is determined by the asymmetry of the on-site Kondo (conduction electron$-4f$ electron) scattering rate. Taking into account the measured Hall mobility, $\mu_H$, the highly unusual thermopower, $S$, of these systems can be semiquantitatively described by $S(T)$ $=$ $-$$\nu(T)/\mu_H(T)$, which explicitly demonstrates that the thermopower originates from the local Kondo scattering process over a wide temperature range from far above to well below the coherence temperature ($\approx$ 20 K for CeCu$_2$Si$_2$). Our results suggest that the Nernst effect can act as a proper probe of local charge-carrier scattering. This promises an impact on exploring the unconventional enhancement of the thermopower in correlated materials suited for potential applications.

Abstract:
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. Heavy fermion metals have in recent years emerged as prototypical systems to study quantum critical points. There have been considerable efforts, both experimental and theoretical, which use these magnetic systems to address problems that are central to the broad understanding of strongly correlated quantum matter. Here, we summarize some of the basic issues, including i) the extent to which the quantum criticality in heavy fermion metals goes beyond the standard theory of order-parameter fluctuations, ii) the nature of the Kondo effect in the quantum critical regime, iii) the non-Fermi liquid phenomena that accompany quantum criticality, and iv) the interplay between quantum criticality and unconventional superconductivity.

Abstract:
Quantum criticality in Yb(Rh0.97Co0.03)2Si2 is investigated by means of resistivity and magnetoresistance. The partial substitution of Co leads to a stabilization of the magnetism as expected according to the application of chemical pressure for Yb systems. However, the signature of the Kondo-breakdown remains at the same position in the temperature-magnetic field phase diagram compared to stoichiometric YbRh2Si2. As a consequence, the Kondo-breakdown is situated within the antiferromagnetic phase. These results fit well within the global phase diagram under chemical pressure [1].

Abstract:
Single crystals of the new ternary compound Ce2Ga12Pt were prepared by the self-flux technique. The crystal structure with the space group P4/nbm was established from single-crystal X-ray diffraction data and presents a derivative of the LaGa6Ni0.6 prototype. Magnetic susceptibility measurements show Curie-Weiss behaviour due to local Ce^3+ moments. At high temperatures, the magnetic anisotropy is dominated by the crystal-electric-field (CEF) effect with the easy axis along the crystallographic c direction. Ce2Ga12Pt undergoes two antiferromagnetic phase transitions at T_N,1 = 7.3K and T_N,2 = 5.5K and presents several metamagnetic transitions for the magnetic field along c. Specific-heat measurements prove the bulk nature of these magnetic transitions and reveal a doublet CEF ground state. The 4f contribution to the resistivity shows a broad maximum at T_max ~ 85K due to Kondo scattering off the CEF ground state and excited levels.

Abstract:
FeSb$_2$ has been recently identified as a new model system for studying many-body renormalizations in a $d$-electron based narrow gap semiconducting system, strongly resembling FeSi. The electron-electron correlations in FeSb$_2$ manifest themselves in a wide variety of physical properties including electrical and thermal transport, optical conductivity, magnetic susceptibility, specific heat and so on. We review some of the properties that form a set of experimental evidences revealing the crucial role of correlation effects in FeSb$_2$. The metallic state derived from slight Te doping in FeSb$_2$, which has large quasiparticle mass, will also be introduced.

Abstract:
The temperature ($T$)-magnetic field ($H$) phase diagram of YbRh$_2$Si$_2$ in the vicinity of its quantum critical point is investigated by low-$T$ magnetization measurements. Our analysis reveals that the energy scale $T^\star(H)$, previously related to the Kondo breakdown and terminating at 0.06 T for $T\to 0$, remains unchanged under pressure, whereas the antiferromagnetic critical field increases from 0.06 T ($p=0$) to 0.29 T ($p=1.28$ GPa), resulting in a crossing of $T_N(H)$ and $T^\star(H)$. Our results are very similar to those on Yb(Rh$_{1-x}$Co$_x$)$_2$Si$_2$, proving that the Co-induced disorder can not be the reason for the detachment of both scales under chemical pressure.

Abstract:
This review discusses the heavy-fermion superconductivity in Ce- and U-based compounds crystallizing in the body-centered tetragonal ThCr2Si2 structure. Special attention will be paid to the theoretical background of these systems which are located close to a magnetic instability.

Abstract:
We have measured the thermopower across the metamagnetic transition of the heavy fermion compound CeRu2Si2 at temperatures down to 0.1K and magnetic fields up to 11.5T. We find a large negative enhancement of the thermopower on crossing the metamagnetic field, as well as a sudden change in slope. We argue that this is consistent with the Zeeman-driven deformation of the Fermi surface through a topological transition. The field dependence of the thermopower highlights the discrepancy between thermodynamic and transport properties across the metamagnetic transition.

Abstract:
The enhanced thermopower of the correlated semiconductor FeSi is found to be robust against the sign of the relevant charge carriers. At $T$\,$\approx$\,70 K, the position of both the high-temperature shoulder of the thermopower peak and the nonmagnetic-enhanced paramagnetic crossover, the Nernst coefficient $\nu$ assumes a large maximum and the Hall mobility $\mu _H$ diminishes to below 1 cm$^2$/Vs. These cause the dimension-less ratio $\nu$/$\mu_H$ $-$ a measure of the energy dispersion of the charge scattering time $\tau(\epsilon)$ $-$ to exceed that of classical metals and semiconductors by two orders of magnitude. Concomitantly, the resistivity exhibits a hump and the magnetoresistance changes its sign. Our observations hint at a resonant scattering of the charge carriers at the magnetic crossover, imposing strong constraints on the microscopic interpretation of the robust thermopower enhancement in FeSi.