Abstract
Considerable efforts have been made in recent years to theoretically understand quantum phase transitions in Kondo lattice systems. A particular focus is on Kondo destruction, which leads to quantum criticality that goes beyond the Landau framework of order-parameter fluctuations. This unconventional quantum criticality has provided an understanding of the unusual dynamical scaling observed experimentally. It has also predicted a sudden jump of the Fermi surface and an extra (Kondo destruction) energy scale, both of which have been verified by systematic experiments. Considerations of Kondo destruction have in addition yielded a global phase diagram, which has motivated the current interest in heavy fermion materials with variable dimensionality or geometrical frustration. Here we summarize these developments, and discuss some of the ongoing work and open issues. We also consider the implications of these results for superconductivity. Finaly, we address the effect of spin-orbit coupling on the global phase diagram, suggest that SmB6 under pressure may display unconventional superconductivity in the transition regime between a Kondo insulator phase and an antiferroamgnetic metal phase, and argue that the interfaces of heavy-fermion heterostructures will provide a fertile setting to explore topological properties of both Kondo insulators and heavy-fermion superconductors.
Highlights
Quantum criticality is currently being studied in a wide variety of strongly correlated electron systems
The conduction electrons acquire a Berry phase through their coupling to the hedgehog configurations of the Neel order, which cancels the Berry phase of the local moments. These results demonstrate the competition between the Kondo-singlet formation and spin-Peierls order when the AF order is suppressed, in a way that is compatible with the global phase diagram discussed earlier
With the ever expanding family of heavy fermion materials suitable for studying quantum criticality, there is no doubt that new insights will continue to be gained from these systems on general issues of non-Fermi liquid behavior and unconventional superconductivity
Summary
Quantum criticality is currently being studied in a wide variety of strongly correlated electron systems. It provides a mechanism for both non-Fermi liquid excitations and unconventional superconductivity. Heavy fermion metals represent a prototype system to study the nature of quantum criticality, as well as the novel phases that emerge in the vicinity of a quantum critical point (QCP) [1, 2]. Various studies have revealed a class of unconventional QCPs that goes beyond the Landau framework of order-parameter fluctuations. This local quantum criticality incorporates the physics of Kondo destruction. We point out several outstanding issues and some new avenues for future studies
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