Unconventional non-Fermi liquid properties of two-channel Anderson impurities system

A theory for treating the unconventional non-Fermi liquid temperature dependence of physical quantities, such as the resistivity, in the Pr-based two-channel Anderson impurities system is developed. It is shown that their temperature dependences are essentially the same as those in the pure lattice system except for the case of extremely low concentration of Pr ions that is difficult to realize by the controlled experiments. This result is consistent with recent observations in diluted Pr-1-2-20 system Y1−xPrxIr2Zn20 (x = 0.024, 0.044, 0.085, and 0.44) reported in Yamane et al. Phys. Rev. Lett. 121, 077206 (2018), and is quite different from that in the case of single-channel Anderson impurities system in which the crossover between behaviors of the local Fermi liquid and heavy Fermi liquid occurs at around moderate concentration of impurities as observed in Ce-based heavy fermion system La1−xCexCu6.

Understanding the index theorems with massive fermions

The index theorems relate the gauge field and metric on a manifold to the solution of the Dirac equation on it. In the standard approach, the Dirac operator must be massless to make the chirality operator well defined. In physics, however, the index theorem appears as a consequence of chiral anomaly, which is an explicit breaking of the symmetry. It is then natural to ask if we can understand the index theorems in a massive fermion system which does not have chiral symmetry. In this review, we discuss how to reformulate the chiral anomaly and index theorems with massive Dirac operators, where we find nontrivial mathematical relations between massless and massive fermions. A special focus is placed on the Atiyah–Patodi–Singer index, whose original formulation requires a physicist-unfriendly boundary condition, while the corresponding massive domain-wall fermion reformulation does not. The massive formulation provides a natural understanding of the anomaly inflow between the bulk and edge in particle and condensed matter physics.

Unusual d-electron heavy-fermion behaviour in f-electron ferromagnetic antiperovskite Gd3SnC

Inverted structures of common crystal lattices, referred to as antistructures, are rare in nature due to their thermodynamic constraints imposed by the switched cation and anion positions in reference to the original structure. However, a stable antistructure formed with mixed bonding characters of constituent elements in unusual valence states can provide unexpected material properties. Here, we report a heavy-fermion behaviour of ferromagnetic gadolinium lattice in Gd3SnC antiperovskite, contradicting the common belief that ferromagnetic gadolinium cannot be a heavy-fermion system. The specific heat shows an unusually large Sommerfeld coefficient of ~ 1114 mJ⋅mol− 1⋅K− 2 with a logarithmic behaviour of non-Fermi-liquid state. We demonstrate that the heavy-fermion behaviour in the non-Fermi-liquid state appears to arise from the hybridized electronic states of gadolinium 5d-electrons participating in metallic Gd–Gd and covalent Gd–C bonds. These results accentuate unusual chemical bonds in CGd6 octahedra with the dual characters of gadolinium 5d-electrons for the emergence of heavy-fermions.