We discuss the two-channel Kondo problem with a pseudogap density of states, ρ(ω) ∝ |ω| r , of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic r = 0 case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for 0 < r < rmax ≈ 0.23. For r > rmax, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin-channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose lowenergy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions r = 0 and r = 1, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.

We show that the scenario of a multiscale Kondo-breakdown quantum critical point gives rise to a divergent Grüneisen ratio with an anomalous exponent 0.7. In particular, we fit the experimental data of YbRh2(Si0.95Ge0.05)2 for a specific heat, thermal expansion, and Grüneisen ratio based on our simple analytic expressions. A reasonable agreement between the experiment and theory is found for the temperature range between 0.4 and 10 K. We discuss how the Grüneisen ratio is a key measurement to discriminate between the Kondo-breakdown and spin-density wave theories.

While standard heavy fermion metals feature a single spin-1/2 local moment per unit cell, more complicated systems with multiple distinct local moments have been synthesized as well, with Ce3Pd20(Si,Ge)6 being one example. Here, we discuss the physics of a Kondo lattice model with two local-moment sublattices, coupled with different Kondo couplings to conduction electrons. The phase diagram will be strongly modified from that of the standard Kondo lattice if the characteristic screening temperatures of the distinct moments are well separated. Therefore, we investigate the interplay between the two Kondo effects using a local self-energy approximation via slave bosons. We find that the two Kondo effects can either compete or co-operate depending on the conductionband filling. In the regime of competition, small differences in the two Kondo couplings can lead to huge differences in the respective Kondo scales, due to non-trivial many-body effects. We also study the low-temperature properties of the collective heavy Fermi-liquid state and propose a connection to depleted Kondo lattice systems.