Kondo Breakdown and Quantum Oscillations in ${\mathrm{SmB}}_6$

Recent quantum oscillation experiments on ${\mathrm{SmB}}_6$ pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, ${\mathrm{SmB}}_6$ remains robustly insulating to very high magnetic fields. Moreover, a sudden low temperature upturn in the amplitude of the oscillations raises the possibility of quantum criticality. Here we discuss recently proposed mechanisms for this effect, contrasting bulk and surface scenarios. We argue that topological surface states permit us to reconcile the various data with bulk transport and spectroscopy measurements, interpreting the low temperature upturn in the quantum oscillation amplitudes as a result of surface Kondo breakdown and the high frequency oscillations as large topologically protected orbits around the $X$ point. We discuss various predictions that can be used to test this theory.

Figure 1

Low frequency oscillations extracted and replotted from Ref. [16] (red, closed symbols) and Ref. [17] (blue, open symbols). Lines are model fits based on (a) two-dimensional surface states [16], (b) three-dimensional bulk bands [17]. Error bars are the size of symbols which include both experimental error bars and also errors from extracting data from a logarithmic plot. Given the error bars, there is a good agreement between two experiments for low frequencies and it is not possible to distinguish if a 2D or a 3D model fits better a priori.

Figure 2

Kondo breakdown and onset of the surface Kondo effect. 3D strip calculations are done for varying $⟨b_{(s)}{⟩}^2/⟨b{⟩}^2$, where $⟨b_{(s)}{⟩}^2$ is the bulk (surface) slave-boson amplitude indicating the amount of hybridization between the local moments on the surface and the topological surface states. For (a), $⟨b_s{⟩}^2/⟨b{⟩}^2=1$, the hybridization on the surface is the same as the bulk, leading to heavy surface quasiparticles with a small Fermi surface. As $⟨b_s{⟩}^2/⟨b{⟩}^2$ gets smaller in (b) and (c), the Fermi surface area increases as a result of Luttinger’s sum rule and a new larger Fermi surface orbit appears. For $⟨b_s{⟩}^2/⟨b{⟩}^2=0$ (d), local moments decouple from the surface, giving rise to a large Fermi surface with light quasiparticles. Insets show the Fermi surfaces for each figure.