Quantum critical scaling in beta-YbAlB4 and theoretical implications

Emergent phenomena in quantum materials are subject of intense experimental and theoretical research at present. A wonderful example thereof are the sister phases of YbAlB$_4$ - a newly discovered heavy fermion material [1]. While one phase ($\alpha$-YbAlB$_4$) is a heavy Fermi liquid, its sibling $\beta$-YbAlB$_4$ is quantum critical, supporting an unconventional superconductivity with a tiny transition temperature of $\sim80$ mK. Latest experiments [2] uncover the quantum critical $T/B$-scaling in $\beta$-YbAlB$_4$ and prove that superconductivity emerges from a strange metal governed by an extremely fragile quantum criticality, which apparently occurs at zero field, without any external tuning. \newline Here, we will present a theoretical perspective on the quantum critical scaling in $\beta$-YbAlB$_4$ and will show that the critical exponents can be derived from the nodal structure of the hybridization matrix between Yb $f$-band and the conduction electrons. It follows that the free energy at low temperatures can be written in a scaling form $F\propto [(k_B T)^2 + (g\mu_B B)^2]^{3/4}$, which predicts the divergent Sommerfeld coefficient $\gamma$ and quasi-particle effective mass as $B\to 0$: $\gamma\sim m^*/m \propto B^{-1/2}$. This is indeed observed in the experiment [1,2], which places a tiny upper bound on the critical magnetic field $B_c<0.2$~mT. We will discuss theoritical implications of this fragile intrinsic quantum criticality in $\beta$-YbAlB$_4$ and discuss the possibility of a quantum critical phase, rather than a quantum critical point, in this material. \newline \newline [1] S. Nakatsuji \emph{et al.}, Nature Physics {\bf 4}, 603 (2008). \newline [2] Y. Matsumoto, S. Nakatsuji, K. Kuga, Y. Karaki, Y. Shimura, T. Sakakibara, A. H. Nevidomskyy, and P. Coleman, Science {\bf 331}, 316 (2011).