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Reply to Comment by S. Friedemann et al. on "Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2"

A reply to the comment by S. Friedemann et al. [arXiv:1207.0536] on our article [Phys. Rev. Lett. 106, 137002 (2011), arXiv:1012.0303].Comment: 2 pages, 1 fi

Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh_2Si_2

The heavy-fermion metal YbRh_2Si_2 displays a field-driven quantum phase transition where signatures of a Fermi-surface reconstruction have been identified, often interpreted as a breakdown of the Kondo effect. We argue that instead many properties of the material can be consistently described by assuming a Zeeman-driven Lifshitz transition of narrow heavy-fermion bands. Using a suitable quasiparticle model, we find a smeared jump in the Hall constant and lines of maxima in susceptibility and specific heat, very similar to experimental data. An intermediate non-Fermi-liquid regime emerges due to the small effective Fermi energy near the transition. Further experiments to discriminate the different scenarios are proposed

Growing and Destroying Catalan-Stanley Trees

Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers. By the standard bijection in this context, these special Dyck paths correspond to a class of rooted plane trees, so-called Catalan-Stanley trees. This paper investigates a deterministic growth procedure for these trees by which any Catalan-Stanley tree can be grown from the tree of size one after some number of rounds; a parameter that will be referred to as the age of the tree. Asymptotic analyses are carried out for the age of a random Catalan-Stanley tree of given size as well as for the "speed" of the growth process by comparing the size of a given tree to the size of its ancestors

Thermodynamic and transport signatures of a fractionalized Fermi liquid

Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different temperature regimes. We derive a variational functional for the thermal conductivity and solve it with a variational ansatz dictated by Keldysh formalism. In sufficiently clean samples and for an appropriate temperature window, we find that thermal transport is dominated by the spinon contribution which can be detected by a characteristic maximum in the Wiedemann-Franz ratio. For the spin susceptibility, the conduction electron Pauli paramagnetism is much smaller than the spinon contribution whose temperature dependence in three dimensions is logarithmically enhanced as compared to the Fermi liquid result