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Anisotropic Violation of the Wiedemann-Franz Law at a Quantum Critical Point

M. A. Tanatar, J. Paglione, C. Petrovic, L. Taillefer

2007
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Science
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A quantum critical point transforms the behavior of electrons so strongly that new phases of matter can emerge. The interactions at play are known to fall outside the scope of the standard model of metals, but a fundamental question remains: Is the basic concept of a quasiparticle-a fermion with renormalized mass-still valid in such systems? The Wiedemann-Franz law, which states that the ratio of heat and charge conductivities in a metal is a universal constant in the limit of zero temperature,
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... is a robust consequence of Fermi-Dirac statistics. We report a violation of this law in the heavy-fermion metal CeCoIn 5 when tuned to its quantum critical point, depending on the direction of electron motion relative to the crystal lattice, which points to an anisotropic destruction of the Fermi surface. D iscovered in 1853, the Wiedemann-Franz (WF) law (1) has stood as a robust empirical property of metals, whereby the thermal conductivity k of a sample is related to its electrical conductivity s through a universal ratio. In 1927, Sommerfeld (2) used quantum mechanics, applying to electrons the new Fermi-Dirac statistics, to derive the following theoretical relation where T is the absolute temperature, k B is Boltzmann's constant and e is the charge of the electron. The extremely good agreement between the theoretical constant L 0 ≡ p 2 3 ð kB e Þ 2 and the empirical value played a pivotal role in establishing the quantum theory of solids. In 1957, Landau went on to show that, even in the presence of strong interactions, electrons in a metal can still be described as weakly interacting fermions ("quasiparticles") with renormalized mass (3) . This is the essence of what became known as Fermi-liquid (FL) theory, the "standard model" of metals. In the limit of zero temperature, the WF law survived unchanged because it does not depend on mass. (Eq. 1 is only a law at T→0, as only in that limit is energy conserved in collisions.) It has since been shown that the WF law remains valid as T→0 for arbitrary strong scattering, disorder, and interactions (4). It is built into the fabric of matter, valid down to the quanta of conductance, respectively equal to p 2 3 kB 2 T h for heat and e 2 h for charge (5). In the past decade, however, departures from FL theory have been observed in d-and felectron metals when tuned to a quantum critical point (QCP), a zero-temperature phase transition between distinct electronic ground states (6). These typically show up as an anomalous tem-perature dependence of properties at the QCP, for example, a specific heat coefficient that never saturates, growing as C/T~log(1/T) (7), and an electrical resistivity that grows linearly with T (8). Quantum criticality also appears to be linked to the emergence of exotic forms of superconductivity (9-11) and nematic (12) electronic states of matter. To determine whether Landau quasiparticles survive at a QCP, we have measured the transport of heat and charge in CeCoIn 5 , a heavy-fermion metal with a QCP tuned by magnetic field H. In its phase diagram (Fig. 1) , the QCP is located on the border of superconductivity and marks the end of a FL regime at H = H c = 5.0 T, where the electrical resistivity obeys the FL form r = r 0 + AT 2 (13). A power-law fit to the A coefficient yields A~(H -H c ) -a , with a ≅ 4/3 and H c = 5.0 ± 0.1 T (13). At H c , C/T never saturates (14). The same phenomenology is found at the fieldtuned QCP of YbRh 2 Si 2 (with a ≅ 1) (15). In Fig. 2 , we show how the thermal and electrical resistivities in the T = 0 limit behave in CeCoIn 5 as the field is tuned toward H c . These are extrapolations to T = 0 of the low-temperature thermal resistivity, defined as w ≡ L 0 T/k, and electrical resistivity r, for current directions parallel (J || c) and perpendicular (J ⊥ c) to the tetragonal axis of the crystal lattice. The raw data and their extrapolation are shown in detail in (4). For H = 10 T, far away from H c , w(T) and r(T) converge as T→0 for both current directions. However, very close to the QCP, for H = 5.3 T, they only converge for in-plane transport. In other words, transport along the c axis violates the WF law, with w c extrapolating to a distinctly larger value than r c as T→0. In the supporting material (4), we show that extrapolations are not needed to conclude in a violation of the WF law, as the difference data, w c (T) -r c (T) versus T, shows a rigid T-independent shift from field to field. The normalized Lorenz ratio, L L0 ≡ k L0s ≡ r

doi:10.1126/science.1140762
pmid:17540899
fatcat:wcrdpbbye5bkrggrdnk7jbsew4