The Wiedemann-Franz law in the putative one-dimensional metallic phase of PrBa2Cu4O8

Abstract

The nature of the electronic state of a metal depends strongly on its dimensionality. In a system of isolated conducting chains, the Fermi-liquid (quasiparticle) description appropriate for higher dimensions is replaced by the so-called Tomonaga-Luttinger liquid picture characterized by collective excitations of spin and charge. Temperature is often regarded as a viable tuning parameter between states of different dimensionality, but what happens once thermal broadening becomes comparable to the interchain hopping energy remains an unresolved issue, one that is central to many organic and inorganic conductors. Here we use the ratio of the thermal to electrical conductivities to probe the nature of the electronic state in PrBa 2 Cu 4 O 8 as a function of temperature. We find that despite the interchain transport becoming non-metallic, the charge carriers within the CuO chains appear to retain their quasiparticle nature. This implies that temperature alone cannot induce a crossover from Fermi-liquid to Tomonaga-Luttinger-liquid behaviour in quasi-one-dimensional metals. U nderstanding how the electronic state evolves in quasi-one-dimensional (q1D) metals as coupling between individual chains is strengthened or weakened, and determining the energy scale for the Fermi-liquid to Tomonaga-Luttinger liquid (FL-TLL) crossover, remain profound theoretical problems that are relevant to a host of organic and inorganic q1D conductors 1 . Temperature T is often regarded as a viable tuning parameter between states of different dimensionality in q1D metals. For k B T , 2t H , the interchain hopping integral, charge hops coherently in all three dimensions, albeit with anisotropic velocities. Once thermal broadening is comparable to the warping of the Fermi sheets however, hopping between chains is predicted to become incoherent, leading to a putative 3D-1D dimensional crossover 2 and contrasting behaviour in the intra-and inter-chain resistivities at high T. As a result, signatures of TLL physics are expected to emerge with increasing temperature 3 . In an alternative picture, it is argued that interchain coherence in a q1D FL is robust provided the intrachain scattering rate C , e F , the Fermi energy 4 . Accordingly, there is no dimensional crossover with increasing T, and by inference, no FL-TLL crossover at elevated temperatures -the crossover to non-metallic behaviour in the interchain resistivity being simply due to the emergence of a second, incoherent hopping process which shorts out the small, but nonetheless metallic component 4 . In order to address this outstanding issue experimentally, it is necessary to identify both a material whose anisotropic resistivity exhibits behaviour consistent with predictions for a thermally-induced dimensional crossover and a physical property that shows marked differences in the putative TLL and FL regimes. According to both theory and experiment, the Wiedemann-Franz (WF) law is a viable litmus test of TLL physics in the bulk. The WF law states that the ratio of the thermal k to the e...

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