The Kadowaki–Woods ratio is the ratio of ''A'', the quadratic term of the resistivity and ''γ''², the linear term of the

specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...

. This ratio is found to be a constant for

transition metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...

s, and for heavy-

fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...

compounds, although at different values. :

R_\mathrm = \frac

In 1968 M. J. Rice pointed out that the coefficient ''A'' should vary predominantly as the square of the linear electronic specific heat coefficient γ; in particular he showed that the ratio ''A/γ''² is material independent for the pure 3d, 4d and 5d transition metals. Heavy-fermion compounds are characterized by very large values of A and γ. Kadowaki and Woods showed that ''A/γ''² is material-independent within the heavy-fermion compounds, and that it is about 25 times larger than in aforementioned transition metals. According to the theory of electron-electron scattering the ratio ''A/γ''² contains indeed several non-universal factors, including the square of the strength of the effective electron-electron interaction. Since in general the interactions differ in nature from one group of materials to another, the same values of ''A/γ''² are only expected within a particular group. In 2005 Hussey proposed a re-scaling of ''A/γ''² to account for unit cell volume, dimensionality, carrier density and multi-band effects. In 2009 Jacko, Fjaerestad, and Powell demonstrated ''f''_dx''(n)A/γ''² to have the same value in transition metals, heavy fermions, organics and oxides with ''A'' varying over 10 orders of magnitude, where ''f''_dx''(n)'' may be written in terms of the dimensionality of the system, the electron density and, in layered systems, the interlayer spacing or the interlayer hopping integral.

References

Correlated electrons Condensed matter physics Fermions {{CMP-stub

See also

References