Kadowaki Woods Ratio
Encyclopedia
The Kadowaki–Woods ratio is the ratio of A, the quadratic term of the resistivity
and γ2, the linear term of the specific heat. This ratio is found to be a constant for transition metal
s, and for heavy-fermion
compounds, although at different values.
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/γ2 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/γ2 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/γ2 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/γ2 are only expected within a particular group.
In 2005 Hussey proposed a re-scaling of A/γ2 to account for unit cell volume, dimensionality, carrier density and multi-band effects. In 2009 Jacko, Fjaerestad, and Powell demonstrated fdx(n)A/γ2 to have the same value in transition metals, heavy fermions, organics and oxides with A varying over 10 orders of magnitude, where fdx(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.
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
and γ2, the linear term of the specific heat. This ratio is found to be a constant for transition metal
Transition metal
The term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...
s, and for heavy-fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
compounds, although at different values.
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/γ2 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/γ2 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/γ2 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/γ2 are only expected within a particular group.
In 2005 Hussey proposed a re-scaling of A/γ2 to account for unit cell volume, dimensionality, carrier density and multi-band effects. In 2009 Jacko, Fjaerestad, and Powell demonstrated fdx(n)A/γ2 to have the same value in transition metals, heavy fermions, organics and oxides with A varying over 10 orders of magnitude, where fdx(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.