Homes's law
Encyclopedia
In superconductivity
, Homes's law is an empirical relation that states that a superconductor's
critical temperature (Tc) is proportional
to the strength of the superconducting state for temperatures well below Tc close to zero temperature (also referred to as the fully formed superfluid density,
) multiplied by the electrical resistivity 
measured just above the critical temperature. In cuprate high-temperature superconductors the relation follows the form
,
or alternatively
.
Many novel superconductors are anisotropic, so the resistivity and the superfluid density are
tensor quantities; the superscript
denotes the crystallographic direction
along which these quantities are measured.
Note that this expression assumes that the conductivity and temperature have both been recast in units
of cm−1 (or s−1), and that the superfluid density has units of cm−2
(or s−2); the constant is dimensionless. The expected form for a BCS dirty-limit superconductor
has slightly larger numerical constant of ~8.1.
The law is named for physicist
Christopher Homes and was first presented in the July 29, 2004 edition of Nature
, and was the subject of a News and Views article by Jan Zaanen in the same issue in which he speculated that the high transition temperatures observed in the
cuprate superconductors are because the metallic states in these materials are as viscous as
permitted by the laws of quantum physics. A more detailed version of this scaling relation subsequently appeared in
Physical Review B in 2005.
Francis Pratt and Stephen Blundell
have argued that Homes's law is violated in the organic superconductor
s. This work was first presented in Physical Review Letters
in March 2005.
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
, Homes's law is an empirical relation that states that a superconductor's
critical temperature (Tc) is proportional
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
to the strength of the superconducting state for temperatures well below Tc close to zero temperature (also referred to as the fully formed superfluid density,
) multiplied by the electrical resistivity measured just above the critical temperature. In cuprate high-temperature superconductors the relation follows the form ,or alternatively
.Many novel superconductors are anisotropic, so the resistivity and the superfluid density are
tensor quantities; the superscript
denotes the crystallographic directionalong which these quantities are measured.
Note that this expression assumes that the conductivity and temperature have both been recast in units
of cm−1 (or s−1), and that the superfluid density has units of cm−2
(or s−2); the constant is dimensionless. The expected form for a BCS dirty-limit superconductor
has slightly larger numerical constant of ~8.1.
The law is named for physicist
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
Christopher Homes and was first presented in the July 29, 2004 edition of Nature
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
, and was the subject of a News and Views article by Jan Zaanen in the same issue in which he speculated that the high transition temperatures observed in the
cuprate superconductors are because the metallic states in these materials are as viscous as
permitted by the laws of quantum physics. A more detailed version of this scaling relation subsequently appeared in
Physical Review B in 2005.
Francis Pratt and Stephen Blundell
Stephen Blundell
Stephen Blundell is a Professor of Physics at the University of Oxford. He is the current head of Condensed Matter Physics at Oxford and is also a Professorial Fellow of Mansfield College, Oxford...
have argued that Homes's law is violated in the organic superconductor
Organic superconductor
In physical chemistry and condensed matter physics, an organic superconductor is an organic compound which exhibits superconductivity at low temperatures...
s. This work was first presented in Physical Review Letters
Physical Review Letters
Physical Review Letters , established in 1958, is a peer reviewed, scientific journal that is published 52 times per year by the American Physical Society...
in March 2005.