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PHYSICAL SCIENCES / PHYSICS
Branch-cut singularities in thermodynamics of Fermi liquid systems
Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
Communicated by Elihu Abrahams, Rutgers, The State University of New Jersey, Piscataway, NJ, August 21, 2006 (received for review June 10, 2006)
The recently measured spin susceptibility of the two-dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. In this article, we show that the observed temperature behavior is inherent to ballistic two-dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate nonanalyticities in the thermodynamic potential that reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a nonperturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can effectively be described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and in magnitude.
2D electron gas | electron–electron interaction | nonperturbative phenomena | spin susceptibility
The authors declare no conflict of interest.
We work with the dimensionless static amplitudes known in Fermi liquid theory (13) as 
, whereas the propagation of a p–h pair is described by the dynamic correlation function S(
) = 
/( + 
– qvF cos ); see Eq. 7 in Supporting Text. Repulsion corresponds to > 0, and Pomeranchuk's instability is at 
.
An alternative calculation without referring to the complex q plane is presented in Supporting Text.
We are not aware of a similar discussion of the thermal expansion coefficient (as well as elastic constants) at low temperatures. In the context of the spin susceptibility, the question has been raised by Misawa (17) who guessed (incorrectly) a nonanalytic form of the thermodynamic potential.
¶ In fact, an arbitrary number of rescattering sections appears in the Cooper channel after such twisting, but only two of them are used here for the extraction of the anomalous in temperature terms. The role of all other sections is to renormalize logarithmically the e–e interaction amplitudes in the Cooper channel. In the text, we refer the term "section" in the Cooper channel only to those of them that generate linear in T terms; this allows us to speak simultaneously about two sections and the renormalized e–e amplitudes without confusion.
|| A calculation with the use of angular harmonics has been performed in ref. 11 for the anomalous terms in the specific heat; it also leads to the backward-scattering amplitude (
).
*To whom correspondence should be addressed. E-mail: arcadi.shehter{at}weizmann.ac.il
© 2006 by The National Academy of Sciences of the USA
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