de Haas-van Alphen Effect and the Specific Heat of an Electron Gas

Abstract

A model electron gas is studied in order to provide a microscopic justification of the Shoenberg conjecture that the harmonic content of the de Haas-van Alpen oscillations of the magnetization M can properly be explained by replacing the applied field H in the elementary expression for M(H) by the total induction B = H + M The model contains a current-current interaction between the electrons;and it is shown that the unscreened long-range nature of this interaction leads to a term in the low-temperature specific heat proportional to T lnT. For a gas with terrestrial densities the coefficient of this anomalous term is very small and probably beyond detection.

Fermi surfaces and gauge-gravity duality

“…In particular, the d = 3 model of Gubser and Rocha [10] is a promising model for future study. The problem of a Fermi surface coupled to a gauge field appears to be under control in d = 3: the results of the self-consistent one-loop theory [75][76][77] are expected to be robust to higher order corrections [41,42]. Such a theory only gives marginal corrections to the FL results: the low T specific heat behaves as T log T .…”

Singular or non-Fermi liquids

“…while for the entropy for the electrons interacting with the electromagnetic ÿeld one ÿnds from the above results [127] S N ≈ 2 2 3…”

“…Coulomb interactions will not do in this regard, since they are always screened in a metal, but transverse electromagnetic ÿelds do give rise to long-range interactions. The fact that as a result no metal is a Fermi liquid for su ciently low temperatures was already realized long ago [127]-from a practical point of view, this mechanism is not very relevant, since the temperatures where these e ects become important are of order 10 −16 K; nevertheless, conceptually this is important since it is a simple example of a gauge theory giving rise to SFL behavior. Gauge theories on lattices have been introduced to discuss problems of fermions moving with the constraint of only zero or single occupation per site.…”

“…Almost 30 years ago, Holstein et al [127] (see also Reizer [221]) showed that the coupling of electrons to the electromagnetic ÿelds gives rise to SFL behavior. Since the typical temperatures where the e ects become important are of the order of 10 −15 K, the e ect is not important in practice.…”

Hard loops, soft loops, and high density effective field theory

“…First of all, it is well known that resummation is required in order to make the perturbative expansion in a many body system well defined [12]. It is also well known that additional problems arise in systems with unscreened transverse gauge boson interactions [13,14]. In a degenerate Fermi system the effect of the BCS or other pairing instabilities have to be taken into account.…”