Quantum oscillations such as the de Haas - van Alphen and Shubnikov - de Haas oscillations are generally viewed as a distinct signature of a well-defined Fermi surface. These oscillations have proven to be a powerful probe of the electronic properties of metals: in elemental metals they have provided information about the geometry of the Fermi surface, effective masses, and scattering times. This information is extracted by making use of the expressions of Lifshitz and Kosevich (LK) for the dependence of the amplitude of the oscillations on the temperature and magnetic field. They derived their results for non-interacting electrons in three dimensions, but have since been extended to two dimensions and quasi-two dimensions. Kartsovnik has given a nice review of how magnetic oscillations have also provided significant information about layered organic metals. Most experiments are consistent with the LK form, but there are exceptions, e.g., in α-(BEDT-TTF)2NH4Hg(SCN)4 and β″-(BEDT-TTF)2SF5CH2CF2SO3.
The effect of many-body effects on the LK form has been considered and reviewed by Wasserman and Springford. But what happens in a non-Fermi liquid has been an open question. Long ago Pelzer considered the case of a marginal Fermi liquid. [We were postdocs with John Wilkins together]. Unfortunately, his paper is rarely referenced (e.g., in the paper below).
Given all of the above I was very interested to see a recent paper Generalized Lifshitz-Kosevich scaling at quantum criticality from the holographic correspondence. One of their many results is that the amplitude of the oscillations can be a non-monotonic function of temperature, as is observed in β″-(BEDT-TTF)2SF5CH2CF2SO3. Before I read this paper I was rather skeptical about attempts of some string theorists to obtain results of relevance and use to condensed matter physics, but this paper certainly has some very concrete results which can be compared to experimental results. It is certainly worth digesting.
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