Reply to "Comment on 'Origin of combination frequencies in quantum magnetic oscillations of two-dimensional multiband metals' " by A.S. Alexandrov and A.M. Bratkovsky [cond-mat/0207173]

TL;DR

This paper critically examines a previous comment on a theory of quantum oscillations in multiband metals, clarifying the correct mathematical conditions and limits of the analytical approach.

Contribution

It corrects a mathematical inconsistency in the previous comment, clarifying the valid conditions for the analytical theory of combination frequencies.

Findings

The original claim about chemical potential oscillations is contradicted.

The correct mathematical condition for the expansion is identified.

Limits of validity of the analytical theory are clarified.

Abstract

In their comment on the paper (Phys. Rev. B 65, 153403 (2002); cond-mat/0110154), Alexandrov and Bratkovsky (cond-mat/0207173) argue that they correctly took into account the chemical potential oscillations in their analytical theory of combination frequencies in multiband low-dimensional metals by expanding the free energy in powers of the chemical potential oscillations. In this reply, we show that this claim contradicts their original paper (Phys. Rev. B 63, 033105 (2001)). We demonstrate that the condition given for the expansion is mathematically incorrect. The correct condition allows to understand the limits of validity of the analytical theory.