On Pendry's effective electron mass

TL;DR

This paper examines Pendry's concept of effective electron mass in metal wire mesh structures, analyzing its applicability and limitations, and establishing its analogy with solid-state effective mass.

Contribution

It clarifies the properties and physical interpretation of Pendry's effective mass and demonstrates its limited applicability beyond dielectric response problems.

Findings

Effective mass $m_{eff}$ has specific properties derived from its definition.

An analogy between $m_{eff}$ and solid-state $m^{*}$ is established.

Using $m_{eff}$ outside dielectric response contexts can lead to incorrect results.

Abstract

In 1996, J. Pendry, an English theoretical physicist put forward an idea about the dependence of the effective electron mass on the magnetic field, while interpreting the dielectric response of metal wire mesh structures. The idea was based on the well-known relation between the kinematic and canonical momenta of a charged particle moving in the magnetic field. In this paper, proceeding from the universal character of that relation, the applicability of Pendry's effective electron mass $m_{\text{eff}}$ to the problem of electrons in metal mesh structures, as well as to a wide class of problems for charges moving in the magnetic field, has been examined. The general properties of $m_{\text{eff}}$ following directly from its definition were found, and an analogy between the effective electron mass $m_{\text{eff}}$ and $m^{\ast}$ known in the solid-state theory was established. A physical interpretation of $m_{\text{eff}}$ was proposed. It was demonstrated in several examples that, despite the generality of the defining relation for the effective mass $m_{\text{eff}}$, the use of $m_{\text{eff}}$ beyond the problem of the dielectric response of metal wire mesh structures leads to incorrect results.