Cyclotron Resonance

Abstract

Cyclotron resonance (CR) is a method for measuring the effective masses of charge carriers in solids. It is by far the most direct and accurate method for providing such information. In the simplest description, the principle of the method can be stated as follows. A particle of effective mass and charge in a DC magnetic field executes a helical motion around with the cyclotron frequency . If, at the same time, an AC electric field of frequency is applied to the system, perpendicular to , the particle will resonantly absorb energy from the AC field. Since and/or ω can be continuously swept through the resonance and known to a very high degree of accuracy, can be directly determined with high accuracy by . As a secondary purpose, one can also use CR to study carrier scattering phenomena in solids by examining the scattering lifetime τ (the time between collisions, also known as the collision time or the transport/momentum relaxation time), which can be found from the linewidth of CR peaks. Although this article is mainly concerned with the simplest case of free carrier CR in bulk semiconductors, one can also study a wide variety of FIR magneto‐optical phenomena with essentially the same techniques as CR. These phenomena (“derivatives” of CR) include: (a) spin‐flip resonances, (b) resonances of bound carriers, (c) polaronic coupling, and (d) 1‐D and 2‐D magneto‐plasmon excitations. It is important to note that all the early CR studies were carried out on semiconductors, not on metals. Many techniques can provide information on effective masses, but none can rival CR for directness and accuracy. Effective masses can be estimated from the temperature dependence of the amplitude of the galvanomagnetic effects. The basic theory and experimental methods of cyclotron resonance are presented in this article. Basic theoretical background is presented. A detailed description is given of the actual experimentation procedures. Finally, typical data analysis procedures are presented.

Application of Berry's phase to the effective mass of Bloch electrons

“…By changing ω, an experimenter can find ω c and hence determine m * through equation ( 6). In practice, such experiments are performed by placing a sample in a magnetic field and then exposing the sample to either microwave or far-infrared radiation [19]; at the cyclotron resonance frequency ω c there will be a peak in the radiation absorption spectrum. At this point, the cyclotron effective mass m * can be linked with the inverse effective mass tensor as given by equation (12.29) of [6].…”

“…p 239 of [6]). The magnetic field is assumed to be in the z-direction, and M −1 is assumed to have a matrix inverse M. Since cyclotron resonance experiments yield m * , which purportedly give the components of M −1 , such experiments can be used to determine the curvature of band energy surfaces ε(k) [19].…”

“…Specifically, we find that the BP necessitates changes to the traditional definitions of the inverse effective mass tensor M −1 and the cyclotron effective mass m * . It is through a relation between these two quantities (M −1 and m * ), and through analysis of de Haas-van Alphen frequency spectra, that band energy surfaces are often mapped [19,20]. Since any crystal that lacks inversion symmetry or time-reversal symmetry can be expected to have a non-zero Berry curvature [3], one can expect the geometric phase to be important in the cyclotron resonance of such systems.…”

Infrared Spectroscopy of Tunable Dirac Terahertz Magneto-Plasmons in Graphene

“…Graphene is emerging as a very promising plasmonic material − due to its carrier density tunability and high carrier mobility. Recent optical experiments have revealed the great prospects of plasmons in graphene for photonic device applications in the infrared (IR) and terahertz frequency ranges. − Theoretical studies have predicted many new phenomena and applications in photonics, transformation optics, and quantum optics due to the unique properties of Dirac plasmons. − Moreover, plasmons are important for understanding the many-body physics of graphene. , Unlike plasmons in metals, the plasmons in graphene are expected to be strongly affected by an external magnetic field due to a comparable cyclotron frequency − and plasmon frequency. Therefore, it is of great fundamental and practical interest to explore the response of plasmons in graphene to a magnetic field.…”