Cyclotron Resonance

The physics of cyclotron resonance (CR) and angle-dependent magneto-resistance oscillations (AMRO - See DC Transport) in low-dimensional metals is the same [1]. Application of a magnetic field gives rise to a Lorentz force that drives quasiparticles (correlated electrons) across the Fermi surface (FS) at a constant rate of change of momentum, resulting in periodic oscillations of their velocities as they traverse the warped FS. The resulting ‘cyclotron’ frequency, ω_c, may be related directly to the underlying band structure and, in particular, to the effective mass, m*, or the Fermi velocity, v_F. In fact, the motion need not be cyclical—merely periodic. Hence, this effect is sometimes termed periodic orbit resonance (POR [2]). In the Boltzmann picture, an oscillatory velocity leads to a modification of the Drude conductivity formula, i.e., σ(ω,B) = σ_o[1 + i(ω − ω_c)τ]⁻¹, where τ is the transport scattering time and σ_o is the zero-field DC conductivity. The key point is that ω and ω_c play identical roles, hence the correspondence between AMRO, POR and the Drude optical conductivity [1]. Thus, it becomes clear that narrow-band POR measurements performed at fixed microwave frequency, (ω, whilst sweeping the ‘cyclotron’ frequency, (ω_c (i.e., the field), may be compared directly with zero-field (ω_c = 0) broadband optical studies in which (ω is swept. An example of such a measurement is displayed in the figure above. This technique may be applied to a vast array of low-dimensional conductors, provided they are reasonably clean, i.e., ω_c τ > 1.

The CR/POR technique is extremely powerful. For example, angle-dependent studies provide extremely precise information concerning FS topology [3-6]. In fact, the POR harmonic content is directly related to the Fourier spectrum of the FS warping (through tight-binding matrix elements) [1]. Knowledge of this harmonic content is crucial for understanding FS instabilities, which ultimately may be responsible for the pairing that gives rise to the superconductivity in many low-dimensional metals. Angle-dependent studies also provide momentum-resolved measurements of m* and τ [4]. In this way, one may study if and how correlations develop locally on the FS. We note also that m* and τ are obtained completely independently: m* (= eB/ω) from the resonance field, and τ from the resonance linewidth [7].