Recently I am investigating the energy dispersions of magnetoplasmon and I found two "different" energy dispersions in two references [1,2]. I would like to know the difference between them and also whether I understand them correctly.
According to refs. 1 and 2, we can derive the energy dispersion of magnetoplasmon by writing down the Drude conductivity tensor and permitivity tensor.
Under perpendicular B-field along Z-axis, the Drude permitivity tensor in vacuum reads as
$\varepsilon = \begin{bmatrix} \varepsilon_{xx} & \varepsilon_{xy} & 0 \\ \varepsilon_{yx} & \varepsilon_{yy} & 0 \\ 0 & 0 & \varepsilon_{zz} \\ \end{bmatrix}$,
where $\varepsilon_{xx} = \varepsilon_{yy} = 1 - \frac{\omega_{p}^2}{\omega} \frac{v-i\omega}{(v-i\omega)^2+\omega_c^2}$, $\varepsilon_{xy} = -\varepsilon_{yx} = \frac{\omega_{p}^2}{\omega} \frac{\omega_c}{(v-i\omega)^2+\omega_c^2}$. Here $\omega_{p}$ is the plasmon frequency, $v$ is the scattering frequency (the inverse of scatter time) and $\omega_{c} = \frac{eB}{m}$ is the cyclotron frequency.
With these expression, if we consider some linearly polarized E-fields along X-axis, we can let $\varepsilon_{xx}=0$ and assume $v \simeq 0$, and derive the first energy dispersion of magnetoplasmon:
- $\omega = \sqrt[]{\omega_p^2+\omega_c^2}$
This dispersion has been used in some references, for example [3].
On the other hand, if we consider some circular polarized E-fields, we can let $\varepsilon_{xx} \pm i\varepsilon_{xy}=0$. In this case, I obtain the second energy dispersion, which has two branches:
- $\omega_{\pm} = \sqrt[]{\omega_p^2+\omega_c^2/4}\pm\omega_c/2$
The second dispersion has also been observed in several references, for instance [4].
Here are my questions:
- Since we have two different magnetoplasmon dispersions, does it mean that different polarizations excite different kinds of magnetoplasmon?
- For linear polarization, we can decompose it into the sum of two opposite circular polarized modes. Then can we excite the "circular" magnetoplasmon with linear polarization?
- Is there any relationship between the edge magnetoplasmon (which has a dispersion that decreases with B-field as 1/B) and the minus branch in the second dispersion $\omega_{-}$?
Thank you very much!
Jing
References:
[1] PLASMONS IN INVERSION LAYERS, by Thomas N. THEIS, page 520
[2] Infrared and microwave magnetoplasma effects in semiconductors, by E D Palik and J K Furdyna, page 1209
[3] Gate and magnetic field tunable ultrastrong coupling between a magnetoplasmon and the optical mode of an LC cavity, by Gian L. Paravicini-Bagliani*, Giacomo Scalari†, Federico Valmorra, Janine Keller, Curdin Maissen, Mattias Beck, and Jérôme Faist
[4] Dimensional resonance of the two-dimensional electron gas in selectively doped GaAs/A1GaAs heterostructures, by S. J. Allen, Jr., H. L. Störmer, and J. C. M. Hwang*
