where β = K$_{B}$T with K$_{B}$ being the Boltzmann constant. Since we have Π −− and Π $^{++}$, this term leads to an extra negative term for the total intraband correlation[10, 11] Π $^{++}$+ Π −− . The interband correlation is negligible in the long wave length limit because electron spins at the same wave vector in different branches are opposite. 

We have derived the expression for ℏ ∼ ω (equation 17) under the condition ℏ ω >> | ε ± ( n, x$_{0}$ + x ′$_{0}$ ) − ε ± ( n, x$_{0}$ ) | as x ′$_{0}$ → 0 which leads to a relation between the energy and the Landau level broadening ℏ ω >> | 2 | V ± n | { sin( π $_{a$_{x}$}$x ′$_{0}$ ) sin[( 2 π $_{a$_{x}$}$)( x$_{0}$ + x ′ 0 2 )] } | . This ensures that Im Π$_{0}$(¯ q, ω ) = 0 and the intra-Landau-band magnetoplasmons are undamped. For a given | V ± n | , this can be achieved with a small but nonzero q$_{y}$ (recall that x ′$_{0}$ = − ℏ q$_{y}$ m ∗ $_{ω$_{c}$}$). In general, the inter- and intra-Landau-band modes are coupled for arbitrary magnetic field strengths. Only the intra-Landau-band mode ( ℏ ∼ ω ) will be excited in the energy regime ℏ ω$_{c}$ > ℏ ω ∼ | V ± n | . 

## IV. DISCUSSION OF RESULTS 

The intra-Landau-band plasmon energy obtained in equation (17) is shown graphically in Figs (1,2,3) as a function of 1 /B for different values of the temperature (T) and RSOI parameter : α = 0 , and α = 1 . 2 × α$_{0}$ . The parameters used in all of our figures are [13–17, 19]: α$_{0}$ = 1 × 10 − 11 eVm, m ∗ = 0 . 05 m$_{e}$ , g = 2, µ$_{B}$ = 5 . 78 × 10 − 5 eV/Tesla , k = 14 . 5, n$_{D}$ = 3 . 16 × 10 − 15 m − $^{2}$, a = 380 nm, and V$_{0}$ = 0.5 meV. We also take q$_{x}$ = 0 and q$_{y}$ = 0 . 01 k$_{F}$ , with k$_{F}$ = (2 πn$_{D}$ ) 1 / 2 being the Fermi wave number of the unmodulated 2DEG in the absence of magnetic field. Furthermore, in Fig (3) the intra-Landau-band plasma energy is shown as a function of 1 /B for RSOI strength ( α = 1 . 2 × α$_{0}$ ), temperature T=1K and all other parameters are the same as in Fig. (2). The beating of Weiss oscillations is solely due to + and - branch of the banwidth of the intra-landau band plasmon energy satisfying the condition given in Eq. (8). In Fig. (1), we show the intra-Landau band magnetoplasmon spectrum in the absence of spin-orbit interaction α = 0 at two different temperatures T=0.25 K, 3 . 0 K. The minima of Weiss oscillations in Fig. (1) satisfy the flat band condition obtained in Eq. (8) for zero Rashba coupling strength. In this figure, the SdH oscillations are washed out completely at 3K but Weiss persist and are undamped, which confirm the weak dependence of Weiss oscillations on temperature compared to SdH oscillations. To highlight the effects of RSOI, Figs.(2,3) should be compared with Fig.(1). As 

