Solve a system of complex equations and plot the solution

I’m trying to solve a system of 2 equations with an unknown real parameter k0, the solution is complex. then I want to plot the obtained solution function of k0: here is my code: (I here is the complex number). Please I need your help

nm = 10^-9;
a = 10 nm;
d1 = 21 nm;
[Omega]p = 17.2 10^15;
[Gamma] = 0.0835 10^15;
c = 3 10^8;
[Epsilon]0 = 2.25;
[Alpha]1 = (5.45 - 0.73 [Omega]p^2/((c k0)^2 + I c k0 [Gamma]) - [Epsilon]0)/(5.45 - 0.73 [Omega]p^2/((k0)^2 + I c k0 [Gamma]) + 2 [Epsilon]0)a^3;
[Alpha] = (k0^2 [Alpha]1)/(6 [Pi] [Epsilon]0);
d = k0 d1;
 L = 3 d^-3 (PolyLog[3, E^(I ([Beta] - 1) d)] + PolyLog[3, E^(-I ([Beta] - 1) d)] - I d (PolyLog[2, E^(I ([Beta]- 1) d)] + PolyLog[2, E^(-I ([Beta] - 1) d)])) - [Alpha]^-1 == 0;

T = -((3 d^-3)/2) (PolyLog[3, E^(I ([Beta] - 1) d)] + PolyLog[3, E^(-I ([Beta] - 1) d)] - 
   I d (PolyLog[2, E^(I ([Beta] - 1) d)] + PolyLog[2, E^(-I ([Beta] - 1) d)]) - d^2 (PolyLog[1, E^(I ([Beta] - 1) d)] + PolyLog[1, E^(-I ([Beta] - 1) d)])) - [Alpha]^-1 == 0;
 Plot[Re[Solve[T&&L,[Beta]]], {k0, 300, 700}]
 Plot[Im[Solve[T&&L,[Beta]]], {k0, 300, 700}]