"why I have this discontinuity when I plot the following function by using the MATLAB?"
Because that's how the function behaves
%Function
f_k = @(z) (-0.1540 + 0.2600i)+ ( 0.4347 + 0.0914i)*z+( 0.7756 - 0.4566i)*z.^2;
%Phase of the function
fphase = @(z) angle(f_k(z));
vec = linspace(-6,6,200);
[X,Y] = meshgrid(vec);
Z = X+i*Y;
surf(X,Y,fphase(Z))
view(2)
