I am trying to use gnuplot to plot the graphene band structure as both surfaces and a countour plot at the base, set with set contour base, but I can't get rid of some axis lines and the plane where the contour is drawn is too far away from the surfaces when I place them in the adequate viewing angle.
Here is the code to plot the graph
# Setting ranges and function parameters
set xrange [-.55:.55]
set yrange [-1:1]
t=-3.033 s=0.129 a=1.43 * sqrt(3)
# Auxiliary functions
kx(x,y) = (2*pi/a) * (cos(pi/6)*x + sin(pi/6)*y) ky(x,y) = (2*pi/a) * (cos(pi/6)*x - sin(pi/6)*y)
w(x,y) = sqrt(1+4*cos(0.5*sqrt(3)*kx(x,y)*a)*cos(0.5*a*ky(x,y)) + 4*(cos(0.5*ky(x,y)*a))**2)
#functions to be plotted
e(x,y) = (t*w(x,y))/(1+s*w(x,y))
e_estrela(x,y) = (-t*w(x,y))/(1-s*w(x,y))
# Setting up 3D plot appearance
set hidden3d
set contour base set cntrparam levels discrete 0,0.5,1,2,4,8
set view 75, 31, 0.601098, 1.4385
set isosamples 60
# Removing unwanted stuff
unset xtics
unset ytics
unset ztics
unset key
splot e_estrela(x,y), e(x,y)
And the output I get (with the pngcairo terminal, but that's not relevant, I guess) is:

Is it possible to draw the contour base plane closer to the surfaces? And how about removing those vertical black lines?
For the first part, I tried playing wioth set zrange with no success. The base plane seems to be drawn a certain z-distance below the lowest z-range limit everytime.
Ideas? Thanks in advance!