documentclass[border=5mm]{standalone}
usepackage{pgfplots}
usepackage{tikz}
pgfdeclarefunctionalshading{sphere}{pgfpoint{-25bp}{-25bp}}{pgfpoint{25bp}{25bp}}{}{
%% calculate unit coordinates
25 div exch
25 div exch
%% copy stack
2 copy
%% compute -z^2 of the current position
dup mul exch
dup mul add
1.0 sub
%% and the -z^2 of the light source
0.3 dup mul
-0.5 dup mul add
1.0 sub
%% now their sqrt product
mul abs sqrt
%% and the sum product of the rest
exch 0.3 mul add
exch -0.5 mul add
%% max(dotprod,0)
dup abs add 2.0 div
%% matte-ify
0.6 mul 0.4 add
%% currently there is just one number in the stack.
%% we need three corresponding to the RGB values
dup
0.4
}
begin{document}
      begin{tikzpicture}
          begin{axis}[  axis lines=center, axis on top = false,
    view={140}{25},axis equal,title={The Mexican hat potential},
          colormap={blackwhite}{gray(0cm)=(1); gray(1cm)=(0)},
            samples=50,
            domain=0:360,
            y domain=0:1.25,
            zmin=0,
        xmax=1.5,
        ymax=1.5,
        zmax=1.5,
        x label style={at={(axis description cs:0.10,0.25)},anchor=north},
        y label style={at={(axis description cs:0.9,0.2)},anchor=north},
        z label style={at={(axis description cs:0.5,0.9)},anchor=north},
        xlabel = $mathrm{Re}(phi)$,
        ylabel=$mathrm{Im}(phi)$,
        zlabel=$V(phi)$,
        yticklabels={,,},
        xticklabels={,,},
        zticklabels={,,}
        ]
        addplot3 [surf, shader=flat, draw=black, fill=white, z buffer=sort] ({sin(x)*y}, {cos(x)*y}, {(y^2-1)^2});
        end{axis}
        shade[shading=sphere] (3.47,3.5) circle [radius=0.15cm];
        shade[shading=sphere] (5.2,2.2) circle [radius=0.15cm];
        node[anchor=east] at (4.05,3.71) (text) {A};
  node[anchor=west] at (5.5,3.0) (description) {B};
  draw (description) edge[out=180,in=0,<-] (text);
    end{tikzpicture}
end{document}