I'm trying to plot two branches of the complex multi-valued function: (In [a previous post][1], Mathematica finds the branch cut of the following function between -1 and 0)

$1-z\ln[(1+z)/z]$.

So, for the real parts of the two sheets, I have:

    Plot3D[{Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y])], 
    Re[1 - (x + I y) (Log[1 + x + I y] - Log[x + I y] - 
    I 2 Pi)]}, {x, -2, 2}, {y, -3, 3}, BoxRatios -> {1, 1, 1.5}, 
    PlotRange -> All, PlotPoints -> 50, Mesh -> 30, 
    MeshFunctions -> {Im[Log[#1 + I #2]] &, Re[Log[#1 + I #2]] &}, 
    ImageSize -> Large, ColorFunction -> mycolor]

which as expected the two sheets are connected through the branch cut between -1 and 0 on the x-axis:

[![enter image description here][2]][2]


However, the pictures shows another branch cut between -2 and -1. How come?


  [1]: https://mathematica.stackexchange.com/questions/203899/to-plot-branch-cut-of-logarithm
  [2]: https://i.sstatic.net/qCsYe.jpg