How to plot a 2D triangular lattice

I wonder if I could plot the Fig1.(a) in Physical Review A 87, 063421 (2013), a triangular lattice in MMA. I undetstand that those atoms and interactions can be added by Adobe AI after obtaining the eps by MMA.

Actually I've tried by defining a piecewise function and Plot3D, but it seems to be wierd and the figure is uncontinuous at the boundaries.

Thanks a lot.

• What have you tried? Please share the code. What is the formula for the potential? Not providing necessary information won't help you here. – Henrik Schumacher Aug 15 '18 at 7:36
• arxiv.org/pdf/1305.6687.pdf – Alex Trounev Aug 15 '18 at 8:18
• The point is that I gave the reference clearly enough, and I would be able to plot if I know the potential. Thanks anyway. – 2ez4rtz Aug 15 '18 at 10:12
• In this article there is nothing about the potential. They write under the FIG.1: "Schematic diagram of the smallest triangular cell of three atoms (a, b and c) trapped in a two-dimensional triangular lattice". – Alex Trounev Aug 15 '18 at 11:57

Show[
Plot3D[
Evaluate@Sum[
-Exp[-(((x - xo + yo/2)^2 + (y - yo Sqrt[3]/2)^2)/(2/25))]
, {yo, -1, 6}
, {xo, Round[yo/2] - 1, 4 + Round[yo/2]}
]
, {x, -0.2, 3.2}
, {y, -0.5, 2.5}
, Mesh -> None
, PlotPoints -> 100
, PlotRange -> {-1, 1}
, BoxRatios -> {3.4, 3, 2}
],
Graphics3D[
{
Blue, Sphere[{1, Sqrt[3]/2 2, -1/2}, .2],
Purple, Sphere[{3/2, Sqrt[3]/2, -1/2}, .2],
Green, Sphere[{1/2, Sqrt[3]/2, -1/2}, .2]

}]
]


• I tried the Cos type, and now I now it's an exponential trap. Thanks for the nice answer. – 2ez4rtz Aug 15 '18 at 10:14