documentclass{standalone}
usepackage{pgfplots}
begin{document}
begin{tikzpicture}
  begin{axis}[
  axis x line=bottom,
  axis y line=left,
  ultra thick,
  y coord trafo/.code={pgfmathparse{sqrt(#1)}},
  y coord inv trafo/.code={pgfmathparse{pow(#1,2)}}
  ]
    addplot coordinates {
    (0,0)
    (0.3,0)
    (0.44,0.00016)
    (0.45,0.00045)
    (0.49,0.00071)
    (0.5,0.001)
    (0.51,0.00139)
    (0.54,0.00176)
    (0.56,0.00214)
    (0.57,0.00243)
    (0.61,0.00279)
    (0.63,0.00327)
    (0.64,0.00386)
    (0.67,0.00433)
        };
        end{axis}
        end{tikzpicture}
        end{document}

documentclass{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.14}
begin{document}
    begin{tikzpicture}
      begin{axis}[
          axis lines=middle,
          ultra thick,
          xlabel= $V$, ylabel=$I$,
          x label style={at={(current axis.right of origin)}, anchor=west},
%         y coord trafo/.code={pgfmathparse{sqrt(#1)}},
%         y coord inv trafo/.code={pgfmathparse{pow(#1,2)}},
          ]
            addplot coordinates {
            (-0.48, -0.002)
            (-0.43, -0.0002)
            (-0.3, -0.0001)
            (0,0)
            (0.3,0)
            (0.44,0.00016)
            (0.45,0.00045)
            (0.49,0.00071)
            (0.5,0.001)
            (0.51,0.00139)
            (0.54,0.00176)
            (0.56,0.00214)
            (0.57,0.00243)
            (0.61,0.00279)
            (0.63,0.00327)
            (0.64,0.00386)
            (0.67,0.00433)
             };
         draw[red, dashed] (axis cs:0.6, 0)--(axis cs:0.6, 0.004);
        end{axis}
    end{tikzpicture}
end{document}