FFT showing peaks at 0Hz?
[EDITED FROM DISCUSSION]

On the first order, your data looks like a decay with a positive origin on a small-valued range $[0.7 \; 0.49]\times 10^{-7}$, and very tiny fluctuations with respect to the area under the curve.

So from afar, your data is much closer to an almost constant function than to some putative oscillations. So the the zero, or DC-component, is important. Indeed, the amplitude of your maximum FFT is around $5.9 \times 10^{-7}$, which happens to match the average value of your data, if I use the trapezoidal approximation $(0.7+0.49)/2= 0.595$ (I hope your FFT is normalized). 

For second order observations, you can try to remove the exponential-looking decay trend (by an exponential fit, or a low-degree polynomial, of 2nd or 3rd order for instance). With the sufficiently dense number of points, you can also try again on the derivative (taking care of end-points) or second derivative, to see if periodic phenomena  appear. But this is likely to amplify noise.

At the third order, on the index interval $[0,\,2000]$, I see a kind of dropout around an order of magnitude of $0.05 \times 10^{-7}$. Once you remove the trend, this could appear like a single step down, which may cause a low-frequency effect in your signal.