I think you've got your terminology crossed here (but it's not your fault - your sources don't seem to clear on it either).
A hang glider is by definition a solar vehicle: They're non-motorized, and the pilot keeps them aloft by seeking thermal lift (created by the sun shining on the ground and heating it up) or ridge lift (created by wind striking the side of a mountain/hill (ridge) and being deflected up.
Both of these rely on the sun (either directly heating the local ground, or unevenly heating various parts of the Earth's surface, ultimately creating wind).
What you're referring to would be a solar-powered ultralight aircraft -- basically a hang glider with a motor strapped to it, or possibly an electric powered paraglider.
One could conceivably create a solar-powered ultralight using flexible solar cells on the wing -
in fact a little Googling reveals that it has apparently been done with an electric paramotor (a type of powered parachute) (A little more Googling reveals this wasn't as cool as I previously thought - they seem to have been using a support vehicle to recharge their battery packs (with solar cells).
As far as I'm aware no such vehicle is commercially available at this time (May 2014), but the materials and technology to construct such a vehicle are certainly available (the folks over at the Experimental Aircraft Association could probably provide guidance on building something like this), and it wouldn't surprise me if commercial or kit-build solar ultralights become available at some point in the future.
I don't believe it can be done. The area of a tandem wing isn't large enough. With solar power at 1kW per square meter that will be 15 horse power but the conversion efficiency is not 100%. It is more like 20% so you are looking at 3 horse power. A typical trike needs a minimum of a 25 horse power motor. For example the electric Icaro uses a 10kW motor and it's not even Tandem. The wing area would only be enough to provide 20% of the needed power.
Solar power on Earth peaks at somewhere between 400W and 1.3kW per square metre, in theory, at midday.
In practice, we can typically expect more like 40-70% of this to be available due to inefficiencies in the solar panels and the fact the wing wouldn't be pointing directly at the sun. This is discounting clouds, and only at midday. At any other time, the amount available is lower.
Taking the best case scenario (1.3kW at midday at the equator, 70% available) then we still only have ~910 watts, or a little over 1.2 horsepower, per m^2
Let's take a typical hang glider: a Wills Wing Alpha 210 has 19 square metres of wing area. That would give 17 kW, or 22.5 BHP. In theory, that's more than enough to get a microlight into the air, if you can keep the weight of the battery, motor, and solar panels down.
In practice, though, are you really going to be flying at the equator, with your wings perfectly level, at midday?
And more importantly, are you really going to get a 17kW motor, 20 m^2 of solar panels, wires, and a battery (pretty much required) into the weight of a hang glider that weighs, itself, less than a typical person?
It's theoretically possible to make some kind of small ultralight type aircraft solar powered, but probably not until we find a way to make lighter motors and lighter solar panels that can take advantage of the wing area without causing weight/stability issues
If you only need a few minutes prop power to gain altitude and have flexible lightweight panels on top charging the batteries for several hours then you could theoretically travel anywhere without an aerotow or hill thermal to get you up each time. The others replying here seem to be assuming continuous power capable of supporting the engine at full revs is necessary when actually you only require a few minutes to reach enough altitude. Then you can catch thermals and only fall back on the motor if you lose too much height.
These small motors taken from model aircraft give 10 minutes of thrust but can be used intermittently for hours. Combined weight of 4.4kg I think including the batteries. That is without adding a 1.8kg flexible 100 watt panel.