This 2014 preprint describes a way of pushing photovoltaics to 69% efficiency:
Optical Refrigeration for Ultra-Efficient Photovoltaics
[NB: The trio of authors have produced multiple papers since, along similar lines]
The operating temperatures are high, but doable with concentrators and the right materials. That makes it very attractive for Solar Power Satellite deployment, so long as the cold end can be kept cold efficiently. The hot end is ~1200 K, while the effective temperature at Earth’s orbit is ~400 K. Thus ~81 times concentration is needed. Say we want to produce 1 GW power on the ground, so with 50% power-transfer efficiency that’s 2 GW to be produced in orbit. At ~67% efficiency we need 3 GW of raw sunlight, about 2.3 square kilometres of collector.
Sounds like a lot, but SPS studies from the 1970s assumed 13 square kilometres per gigawatt. Being a concentrator system it means low-mass reflectors are needed, focussed on the much smaller convertor systems. Thus the mass could be ~1/30-1/100th of the 1970s designs. A 1970s 5 GW SPS would’ve massed ~50,000 tonnes, A 1 GW 2014 SPS design might mass ~200 tonnes(?)
SpaceX expect to slash costs of Space Launch by 70% or more with reusable 1st Stages. Imagine the Falcon Heavy lofting 28 tonnes of SPS modules. Part of the array opens up to power an electric propulsion system, using ~3 tonnes propellant for a GEO transfer. Once in the correct orbit it opens up fully, like some field of solar flowers. Eight components are lofted, meeting up and joining together to form a Solar Power Satellite, for a Launch cost of 8 x $90 M, thus $720 M.
The SPS sends 2 GW of microwave power Earthwards, picked up by a Rectenna Farm – conducting wires on poles, with crops growing underneath. Thus colocation with another income stream. After factoring in all the losses, the system supplies 1 GW of totally carbon-free power to the grid. 24 hours a day, 7 days a week – even in bad weather and at night. No giant flow-batteries needed, no vast tanks of molten salt to store heat for night-power supply.
Sold at ~$0.26/kW.hr (retail here in Oz) that 1 GW.h/hr earns $2.28 G/yr (8,766 hours). Over a 15 year lifetime it might earn ~$34.2 G (constant value $). Thus space-launch is a small fraction of that, so if manufacturing, construction and maintenance can be kept minimal, it’ll produce a significant Return-on-Investment (RoI).
By comparison CASSIOPEIA has a specific mass of 1,000 tonnes per gigawatt. Even in that case, with 80 reusable Falcon Heavy launches required, the launch cost is ~$7.2 G – the trick being partial deployment to power the electric propulsion system. If the efficiency of conversion can hit 70%, then the specific power delivered by CASSIOPEIA goes up and the RoI improves.