Key to Sony's next-gen batteries are sulfur-based electrodes. Lithium-sulfur cells are well known to have better capacities, but the sulfur degrades so rapidly in this environment that commercial, rechargeable batteries of this kind have been out of the question. Presumably, Sony's solved or is close to solving this issue. More interesting, though, is that the company is also developing magnesium-sulfur batteries, removing lithium from the equation altogether. Magnesium is the significantly more abundant element, making for cheaper batteries that also last longer. They should be safer, too, since lithium-based batteries degenerate over time to the point of becoming a fire risk.
All next-gen battery promises seem to come with a long wait attached, and Sony's are no different. The company is aiming to make its sulfur-based batteries available in 2020, with smartphones being the first to benefit before other types of devices. It's likely, then, that we're gonna have to wait until the Xperia Z10 before that 40 percent battery life improvement comes true (if at all).