Lots of (very) new building materials being researched at MIT/Mediated Matter Group by Neri Oxman. As it's work out of the Media Lab, it's all mostly art installations/theoretical research, but these have some potential implications in Architecture moving forward.
3D Printed Glass
While glass isn't new, it is really hard to 3D print glass. The potential implications, with more research, are large in architecture/building applications.
Robotically fabricated chitosan, cellulose, pectin, and water
Naturally-occurring materials constructed in a new manner, could lead to new levels of sustainable buildings.
What the extent of these implications in architecture and the building/construction sector remain to be seen, but they are, at the very least, advancing sustainability and design to an extent, and raising questions pertaining to what we construct our buildings from. Not sure what's next for Mediated Matter Group, considering I believe Oxman moved to NYC permanently to set up a studio(?), but her students seemed to be thoroughly invested in continuing work in these realms.
Digital Structures, also out of MIT, is in the more applied/real-world realm of materials and structures. They have a lot of research on the feasibility and physics behind sustainable materials and building methods, mostly timber, but some low-carbon structure work too. They also have some work on robotic fabrication and construction, a rising field of interest in academia and at least part of the design and construction industry.
Steel and concrete are big targets for decreasing emissions in the building sector. Both account for 7-8% of global emissions each.
Boston Metal in Woburn, born out of MIT, backed by Bill Gates and a few other VC's, is working to decarbonize steel and eventually produce emission-free steel using Molten Oxide Electrolysis. They are looking to have a plant up and running in the next 4-5 years.
In concrete, there isn't much promising research to truly decrease emissions, apart from Solida Technologies out of NJ, which is changing the chemical processes involved in producing and curing concrete by using CO2. They promise it is higher performing, cures in 24 hours, and costs less, along with decreasing emissions substantially. I'm a bit weary, however, as they don't present any true/hard numbers on the strength they are getting with their mixes, one of the first things an engineer will ask about your mix.