Global warming can be curbed by pricing carbon emissions and thus substituting fossil fuel with renewable energy consumption. Breakthrough technologies (e.g., fusion energy) can reduce the cost of such policies. However, the chance of such a technology coming to market depends on investment. We model breakthroughs as an irreversible tipping point in a multi-country world, with different degrees of international cooperation. We show that international spill-over effects of R&D in carbon-free technologies lead to double free-riding, strategic over-pollution and underinvestment in green R&D, thus making climate change mitigation more difficult. We also show how the demand structure determines whether carbon pricing and R&D policies are substitutes or complements.