Theory of two-dimensional spatially indirect equilibrium exciton condensates

Research on graphene and other two-dimensional atomic crystals is intense and is likely to remain one of the leading topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can also be reassembled into designer heterostructures made layer by layer in a precisely chosen sequence. The first, already remarkably complex, such heterostructures (often referred to as 'van der Waals') have recently been fabricated and investigated, revealing unusual properties and new phenomena. Here we review this emerging research area and identify possible future directions. With steady improvement in fabrication techniques and using graphene's springboard, van der Waals heterostructures should develop into a large field of their own.

We show that inversion symmetry breaking together with spin-orbit coupling leads to coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides, making possible controls of spin and valley in these 2D materials. The spin-valley coupling at the valence-band edges suppresses spin and valley relaxation, as flip of each index alone is forbidden by the valley-contrasting spin splitting. Valley Hall and spin Hall effects coexist in both electron-doped and hole-doped systems. Optical interband transitions have frequency-dependent polarization selection rules which allow selective photoexcitation of carriers with various combination of valley and spin indices. Photoinduced spin Hall and valley Hall effects can generate long lived spin and valley accumulations on sample boundaries. The physics discussed here provides a route towards the integration of valleytronics and spintronics in multivalley materials with strong spin-orbit coupling and inversion symmetry breaking.

Van der Waals heterostructures have recently emerged as a new class of materials, where quantum coupling between stacked atomically thin two-dimensional layers, including graphene, hexagonal-boron nitride and transition-metal dichalcogenides (MX2), give rise to fascinating new phenomena. MX2 heterostructures are particularly exciting for novel optoelectronic and photovoltaic applications, because two-dimensional MX2 monolayers can have an optical bandgap in the near-infrared to visible spectral range and exhibit extremely strong light-matter interactions. Theory predicts that many stacked MX2 heterostructures form type II semiconductor heterojunctions that facilitate efficient electron-hole separation for light detection and harvesting. Here, we report the first experimental observation of ultrafast charge transfer in photoexcited MoS2/WS2 heterostructures using both photoluminescence mapping and femtosecond pump-probe spectroscopy. We show that hole transfer from the MoS2 layer to the WS2 layer takes place within 50 fs after optical excitation, a remarkable rate for van der Waals coupled two-dimensional layers. Such ultrafast charge transfer in van der Waals heterostructures can enable novel two-dimensional devices for optoelectronics and light harvesting.