Spin-valley locking, bulk quantum Hall effect and chiral surface state in a noncentrosymmetric Dirac semimetal BaMnSb$_2$

Spin-valley locking in the band structure of monolayers of MoS$_2$ and other group-VI dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a bulk Dirac semimetal BaMnSb$_2$. We find valley and spin are inherently coupled for both valence and conduction bands in this material. This is revealed by comprehensive studies using first principle calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy and quantum transport measurements. Moreover, this material also exhibits a stacked quantum Hall effect. The spin-valley degeneracy extracted from the plateau height of quantized Hall resistivity is close to 2. This result, together with the observed Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we have also observed a two-dimensional chiral metal at the side surface, which represents a novel topological quantum liquid. These findings establish BaMnSb$_2$ as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states.