Degrees of Freedom of the 3-User Rank-Deficient MIMO Interference Channel

We provide the degrees of freedom (DoF) characterization for the $3$-user $M_T\times M_R$ multiple-input multiple-output (MIMO) interference channel (IC) with \emph{rank-deficient} channel matrices, where each transmitter is equipped with $M_T$ antennas and each receiver with $M_R$ antennas, and the interfering channel matrices from each transmitter to the other two receivers are of ranks $D_1$ and $D_2$, respectively. One important intermediate step for both the converse and achievability arguments is to convert the fully-connected rank-deficient channel into an equivalent partially-connected full-rank MIMO-IC by invertible linear transformations. As such, existing techniques developed for full-rank MIMO-IC can be incorporated to derive the DoF outer and inner bounds for the rank-deficient case. Our result shows that when the interfering links are weak in terms of the channel ranks, i.e., $D_1+D_2\leq \min(M_T, M_R)$, zero forcing is sufficient to achieve the optimal DoF. On the other hand, when $D_1+D_2> \min(M_T, M_R)$, a combination of zero forcing and interference alignment is in general required for DoF optimality. The DoF characterization obtained in this paper unifies several existing results in the literature.Comment: 28 pages, 7 figures. To appear in IEEE transactions on wireless communication

Anomalous light cones and valley optical selection rules of interlayer excitons in twisted heterobilayers

We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have six-fold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities to optically inject valley polarization and valley current, and the observation of both direct and inverse valley Hall effects, by exciting interlayer excitons. Our findings suggest potential excitonic circuits with valley functionalities, and unique opportunities to study exciton dynamics and condensation phenomena in semiconducting 2D heterostructures.Comment: Including the Supplemental Material