Dirac nodal line semimetals represent a new state of quantum matters in which the electronic bands touch to form a closed loop with linear dispersion. Here, we report a combined study on ZrSiS by density functional theory calculation, scanning tunnelling microscope (STM) and magneto-transport measurements. Our STM measurements reveal the spectroscopic signatures of a diamond-shaped Dirac bulk band and a surface band on two types of cleaved surfaces as well as a spin-polarized surface band at G at E∼0.6 eV on S-surface, consistent with our band calculation. Furthermore, we find the surface termination does not affect the surface spectral weight from the Dirac bulk bands but greatly affect the surface bands due to the change in the surface orbital composition. From our magnetotransport measurements, the primary Shubnikov-de-Haas frequency is identified to stem from the hole-type quasi-two-dimensional Fermi surface between Γ and X. The extracted non-orbital magnetoresistance (MR) contribution D(θ, H) yields a nearly H-linear dependence, which is attributed to the intrinsic MR in ZrSiS. Our results demonstrate the unique Dirac line nodes phase and the dominating role of Zr-d orbital on the electronic structure in ZrSiS and the related compounds.
In this paper, we consider the dynamic subchannel allocation problem in OFDMA-based selective relaying networks. Our goal is to maximize the total throughput under the constraint of total transmission power, while guaranteeing fairness on subchannel occupation by multiple destination nodes (users). Since the optimal solution to this optimization problem is extremely computationally complex to obtain, we decompose the original optimization problem into two subproblems. Firstly, we assign subchannels to the users with the best equivalent channel gains for them under the assumption of equal power distribution among all subchannels. Secondly, water-filling method is adopted to distribute the power to the determined links. Simulation results show that the performance of the proposed algorithm approaches asymptotically to that of the optimal one, while reducing computational complexity from exponential to linear with the numbers of subchannels, relay nodes and users. It is also shown that subchannel permutation (SP) scheme brings additional throughput gain to DF cooperative transmission.
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