While 5G is being widely deployed around the world, the efforts from both academia and industry have started to investigate various promising 6G techniques, among which Terahertz (THz) systems have drawn much research attention. Recent developments in nanotechnology have enabled electromagnetic nano-communications in the THz band for supporting very large bandwidths with ultra-high data rates over 6G big-data-driven nano-networks. One of the major bottlenecks over such networks is the very limited energy that can be accessed by nano devices. Towards this end, novel energy harvesting (EH) mechanisms have been proposed to remedy this energy scarcity problem. However, how to accurately model and characterize the relationships among THz-band wireless channel, energy consumption, and EH models still remains a challenging and open problem. To solve the abovementioned problems, we propose to develop a joint optimal resource allocation policy for self-powered nano devices to achieve the maximum channel capacity in the THz band over EH-based nano-networks. Particularly, using the Time-Spread On-Off Keying (TS-OOK) modulation mechanism, we establish the wireless communication and EH models in the THz band. Then, we formulate and solve the channel capacity maximization problem under several different constraints for our proposed THz-band EH-based schemes. Simulation results are included, which evaluate and validate our proposed EH-based nano-communication schemes in the THz band.