Wireless terabit-per-second (Tb/s) links will become an urgent requirement within the next 10 years. However, current methodology for high data rate wireless communication that keep increasing the M-ary modulation schemes and the order of MIMO spatial multiplexing cannot reach Tb/s with a low power consumption. Thus, a new methodology is required with a large bandwidth in the millimeter-wave (mm-Wave) and sub-Terahertz (sub-THz) bands above 90GHz. In addition, it must be able to provide an extremely high spectral efficiency with a low energy consumption. Note that this consumption can be reduced by using constant-envelope modulations such as continuous phase modulation (CPM). However, the CPM has a very low spectral efficiency that limits the desired data rate. This paper suggests a new methodology to reach 1 Tb/s with a low power consumption by using power efficient single carrier with Index Modulation (IM). Simulation results under various uncorrelated/correlated fading channels show that the systems with power efficient modulations as CPM or QPSK can achieve Tb/s with a good performance. Moreover, the link budget and power estimation prove that the constant and near-constant envelope modulations require less than 1−3 Watts for 1 Tb/s with 10 −4 un-coded BER. Finally, this paper shows that conveying most of the information bits using IM to reach an ultra-high data rate is more power efficient than high order MIMO spatial multiplexing with large M-ary QAM as used in LTE.