An increase in power consumption necessitates a low-power circuit technology to extend Moore’s law. Low-power transistors, such as tunnel field-effect transistors (TFETs)1-5, negative-capacitance field-effect transistors (NC-FETs)6, and Dirac-source field-effect transistors (DS-FETs)7-10, have been realised to break the thermionic limit of the subthreshold swing (SS). However, a low-power diode rectifier, which breaks the thermionic limit of an ideality factor (η) of 1 at room temperature, has not been proposed yet. In this study, we have realised a DS diode, which exhibits a steep-slope characteristic curve, by utilising the linear density of states (DOSs) of graphene7. For the developed DS diode, η < 1 for more than two decades of drain current with a minimum value of 0.8, and the rectifying ratio is large (> 105). The realisation of a DS diode paves the way for the development of low-power electronic circuits.