An optoelectronic oscillator (OEO) for single-frequency microwave generation, enabled by broken parity time (PT) symmetry based on higher-order modulation using a Mach-Zehnder modulator, is proposed and demonstrated. Instead of using two physically separated mutually coupled loops with balanced gain and loss, the PT symmetry is realized using a single physical loop to implement two equivalent loops with the gain loop formed by the beating between the optical carrier and the ±1st-order sidebands and the loss loop formed by the beating between the ±1st-order sidebands and the ±2nd-order sidebands at a photodetector. The gain and loss coefficients are made identical in magnitude by controlling the incident light power to the modulator and the modulator bias voltage. Once the gain/loss coefficient is greater than the coupling coefficient, the PT symmetry is broken, and a single-frequency oscillation without using an ultra-narrow passband filter is achieved. The approach is evaluated experimentally. For an OEO with a loop length of 10.1 km, a single-frequency microwave signal at 9.997 GHz with a 55-dB sidemode suppression ratio and -142-dBc/Hz phase noise at a 10-kHz offset frequency is generated. No mode hopping is observed during a 5-hour measurement period.