Because the output voltage is by definition fixed around 1.25 V for typical bandgap reference circuits, the minimum operating voltage is about 1.4 V, as in a CMOS circuit at least one drain-source voltage of a FET (field effect transistor) has to be added.
When summing a PTAT (Proportional to Absolute Temperature) and a CTAT (Complementary to Absolute Temperature) current, only the linear terms of current are compensated, while the higher-order terms are limiting the TD (Temperature Drift) of the BGR at around 20ppm/oC, over a temperature range of 100 oC.