Hi, should the common mode voltage be at range of 0V to required voltage? Is it also fine to use an IC that has a minimum common mode voltage range of above 0V, for example 2V? like ZXCT1009? are there any consideration in choosing IC like ZXCT1009? What common application must it be chosen? or how should I choose an IC for high side current sensing? what factor must be taken into consideration?
If your high side voltage is above 2v then the ZXCT1009 chip will work fine.
Unless your high side voltage falls below 2v and you still wish to monitor the current, than you will probability have another source to power the shunt amplifier available.
Any op amp that has a common mode voltage reaching down to zero would be more appropriate.