Can a sociopath show love towards their children?

Yes, it is possible for a sociopath to love their children, depending on the context of the word love. The person can in effect care for their children, but showing the genuine emotion of love is a bit more difficult to come by. A sociopath who does not actually display true love for a person 100% of the time can only simulate the emotion and effects of it towards a child through what they have experienced love for another person as or gathered data on the subject. But the fact that a genuine love beyond caring about the person and having a specific attachment to them is non existent.