What is the ruling on the expiation for an oath (kaffarat al-yameen) concerning the statement: "By Allah, if you touch the mobile phone again, you are divorced," if the wife has not touched the phone, but the husband fears she might do so in the future?

What you uttered is a conditional divorce, contingent upon your wife holding the mobile phone. If she holds it, the divorce occurs according to the majority of scholars. If she does not hold it, then there is no consequence for you. Imam Ibn Taymiyyah holds the view that you are obligated to offer an expiation for breaking an oath (kaffarat yamin) if your intention was to threaten or prevent, not to divorce. You cannot retract a conditional divorce by offering an expiation for an oath out of fear of breaking it, unless you are following Ibn Taymiyyah's view, in which case it suffices for you to offer it after breaking the condition if you did not intend divorce.

If the divorce occurs (according to the majority view), you may take your wife back before the expiry of her 'iddah, provided this divorce does not complete the three divorces. Her 'iddah ends upon her purification from the third menstrual cycle, or three months for a non-menstruating woman, or upon giving birth for a pregnant woman. If the 'iddah expires, renewing the marriage contract becomes necessary. If this divorce completes the three divorces, then she becomes unlawful for you until she marries another husband in a marriage of desire, not merely for the purpose of making her lawful for you again. As for your statement "By Allah," you are not obligated to offer an expiation for an oath according to the preponderant view (the majority) because there is no breaking of the oath, whether your wife holds the mobile phone or not.