You have Blackleg, or Black scurf. Blackleg is a bacterial disease which leaves sprouts rotting at soil level, blacklegs. Black scurf is a fungal disease; stems will have brown sunken spots below the soil level. Remove infected plants and destroy infected tubers and change the location next year.
Next year don't plant them that deep, plant them in higher ground as the plant grows green shoots upward, you keep them covered by adding new soil building large mounds of soil with potatoes inside. Grow them higher in the ground Happy gardening.
