There's been much recent interest in 2D materials since they can form monolayer-thick films. Since their crystal structure is periodic along the in-plane directions, the electronic band structure along these directions is quite well understood and can be formulated using approaches used for conventional bulk semiconductors, such as Si.
How can we think of the out-of-plane electronic band structure (which is not periodic) for 2D materials?
I need help bridging the techniques used in solid-state physics for bulk crystalline materials to the calculation of band structure along a non-periodic direction. My initial thought is that the notion of band structure along the out-of-plane direction is ill-conceived.
The reason why I'm interested in the concept of out-of-plane band structure, is that devices have been proposed and fabricated that have electron transport (tunneling) from one 2D layer to another, and the concept of band structure is quite useful in applying conventional techniques to calculate current, rates, etc. [For example, this 2014 paper discusses tunneling between different layers of 2D materials, but uses the in-plane band structure for the out-of-plane direction.]