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Let's suppose we have a two dimensional lattice which is periodic along certain direction, say x-direction, allowing us to define a quasi momentum k_x. The lattice is not periodic along the y-direction (perpendicular to x-direction). Therefore, we are able to obtain the band structure of the system as a function of k_x. If the system is finite along y-direction, for some values, we can observe edge states in such band structure. The question is the following, can we get information about the localization of the wave functions of the system (in particular, localization properties of edge states) by looking at the density of states along the y-direction? If so, how can that be done? I thought this after reading some articles at where the localization of wave functions is indicated by colors that correspond to the density of states along y (see, for example, https://arxiv.org/abs/1407.7747, Fig. 3).

Thanks in advance. I would really appreciate your help and attention.