Variation in LDOS for the Dirac surface states due to Se/Te composition fluctuations in FeTe_0.55Se_0.45

FeTe_0.55Se_0.45 is believed to be a strong topological phase for a narrow range of Te/Se composition as no evidences for non-trivial topology have been observed away from that specific composition. However, atomic-scale topographic image of the sample surface from STM shows in-homogeneity in Te/Se concentration with density correlation length of about 3 nm. The fluctuations in Te/Se composition can destroy the non-trivial topology locally and give rise to topological and trivial regions distributed across the sample. We investigate the effects of such topological-trivial phase boundaries in the sample on the Dirac surface state density distribution. With a minimal model for 3D strong TI, we tune the parameters to match the ARPES band structure and introduce disorder in the topology controlling parameter with correlation length of Te/Se density in-homogeneity. In particular, we study the variation of local density of states (LDOS) within the Dirac dispersion energy window that may be observed in LDOS measurement using STM within the energy window of Dirac dispersion.