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We present an algorithm to determine topological invariants of inhomogeneous systems, such as alloys, disordered crystals, or amorphous systems. Based on the kernel polynomial method, our algorithm allows us to study samples with more than $10^7$ degrees of freedom. Our method enables the study of large complex compounds, where disorder is inherent to the system. We use it to analyse Pb$_{1-x}$Sn$_{x}$Te and tighten the critical concentration for the phase transition.
Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group-symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of
The picture of how a gap closes in a semiconductor has been radically transformed by topological concepts. Instead of the gap closing and immediately re-opening, topological arguments predict that, in the absence of inversion symmetry, a metallic pha
The ratio of the Zeeman splitting to the cyclotron energy ($M=Delta E_Z / hbar omega_c$), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their a
We present angle resolved photoemission spectroscopy measurements of the surface states on in-situ grown (111) oriented films of Pb$_{1-x}$Sn$_{x}$Se, a three dimensional topological crystalline insulator. We observe surface states with Dirac-like di
We study the effect of Hunds splitting of repulsive interactions on electronic phase transitions in the multiorbital topological crystalline insulator Pb$_{1-x}$Sn$_{x}$Te, when the chemical potential is tuned to the vicinity of low-lying Type-II Van