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Topological insulators (TIs) are renowned for their remarkable electronicproperties: quantised bulk Hall and edge conductivities, and robust edgewave-packet propagation, even in the presence of material defects and disorder.Computations of these physical properties generally rely on artificialperiodicity (the supercell approximation), or unphysical boundary conditions(artificial truncation). In this work, we build on recently developed methodsfor computing spectral properties of infinite-dimensional operators. We applythese techniques to develop efficient and accurate computational tools forcomputing the physical properties of TIs. These tools completely avoid suchartificial restrictions and allow one to probe the spectral properties of theinfinite-dimensional operator directly, even in the presence of materialdefects and disorder. Our methods permit computation of spectra, approximateeigenstates, spectral measures, spectral projections, transport properties, andconductances. Numerical examples are given for the Haldane model, and thetechniques can be extended similarly to other TIs in two and three dimensions.

Computing spectral properties of topological insulators without artificial truncation or supercell approximation