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Landauer-B\"uttiker formula describes the electronic quantum transports innanostructures and molecules. It will be numerically demanding for simulationsof complex or large size systems due to, for example, matrix inversioncalculations. Recently, Chebyshev polynomial method has attracted intenseinterests in numerical simulations of quantum systems due to the highefficiency in parallelization, because the only matrix operation it involves isjust the product of sparse matrices and vectors. Many progresses have been madeon the Chebyshev polynomial representations of physical quantities for isolatedor bulk quantum structures. Here we present the Chebyshev polynomial method tothe typical electronic scattering problem, the Landauer-B\"uttiker formula forthe conductance of quantum transports in nanostructures. We first describe thefull algorithm based on the standard bath kernel polynomial method (KPM). Then,we present two simple butefficient improvements. One of them has a timeconsumption remarkably less than the direct matrix calculation without KPM.Some typical examples are also presented to illustrate the numericaleffectiveness.

Chebyshev Polynomial Method to Landauer-B\"uttiker Formula of Quantum Transport in Nanostructures