Transfer matrix in 1D Dirac-like problems

M Ibarra-Reyes; R Pérez-Álvarez; I Rodríguez-Vargas

doi:10.1088/1361-648X/acdfa2

Transfer matrix in 1D Dirac-like problems

J Phys Condens Matter. 2023 Jun 28;35(39). doi: 10.1088/1361-648X/acdfa2.

Authors

M Ibarra-Reyes¹, R Pérez-Álvarez², I Rodríguez-Vargas¹

Affiliations

¹ Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Circuto Marie Curie S/N, Parque de Ciencia y Tecnología QUANTUM Ciudad del Conocimiento, 98160 Zacatecas, Zacatecas, Mexico.
² Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, 62209 Cuernavaca, Morelos, Mexico.

PMID: 37336206
DOI: 10.1088/1361-648X/acdfa2

Abstract

The transfer matrix method is considered to obtain the fundamental properties of 1D Dirac-like problems. The case of 1D problems in monolayer graphene is addressed. The main characteristics of the transfer matrix are analyzed, contrasting them with the ones corresponding to 1D Schrödinger-like problems. Analytic expressions for the transmission coefficient and bound states are obtained. The continuity between bound states and states of perfect transmission is demonstrated in general, and in particular showed for the case of single electrostatic barriers. These findings in principle can be extended to 2D materials with Hamiltonian similar to monolayer graphene such as silicene and transition metal dichalcogenides.

Keywords: 1D Dirac-like problems; bound states; states of perfect transmission; transfer matrix.