Nonlinear Coherent States for
Anisotropic 2D Dirac Materials
E. Díaz-Bautista, Y. Concha-Sánchez, and A. Raya
Abstract We construct nonlinear coherent states for electrons in anisotropic 2D
Dirac materials in a homogeneous magnetic field orthogonal to the sample. By
solving the anisotropic Dirac equation in Landau gauge, we identify the ladder
operators of the system. Nonlinear coherent states are obtained as eigenstates of
a generalized annihilation operator with complex eigenvalues which depends on an
arbitrary function f of the number operator. The anisotropy effects on these states
are analyzed by using the probability density and the Heisenberg uncertainty relation
for three different choices of f .
Keywords Coherent states · Anisotropic Dirac matter · Magnetic field
1 Introduction
2-Dimensional Dirac materials (2DDMs) like graphene [1–3], topological insulators [4, 5], and organic conductors [6, 7] stand out because their charge carriers
at low-energy are described by a Dirac equation. Recently, the interest to control
E. Díaz-Bautista ()
Departamento de Formación Básica Disciplinaria, Unidad Profesional Interdisciplinaria de
Ingeniería Campus Hidalgo, del Instituto Politécnico Nacional, Pachuca: Ciudad del
Conocimiento y la Cultura, San Agustín Tlaxiaca, Hidalgo, Mexico
e-mail: ediazba@ipn.mx; ediaz@fis.cinvestav.mx
Y. Concha-Sánchez
Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C,
Ciudad Universitaria, Morelia, Michoacán, México
e-mail: yconcha@umich.mx
A. Raya
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio
C-3, Ciudad Universitaria, Morelia, Michoacán, México
e-mail: raya@ifm.umich.mx
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_30
317
Anisotropic 2D Dirac Materials
E. Díaz-Bautista, Y. Concha-Sánchez, and A. Raya
Abstract We construct nonlinear coherent states for electrons in anisotropic 2D
Dirac materials in a homogeneous magnetic field orthogonal to the sample. By
solving the anisotropic Dirac equation in Landau gauge, we identify the ladder
operators of the system. Nonlinear coherent states are obtained as eigenstates of
a generalized annihilation operator with complex eigenvalues which depends on an
arbitrary function f of the number operator. The anisotropy effects on these states
are analyzed by using the probability density and the Heisenberg uncertainty relation
for three different choices of f .
Keywords Coherent states · Anisotropic Dirac matter · Magnetic field
1 Introduction
2-Dimensional Dirac materials (2DDMs) like graphene [1–3], topological insulators [4, 5], and organic conductors [6, 7] stand out because their charge carriers
at low-energy are described by a Dirac equation. Recently, the interest to control
E. Díaz-Bautista ()
Departamento de Formación Básica Disciplinaria, Unidad Profesional Interdisciplinaria de
Ingeniería Campus Hidalgo, del Instituto Politécnico Nacional, Pachuca: Ciudad del
Conocimiento y la Cultura, San Agustín Tlaxiaca, Hidalgo, Mexico
e-mail: ediazba@ipn.mx; ediaz@fis.cinvestav.mx
Y. Concha-Sánchez
Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C,
Ciudad Universitaria, Morelia, Michoacán, México
e-mail: yconcha@umich.mx
A. Raya
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio
C-3, Ciudad Universitaria, Morelia, Michoacán, México
e-mail: raya@ifm.umich.mx
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_30
317