Ballistic Transmission of the Relativistic
Quasielectrons Through the Potential
Barrier in the Alfa-T 3 Model
A. M. Korol, N. V. Medvid’, A. I. Sokolenko, and O. Yu. Shevchenko
1 Introduction
Some modern physical structures can be conveniently described using the so-called
α-T 3 model [1–8]. This model can rightly be attributed to a new class of objects that
have received the name of Dirac materials in recent years [9]. These include very
different objects in their structure, in particular, the low- and high-temperature d-wave
superconductors, superfluid phases 3He, graphene, two- and three-dimensional insulators, etc. [9]. The key concept that unites these different objects is a linear dispersion
relation that describes the low-energy excitations of the quasiparticles. Due to the
fact that the Dirac materials have a number of non-trivial, interesting properties, they
are actively studied in the last time. Under low energies, the quasiparticle states of the
Dirac materials are described by a massless Dirac equation in one or two dimensions,
analogous to the equation for the quasielectrons in graphene. The dispersion relation
for the Dirac particles relates to a cone in the three-dimensional case. Some properties
of the quasiparticle states are expressed in terms of topologically invariant quantities
and, importantly, are protected from the influence of moderate perturbations due to
the symmetry of inversion of time in the corresponding Hamiltonian.
The α-T 3 model is an intermediate structure between a dice lattice and graphene. It
is characterized by the parameter α, which determines the coupling strength between
the central atom of the hexagonal lattice and the atoms in the hexagon vertices [1–8].
It is clear that different values of α correspond to different physical states of the α-T 3
model, and it was successfully applied to various physical structures [1–8].
A. M. Korol (B)
Laboratory on Quantum Theory in Linkoping, ISIR, P.O. Box 8017, 580 Linkoping, Sweden
e-mail: korolam@ukr.net
A. M. Korol · N. V. Medvid’ · A. I. Sokolenko · O. Yu. Shevchenko
National University for Food Technologies, Volodymyrska Str. 68, Kiev, Ukraine
© Springer Nature Switzerland AG 2021
O. Fesenko and L. Yatsenko (eds.), Nanomaterials and Nanocomposites,
Nanostructure Surfaces, and Their Applications, Springer Proceedings
in Physics 246, https://doi.org/10.1007/978-3-030-51905-6_12
159
Quasielectrons Through the Potential
Barrier in the Alfa-T 3 Model
A. M. Korol, N. V. Medvid’, A. I. Sokolenko, and O. Yu. Shevchenko
1 Introduction
Some modern physical structures can be conveniently described using the so-called
α-T 3 model [1–8]. This model can rightly be attributed to a new class of objects that
have received the name of Dirac materials in recent years [9]. These include very
different objects in their structure, in particular, the low- and high-temperature d-wave
superconductors, superfluid phases 3He, graphene, two- and three-dimensional insulators, etc. [9]. The key concept that unites these different objects is a linear dispersion
relation that describes the low-energy excitations of the quasiparticles. Due to the
fact that the Dirac materials have a number of non-trivial, interesting properties, they
are actively studied in the last time. Under low energies, the quasiparticle states of the
Dirac materials are described by a massless Dirac equation in one or two dimensions,
analogous to the equation for the quasielectrons in graphene. The dispersion relation
for the Dirac particles relates to a cone in the three-dimensional case. Some properties
of the quasiparticle states are expressed in terms of topologically invariant quantities
and, importantly, are protected from the influence of moderate perturbations due to
the symmetry of inversion of time in the corresponding Hamiltonian.
The α-T 3 model is an intermediate structure between a dice lattice and graphene. It
is characterized by the parameter α, which determines the coupling strength between
the central atom of the hexagonal lattice and the atoms in the hexagon vertices [1–8].
It is clear that different values of α correspond to different physical states of the α-T 3
model, and it was successfully applied to various physical structures [1–8].
A. M. Korol (B)
Laboratory on Quantum Theory in Linkoping, ISIR, P.O. Box 8017, 580 Linkoping, Sweden
e-mail: korolam@ukr.net
A. M. Korol · N. V. Medvid’ · A. I. Sokolenko · O. Yu. Shevchenko
National University for Food Technologies, Volodymyrska Str. 68, Kiev, Ukraine
© Springer Nature Switzerland AG 2021
O. Fesenko and L. Yatsenko (eds.), Nanomaterials and Nanocomposites,
Nanostructure Surfaces, and Their Applications, Springer Proceedings
in Physics 246, https://doi.org/10.1007/978-3-030-51905-6_12
159