Ballistic Transmission of the Relativistic Quasielectrons …
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for the maximum values of the function G(E) corresponds to the supertunneling
phenomenon. The maxima of the function G(E) also hold for the energies for which
the Fabry–Perot resonances are observed. There is a region of energies in which the
function G(E) has minimal values—it is related to the bandgap in the dependence
of T(E). The magnitude of G(E) is an oscillatory function of E, and the amplitude
and period of the oscillations depend on the parameters α, β, and D. As α increases
or β increases, the conductivity values of G(E) increase for most parameters. As the
thickness of the barrier increases, the number of oscillations (peaks) depending on
G(E) in the fixed energy interval increases.
4 Conclusions
We consider here one of the modern structures: the so-called alfa-T 3 model which
interpolates between the dice lattice and the graphene one with the help of the parameter α that allows to change the coupling strength between the honeycomb lattice
(HCL, graphene) and the HCL with the central cite (dice lattice) and varies from
zero to unity.
It is shown that this object, in the general case, is a resonant-tunneling structure,
that is, its transmission spectra are represented by a set of resonance peaks with the
values of the transmission coefficient T close to unity. In particular, for the values
β < 1 (β is equal to the ratio of the Fermi velocities in the barrier and out-of-barrier
regions), there is a clear structure of the resonance peaks of the Fabry–Perot type for
any α values; their position on the energy axis depends on the value of β.
In the case of a zero incidence angle, there is a Klein paradox phenomenon which
occurs for all values of β and α and for any values of the height and width of the
potential barrier. In the vicinity of the energy values close to the height of the potential
barrier, there is a forbidden band (gap) whose width and position are regulated by
the values of the quantities β and φ and do not depend on α.
As the value of α increases, a significant increase of the transmission coefficient
for all values of E and β is observed. For the magnitude α = 1, there is a phenomenon
of supertunneling. The energy for which the supertunneling takes place is the function
of β and is expressed by the formula E = U/ (1 +β), β < 1, provided that α = 1.
The conductivity of the given structure G(E) is evaluated with the help of the
Landauer–Buttiker formalism and, as shown, essentially depends both on the value
of α and on the value of β. Specifically, the conductivity increases with increase in α
and has a complex dependence on β. In particular, for values β > 1, the quantity G(E)
decreases with increasing β for all α. For β < 1, the function G(E) is characterized
by regions with the conduction oscillations, as well as with the regions with a wide
minimum in the vicinity of the energy close to the potential barrier height.
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for the maximum values of the function G(E) corresponds to the supertunneling
phenomenon. The maxima of the function G(E) also hold for the energies for which
the Fabry–Perot resonances are observed. There is a region of energies in which the
function G(E) has minimal values—it is related to the bandgap in the dependence
of T(E). The magnitude of G(E) is an oscillatory function of E, and the amplitude
and period of the oscillations depend on the parameters α, β, and D. As α increases
or β increases, the conductivity values of G(E) increase for most parameters. As the
thickness of the barrier increases, the number of oscillations (peaks) depending on
G(E) in the fixed energy interval increases.
4 Conclusions
We consider here one of the modern structures: the so-called alfa-T 3 model which
interpolates between the dice lattice and the graphene one with the help of the parameter α that allows to change the coupling strength between the honeycomb lattice
(HCL, graphene) and the HCL with the central cite (dice lattice) and varies from
zero to unity.
It is shown that this object, in the general case, is a resonant-tunneling structure,
that is, its transmission spectra are represented by a set of resonance peaks with the
values of the transmission coefficient T close to unity. In particular, for the values
β < 1 (β is equal to the ratio of the Fermi velocities in the barrier and out-of-barrier
regions), there is a clear structure of the resonance peaks of the Fabry–Perot type for
any α values; their position on the energy axis depends on the value of β.
In the case of a zero incidence angle, there is a Klein paradox phenomenon which
occurs for all values of β and α and for any values of the height and width of the
potential barrier. In the vicinity of the energy values close to the height of the potential
barrier, there is a forbidden band (gap) whose width and position are regulated by
the values of the quantities β and φ and do not depend on α.
As the value of α increases, a significant increase of the transmission coefficient
for all values of E and β is observed. For the magnitude α = 1, there is a phenomenon
of supertunneling. The energy for which the supertunneling takes place is the function
of β and is expressed by the formula E = U/ (1 +β), β < 1, provided that α = 1.
The conductivity of the given structure G(E) is evaluated with the help of the
Landauer–Buttiker formalism and, as shown, essentially depends both on the value
of α and on the value of β. Specifically, the conductivity increases with increase in α
and has a complex dependence on β. In particular, for values β > 1, the quantity G(E)
decreases with increasing β for all α. For β < 1, the function G(E) is characterized
by regions with the conduction oscillations, as well as with the regions with a wide
minimum in the vicinity of the energy close to the potential barrier height.