32 research outputs found
Gap Structure of the Hofstadter System of Interacting Dirac Fermions in Graphene
The effects of mutual Coulomb interactions between Dirac fermions in
monolayer graphene on the Hofstadter energy spectrum have been studied. Our
studies indicate that the effects of the interaction depend strongly on the
amplitude of the periodic potential. For large amplitudes the interaction
effects are small and the properties of the system are primarily determined by
the periodic potential but for small amplitudes the interaction greatly
influences the band gap. The signature of the interaction effects in the
Hofstadter system can be probed through magnetization where the Coulomb effects
are dominant for small amplitudes of the periodic potential.Comment: 5 pages, 4 figures, Modified version, accepted for publication in PR
Fractal Butterflies of Dirac Fermions in Monolayer and Bilayer graphene
We present an overview of the theoretical understanding of Hofstadter
butterflies in monolayer and bilayer graphene. After a brief introduction on
the past work in conventional semiconductor systems, we discuss the novel
electronic properties of monolayer and bilayer graphene that helped to detect
experimentally the fractal nature of the energy spectrum. We have discussed the
theoretical background on the Moir\'e pattern in graphene. This pattern was
crucial in determining the butterfly structure. We have also touched upon the
role of electron-electron interaction in the butterfly pattern in graphene. We
conclude by discussing the future prospects of butterfly search, especially for
interacting Dirac fermions.Comment: Invited article for IET Circuits, Devices and Systems, special issue
"Graphene Electronics
Tunability of the Fractional Quantum Hall States in Buckled Dirac Materials
We report on the fractional quantum Hall states of germanene and silicene
where one expects a strong spin-orbit interaction. This interaction causes an
enhancement of the electron-electron interaction strength in one of the Landau
levels corresponding to the valence band of the system. This enhancement
manifests itself as an increase of the fractional quantum Hall effect gaps
compared to that in graphene and is due to the spin-orbit induced coupling of
the Landau levels of the conduction and valence bands, which modifies the
corresponding wave functions and the interaction within a single level. Due to
the buckled structure, a perpendicular electric field lifts the valley
degeneracy and strongly modifies the interaction effects within a single Landau
level: in one valley the perpendicular electric field enhances the interaction
strength in the conduction band Landau level, while in another valley, the
electric field strongly suppresses the interaction effects.Comment: 5 pages, 4 figure
Wannier-Stark states of graphene monolayer in strong electric field
We find theoretically energy spectrum of a graphene monolayer in a strong
constant electric field using a tight-binding model. Within a single band, we
find quantized equidistant energy levels (Wannier-Stark ladder), separated by
the Bloch frequency. Singular interband coupling results in mixing of the
states of different bands and anticrossing of corresponding levels, which is
described analytically near Dirac points and is related to the
Pancharatnam-Berry phase. The rate of interband tunneling, which is
proportional to the anticrossing gaps in the spectrum, is only inversely
proportional to the tunneling distance, in a sharp contrast to conventional
solids where this dependence is exponential. This singularity will have major
consequences for graphene behavior in strong ultrafast optical fields, in
particular, leading to non-adiabaticity of electron excitation dynamics.Comment: 11 pages, 9 figure
Interaction of graphene monolayer with ultrashort laser pulse
We study the interaction of graphene with ultrashort few femtosecond long
optical pulse. For such a short pulse, the electron dynamics is coherent and is
described within the tight-binding model of graphene. The interaction of
optical pulse with graphene is determined by strong wave vector dependence of
the interband dipole matrix elements, which are singular at the Dirac points of
graphene. The electron dynamics in optical pulse is highly irreversible with
large residual population of the conduction band. The residual conduction band
population as a function of the wave vector is nonuniform with a few localized
spots of high conduction band population. The spots are located near the Dirac
points and the number of spots depends on the pulse intensity. The optical
pulse propagating through graphene layer generates finite transferred charge,
which, as a function of pulse intensity, changes its sign. At small pulse
intensity, the charge is transferred in the direction of the pulse maximum,
while at large pulse intensity, the direction of the charge transfer is
opposite to the direction of pulse maximum. This property opens unique
possibility of controlling the direction of the charge transfer by variation of
the pulse intensity.Comment: 11 pages, 11 figure
Ultrafast topological phenomena in gapped graphene
In the model of gapped graphene, we have shown how the recently predicted
topological resonances are solely related to the presence of an energy band gap
at the and points of the Brillouin zone. In the field of a
strong single-oscillation chiral (circularly-polarized) optical pulse, the
topological resonance causes the valley-selective population of the conduction
band. This population distribution represents a chiral texture in the
reciprocal space that is structured with respect to the pulse separatrix as has
earlier been predicted for transition metal dichalcogenides. As the band gap is
switched off, this chirality gradually disappears replaced by an achiral
distribution characteristic of graphene.Comment: 10 pages, 11 figure
Femtosecond valley polarization and topological resonances in transition metal dichalcogenides
We theoretically introduce the fundamentally fastest induction of a
significant population and valley polarization in a monolayer of a transition
metal dichalcogenide (i.e., and ). This may be
extended to other two-dimensional materials with the same symmetry. This valley
polarization can be written and read-out by a pulse consisting of just a single
optical oscillation with a duration of a few femtoseconds and an amplitude of
. Under these conditions, we predict a new
effect of {\em topological resonance}, which is due to Bloch motion of
electrons in the reciprocal space where electron population textures are formed
defined by non-Abelian Berry curvature. The predicted phenomena can be applied
for information storage and processing in PHz-band optoelectronics.Comment: 9 pages, 7 figure
Topological Spaser
We theoretically introduce a topological spaser, which consists of a
hexagonal array of plasmonic metal nanoshells containing an achiral gain medium
in their cores. Such a spaser can generate two mutually time-reversed chiral
surface plasmon modes in the - and -valleys, which
carry the opposite topological charges, , and are described by a
two-dimensional representation of the point symmetry
group. Due to the mode competition, this spaser exhibits a bistability: only
one of these two modes generates, which is a spontaneous symmetry breaking.
Such a spaser can be used for an ultrafast all-optical memory and information
processingComment: 9 pages, 7 figure
Ultrafast strong-field absorption in gapped graphene
We study theoretically the strong-field absorption of an ultrafast optical
pulse by a gapped graphene monolayer. At low field amplitudes, the absorbance
in the pristine graphene is equal to the universal value of percent.
Although the ultrafast optical absorption for low field amplitudes is
independent of the polarization, linear or circular, of the applied optical
pulse, for high field amplitudes, the absorption strongly depends on the pulse
polarization. For a linearly polarized pulse, the optical absorbance is
saturated at the value of percent for the pulse's amplitude of
, but no such saturation is observed for a circularly
polarized pulse. For the gapped graphene, the absorption of a linearly
polarized pulse has a weak dependence on the bandgap, while for a circularly
polarized pulse, the absorption is very sensitive to the bandgap. %Opening a
bandgap in graphene by placing in on, for example, SiC substrate strongly
modify the ultrafast absorption at small field amplitudes
Femtosecond currents in transition metal dichalcogenides monolayers
We theoretically study the interaction of an ultrafast intense linearly
polarized optical pulse with monolayers of transition metal dichalcogenides
(TMDCs). Such a strong pulse redistributes electrons between the bands and
generates femtosecond currents during the pulse. Due to the large bandwidth of
the incident pulse, this process is completely off-resonant. While in TMDCs the
time-reversal symmetry is conserved, the inversion symmetry is broken and these
monolayers have the axial symmetry along armchair direction but not along the
zigzag one. Therefore, the pulse polarized along the asymmetric direction of
TMDC monolayer generates both longitudinal, i.e., along the direction of
polarization, and transverse, i.e., in the perpendicular direction, currents.
Such currents result in charge transfer through the system. We study different
TMDC materials and show how the femtosecond transport in TMDC monolayers depend
on their parameters, such as lattice constant and bandgap