Substrate-induced Gap Research Articles

Magnetic Spin Susceptibility of Graphene in Ferromagnetic State: A Tight-Binding Model Study

We report here a tight-binding model study of frequency-dependent ferromagnetic spin susceptibility of the graphene system. The tight-binding Hamiltonian consists of electron hoppings up to third-nearest-neighbors, substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. To calculate magnetic susceptibility, we calculate the two-particle electron Green’s functions by using Zubarev’s double time Green’s function technique. The electron occupations at A and B sub-lattices for both up and down spins are computed numerically and self-consistently. The frequency-dependent real part of ferromagnetic susceptibility of the system is computed numerically by taking [Formula: see text] grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher energy resonance peak appearing at substrate-induced gap. The [Formula: see text]-peak shifts to a higher energy with the increase of momentum [Formula: see text]. The susceptibility shows that the high energy peak shifts to higher energies due to the corresponding increase of substrate-induced gap observed experimentally. It is observed that the Coulomb interaction suppresses the substrate-induced gap, but the impurity doping at A site enhances the substrate-induced gap, while doping at B site suppresses it.

Gate-tunabe gap of heated monolayer graphene on substrates

Temperature effect of energy gap is researched in the presence of the homogeneous magnetic field based on the electrons/holes - surface optical phonons coupling induced by different polar substrates under monolayer graphene. The quantum statistical theory and LLP variational method are used to calculate the energy gap of monolayer graphene on the polar substrate. We found that substrate-induced gap can be tunable in the landau energy level by controlling the temperature T, confinement strength parameter g, polarization strength η of substrate. The energy gap matches with the recent experimental data. These conclusions obtained highlight the vital role of polaron effect in deciding substrate-induced gap and provide a promising way to increase the substrate-induced gap of monolayer graphene.

Enhancement of the Metallic Behavior of Graphene due to Coulomb Interaction in the Paramagnetic Limit: A Tight-Binding Study

The pristine graphene is a zero band gap semiconductor with valence and conduction bands touching each other at Dirac points. The graphene-on-substrate exhibits a small gap at the Dirac points. The microscopic Hamiltonian describes the nearest-neighbor [Formula: see text]-electron hopping with tight-binding approach. Graphene-on-substrate exhibits a gap at the Dirac points where the energy at A sublattice is raised by [Formula: see text] and the energy at B sublattice is lowered by energy [Formula: see text] leading to asymmetry in the two sublattices. Further, we have introduced impurities at both the sublattices. The Coulomb interaction in graphene-on-substrate is described by Hubbard-type Coulomb interaction with energy U. The Coulomb interaction is treated in the calculation within the mean-field approximation in the paramagnetic limit. The temperature-dependent site-independent electron occupancies at both the sublattices are calculated and computed self-consistently. The difference between the electron occupancies of both the sublattices introduces a charge gap. The effect of charge gap on the electronic band dispersion in graphene-on-substrate is investigated by varying different model parameters of the system like Coulomb energy, substrate-induced gap, temperature, total band filling and impurity concentrations. It is observed that both the valence and conduction bands are shifted above the Fermi level exhibiting a charge gap between the bands. As a result, the partially filled valence band exhibits metallic behavior.

Tight-Binding Model Study of Tunneling Spectra of Monolayer Graphene-on-Substrate

We report here the theoretical model study of antiferromagnetic ordering in graphene. We propose a tight-binding model Hamiltonian describing electron hopping up to third-nearest neighbors in graphene. The Hamiltonian describing inequivalence of [Formula: see text] and [Formula: see text] sublattices in graphene-on-substrate is incorporated. The Hubbard-type repulsive Coulomb interaction is considered for both the sublattices with same Coulomb energy. The electron–electron interaction is considered within mean-field approximation with mean electron occupancies [Formula: see text] at [Formula: see text] sublattice and [Formula: see text] at [Formula: see text] site with [Formula: see text] and [Formula: see text] being the antiferromagnetic magnetizations at [Formula: see text] and [Formula: see text] sublattices, respectively. The total Hamiltonian is solved by Zubarev’s techniques of double time single particle Green’s functions. The magnetizations are calculated from the correlation functions corresponding to the respective Green’s functions. The temperature-dependent magnetizations are solved self-consistently taking suitable grid points for the electron momentum. Finally, the electron density of states (DOS) which is proportional to imaginary part of the electron Green’s functions is calculated and computed numerically at a given temperature varying different model parameters for the system. The conductance spectra show a gap near the Dirac point due to substrate-induced gap and magnetic gap, while the van Hove singularities split into eight peaks due to two different sublattice magnetizations and two different spin orientations of the electron in graphene-on-substrate.

Effect of impurity doping on AFM magnetization in graphene: A tight-binding model approach

We report here a tight-binding theoretical study of anti-ferromagnetism in graphene taking electron hopping up to third nearest neighbors. The graphene on substrate introduces inequivalence in the two sublattices of the honeycomb lattice. The on-site Coulomb interactions at two sublattices of graphene are treated within mean-field approximation and the electron occupancies at two sublattices include spin moments in opposite directions giving rise to anti-ferromagnetism in graphene. The AFM sublattice magnetizations are calculated by using Zubarev’s Green’s function technique and computed self-consistently for different ranges of Coulomb potential, substrate-induced gap and impurity concentrations. It is observed that [Formula: see text]-site magnetization is suppressed by [Formula: see text]-site impurity concentration, while [Formula: see text]-site magnetization remains unaffected. Similar effect has been observed at [Formula: see text]-site when doped with pentavalent dopant, while [Formula: see text]-site magnetization remains unaffected. Furthermore, substrate-induced AFM gap has also been observed at different ranges of temperature.

Magnetic Susceptibility and Neutron Scattering of Graphene in Antiferromagnetic State: a Tight-Binding Approach

We address here a tight-binding model study of the frequency-dependent antiferromagnetic spin susceptibility for the graphene systems. The Hamiltonian consists of electron hopping up to the third-nearest-neighbors, substrate and impurity effects in presence of electron-electron interactions at A and B sub-lattices. To calculate susceptibility, we evaluate the two-particle electron Green’s function by using Zubarev’s Green’s function technique. The frequency-dependent antiferromagnetic susceptibility of the system is computed numerically by taking 1000 X 1000 grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher-energy peak associated with the substrate-induced gap. The evolution of these two peaks are investigated by varying neutron wave vector, Coulomb correlation energy, substrate-induced gap, electron hopping integrals and A- and B-site electron-doping concentrations.

Microscopic theory of substrate-induced gap effect on real AFM susceptibility in graphene

We address here a tight-binding model study of frequency-dependent real part of antiferromagnetic susceptibility for the graphene systems. The Hamiltonian consists of electron hopping upto third nearest-neighbours, substrate and impurity effects in the presence of electron–electron interactions at A and B sublattices. To calculate susceptibility, we evaluate the two-particle electron Green’s function by using Zubarev’s Green’s function technique. The frequency-dependent real part of antiferromagnetic susceptibility of the system is computed numerically by taking $$1000 \times 1000$$ grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher energy peak appearing at substrate-induced gap. The evolution of these two peaks is investigated by varying neutron wave vector, Coulomb correlation energy, substrate-induced gap, electron hopping integrals and A- and B-site electron doping concentrations.

Dielectric constant of graphene-on-polarized substrate: A tight-binding model study

We report here a microscopic tight-binding theoretical study of the dynamic dielectric response of graphene-on-polarizable substrate with impurity. The Hamiltonian consists of first, second and third nearest-neighbour electron hopping interactions besides doping and substrate-induced effects on graphene. We have introduced electron–electron correlation effect at A and B sublattices of graphene which is considered within Hartree–Fock mean-field approximation. The electron occupancies at both sublattices are calculated and solved self-consistently and numerically for both up- and down-spin orientations. The polarization function appearing in the dielectric function is a two-particle Green’s function which is calculated by using Zubarev’s Green’s function technique. The temperature and optical frequency-dependent dielectric function is evaluated and compared with experimental data by varying Coulomb correlation energy, substrate-induced gap and impurity concentrations.

A Model Study of Substrate Effect on the Neutron-Scattering Spectra of Ferromagnetic Ordered Graphene

Graphene as a possible new magnetic material has stimulated research interest for application in spintronic devices. Pristine graphene does not show magnetism due to equivalence of the two sub-lattices of carbon atoms. It is predicted that impurity effects, substrate-induced gap, and defects, are expected to produce in-equivalence in two carbon sub-lattices leading to magnetism. The spins on the same sub-lattices are found to exhibit ferromagnetic order and spins of different sub-lattices are found to exhibit anti-ferromagnetic order. We consider here impurity and substrate effects as the cause of generation of magnetism in graphene. We report here a microscopic tight-binding study of frequency-dependent neutron scattering spectra for ferromagnetic ordering in the graphene systems. The tight-binding Hamiltonian consists of electron hoppings upto third nearest neighbors and substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. We calculate the two-particle electron Green’s functions by using Zubarev’s Green’s function technique. The frequency-dependent scattering intensity of the system is computed numerically. The spectra displays a sharp peak at the neutron momentum transfer energy at low energies and another higher-energy peak appearing at substrate-induced gap.

Electric control of tunneling energy in graphene double dots

We theoretically investigate the spectrum of a single electron double quantum dot, defined by top gates in a graphene with a substrate-induced gap. We examine the effects of electric and magnetic fields on the spectrum of localized states, focusing on the tunability of the interdot coupling. We find that the substrate-induced gap allows for electrostatic control, with some limitations that for a fixed interdot distance, the interdot coupling cannot be made arbitrarily small due to the Klein tunneling. On the other hand, the proximity of the valence band in graphene allows for new regimes, such as an $npn$ double dot, which have no counterparts in GaAs.

Sorting the modes contributing to guidance in strain-induced graphene waveguides

We propose a simple way of probing the number of modes contributing to the channeling in graphene waveguides which are formed by a gauge potential produced by mechanical strain. The energy mode structure for both homogeneous and non-homogeneous strain regimes is carefully studied using the continuum description of the Dirac equation. We found that high strain values privilege negative (instead of positive) group velocities throughout the guidance, sorting the types of modes flowing through it. We also show how the effect of a substrate-induced gap competes against the strain.

Berry-curvature-mediated valley-Hall and charge-Hall effects in graphene via strain engineering

We point out a practical way to induce a finite charge-Hall conductivity in graphene via an off-diagonal strain. Our conclusions are based on a general analysis and supported by numerical examples. The interplay between a substrate-induced gap and the strain is discussed. We show that the substrate-induced gap itself does not break the symmetry that maps one valley onto the other, and hence does not yield a net charge-Hall effect. The net charge-Hall conductivity is found to be sizable and should be observable in the presence of both the gap and the strain. The sign of the Hall conductivity can be tuned by varying the strain parameters. The valley-Hall conductivity is studied as well. The valley and the orbital magnetic moment accumulations on the sample edges may be detected in a Hall conductivity experiment.