Manipulation of resonant tunneling by substrate-induced inhomogeneous energy band gaps in graphene with square superlattice potentials

We investigate the resonant transmission of Dirac electrons through inhomogeneous band gap graphene with square superlattice potentials by transfer matrix method. The effects of the incident angle of the electrons, Fermi energy and substrate-induced Dirac gaps on the transmission are considered. It is found that the Dirac gap of graphene adds another degree of freedom with respect to the incident angle, the Fermi energy and the parameters of periodic superlattice potentials (i.e., the number, width and height of the barriers) for the transmission. In particular, the inhomogeneous Dirac gap induced by staggered substrates can be used to manipulate the transmission. The properties of the conductance and Fano factor at the resonant peaks are found to be affected by the gaps significantly. The results may be helpful for the practical application of graphene-based electronic devices.     

Magnetic Kronig-Penney-type graphene superlattices: finite energy Dirac points with anisotropic velocity renormalization

We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic.     

Magnetic confinement of massless Dirac fermions in graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.     

Gap opening and tuning in single-layer graphene with combined electric and magnetic field modulation

The energy band structure of single-layer graphene under one-dimensional electric and magnetic field modulation is theoretically investigated. The criterion for bandgap opening at the Dirac point is analytically derived with a two-fold degeneracy second-order perturbation method. It is shown that a direct or an indirect bandgap semiconductor could be realized in a single-layer graphene under some specific configurations of the electric and magnetic field arrangement. Due to the bandgap generated in the single-layer graphene,the Klein tunneling observed in pristine graphene is completely suppressed.     

Tunneling of Dirac fermions through magnetic barriers in graphene

We have studied the tunneling of Dirac fermions through magnetic barriers in graphene. Magnetic barriers are produced via delta function-like inhomogeneous magnetic fields in which Dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to Klein paradox caused by electrostatic barriers. The transmission through the magnetic barriers as functions of incident energy and angle of incoming fermions shows characteristic oscillations associated with tunneling resonances. We have also found the confined states in the magnetic barrier region which turn out to correspond to the total internal reflection in the usual optics.     

Band structure and transport property of graphene/h-BN heterostructure under local potentials

We investigate band structure and transport property of lattice-matched graphene/hexagonal boron nitride (h-BN) heterostructure using the tight-binding approach. It shows that local potentials can significantly modify the band structure and the transport property. A method to individually manipulate the edge states by local potentials is proposed, including shifts and other deformations of edge bands. The two-terminal conductance of each layer is quantized but the interlayer conductance is non-quantized due to band mixing. In addition, we explore the Landau level spectrum in graphene/h-BN nanoribbons under both magnetic field and local potentials. The plateaus-like behavior of the interlayer conductance is observed.     

Gate-tunable valley-filter based on suspended graphene with double magnetic barrier structures

We theoretically investigate the effects of strain-induced pseudomagnetic fields on the transmission probability and the ballistic conductance for Dirac fermion transport in suspended graphene. We show that resonant tunneling through double magnetic barriers can be tuned by strain in the suspended region. The valley-resolved transmission peaks are apparently distinguishable owing to the sharpness of the resonant tunneling. With the specific strain, the resonant tunneling is completely suppressed for Dirac fermions occupying the one valley, but the resonant tunneling exists for the other valley. The valley-filtering effect is expected to be measurable by strain engineering. The proposed system can be used to fabricate a graphene valley filter with the large valley polarization almost 100%.     

Wave-vector filtering effect of electric–magnetic barrier in HgTe quantum wells

Because of helicity of electrons in HgTe quantum wells (QWs) with inverted band structure, the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in HgTe QWs. This behavior is similar to Dirac electrons in graphene. In this paper, we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier. We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers. The confining effect will have potential application in nanodevices based on HgTe QWs.     

Demonstration of a new transport regime of photon in two-dimensional photonic crystal

A new transport regime of photon in two-dimensional photonic crystal near the Dirac point has been demonstrated by exact numerical simulation. In this regime, the conductance of photon is inversely proportional to the thickness of sample, which can be described by Dirac equation very well. Both of bulk and surface disorders always reduce the transmission, which is in contrast to the previous theoretical prediction that they increase the conductance of electron at the Dirac point of graphene. However, regular tuning of interface structures can cause the improvement of photon conductance. Furthermore, large conductance fluctuations of photon have also been observed, which is similar to the case of electron in graphene.     

Resonant peak splitting in graphene superlattices with one-dimensional periodic potentials

We have investigated theoretically the resonant tunneling phenomenon of Dirac electrons through graphene superlattices with periodic potentials of square barriers. It is found that there are two resonance conditions for the graphene superlattices. Some of the resonance transmission peaks present N – 1-fold resonance splitting for $ N{\text{-barriers}} $ , which is the analogy of the resonance splitting in semiconductor superlattices. The resonance splitting effect depends on the incidence angle rather than the height and width of the potential. However, there is no explicit splitting rule for the conductance and shot noise, which is different from the magnetic case. Furthermore, the resonant splitting rule of the transmission is not sensitive to the shape of the potential barrier. These properties in graphene superlattices may lead to potential applications in graphene-based electron devices.     

Sub-Poissonian shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.     

Contact conductance between graphene and quantum wires

The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.     

Thermopower and conductance for a graphene p-n junction

The thermopower and conductance in a zigzag graphene p-n junction are studied by using the nonequilibrium Green's function method combined with the tight-binding Hamiltonian. Our results show that the conductance and thermopower of the junction can be modulated by its width, the potential drop, and the applied perpendicular magnetic fields. A narrow graphene p-n junction shows insulating characteristics, and its thermopower is much larger than that of the wider one around the Dirac point. The insulating characteristic of the junction decreases as the width increases. In particular, with increasing junction width or the potential drop, the first conductance plateau is strongly enhanced and the thermopower is inverted around the Dirac point. A perpendicular magnetic field strongly suppresses the conductance and enhances the thermopower in the p-n region. The influence of edge vacancy defects on the conductance and thermopower is also discussed. Our results provide theoretical references for modulating the electronic and thermal properties of a graphene p-n junction by tuning its geometry and working conditions.     

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking(symmetry of sublattices).We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for "local chemical potential" and "local gap".The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states(BSs) has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~+(r),g_m~+(r),and f_m~-(r),g_m~-(r),can be established by SO(2) group.     

Electrical and optoelectronic properties of graphene Schottky contact on Si-nanowire arrays with and without H2O2 treatment

We show a methodology for how to construct Dirac points that occur at the corners of Brillouin zone as the Photonic counterparts of graphene. We use a triangular lattice with circular holes on a silicon substrate to create a Coupled Photonic Crystal Resonator Array (CPCRA) which its cavity resonators play the role of carbon atoms in graphene. At first we draw the band structure of our CPCRA using the tight-binding method. For this purpose we first designed a cavity which its resonant frequency is approximately at the middle of the first H-polarization band gap of the basis triangular lattice. Then we obtained dipole modes and magnetic field distribution of this cavity using the Finite Element Method (FEM). Finally we drew the two bands that construct the Dirac points together with the frequency contour plots for both bands and compared with the Plane Wave Expansion (PWE) and FEM results to prove the existence of Dirac point in the H-polarization band structure of lattices with air holes.     

Fano resonance in electronic transport induced by the magnetic confinement in a graphene nanoribbon

Based on the Floquet scattering theory, a model of graphene-based electronic device is presented, in which electrical transport is controlled by adjusting Dirac fermions energy near resonance conditions. The presence of an oscillating field leads to the Fano resonance in transport through a magnetic structure in an armchair graphene nanoribbon (AGNR). The Fano resonance originates from bound states of the magnetic confinement, according to subband indices in the AGNR. The ballistic conductance is markedly affected by the Fano resonance due to the quasi-one-dimensional nature of AGNRs. The results may help realizing graphene electronics with the resonant characteristics in the conductance.     

Four-terminal impedance of a graphene nanoribbon based structure

The four-terminal impedance is studied in a typical graphene nanoribbon based structure. When two additional voltage probes are attached, the results show that at the Dirac point, both the real and imaginary parts of the impedance are negative. As the Fermi energy deviates from the Dirac point, the real part of impedance oscillates with its sign changing frequently, while the imaginary part becomes vanishingly small. The phase incoherent processes introduced by the voltage probes contribute to inelastic scattering and charge redistribution in the central device region. As a result, the measured conductance is substantially different from the two-terminal measurement of a perfect graphene nanoribbon, indicating the important role of voltage probes in realistic four-terminal measurement.     

Magnetotransport in a graphene monolayer with two tunable magnetic barriers

The magnetotransport property for a monolayer graphene with two turnable magnetic barriers has been investigated by the transfer-matrix method. We show that the parameters of barrier height, width, and interval between two barriers affect the electron wave decaying length, which determine the conductance with parallel or antiparallel magnetization configuration, and consequently the tunneling magnetoresistance (TMR) for the system. Interestingly, a graphene attached by two barriers with different heights can produce a resonant TMR peak at low energy region one order of magnitude larger than that for the system with two same height barriers because that the asymmetry of magnetic barriers block the electron transmission in the case of antiparallel magnetization configuration. The results obtained here may be useful in understanding of electron tunneling in graphene and in designing of graphene-based nanodevices.     

Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schr?dinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.     

Wave-vector filtering effect of the electric-magnetic barrier in HgTe quantum wells

Because of the helicity of electrons in HgTe quantum wells(QWs) with inverted band structures,the electrons cannot be confined by electric barriers since electrons can tunnel the barriers perfectly without backscattering in the HgTe QWs.This behavior is similar to Dirac electrons in graphene.In this paper,we propose a scheme to confine carriers in HgTe QWs using an electric-magnetic barrier.We calculate the transmission of carriers in 2-dimensional HgTe QWs and find that the wave-vector filtering effect of local magnetic fields can confine the carriers.The confining effect will have a potential application in nanodevices based on HgTe QWs.