Original Dirac Point Research Articles

Coulomb Drag in Graphene/h-BN/Graphene Moiré Heterostructures.

We report on the observation of Coulomb drag between graphene-hexagonal boron nitride (h-BN) moiré heterostructure with a moiré wavelength of ∼14 nm and an intrinsic graphene with a lattice constant of ∼0.25 nm. By tuning carrier densities of each graphene layer independently, we find that charge carriers in moiré minibands, i.e., near satellite Dirac point (sDP), can be coupled with massless Fermions near the original Dirac point (oDP), strongly enough to generate a finite drag resistivity. At high temperature (T) and large density (n), the drag resistivities near both oDP and sDP follow a typical n^{-α} (α=1.3-1.7) and T^{2} power law dependence as expected for the momentum transfer process and it also satisfies the layer reciprocity. In contrast, at low T, the layer reciprocity is broken in both oDP-oDP and sDP-oDP coupled regions that suggest dominant energy drag. Furthermore, quantitatively, the drag resistivities near sDPs are smaller than those near oDP and they deviate from T^{2} dependence below ∼100 K. Our work demonstrates that the drag experiment can be used to investigate the coupling between the carriers in moiré minibands and those in original Dirac bands which can be extended to other moiré materials.

Emergence of symmetric and asymmetric Dirac points under periodic electric and vector potentials in ABA-trilayer graphene superlattice.

We have theoretically investigated the impact of both periodic electric and vector potentials on the low energy spectrum of ABA-trilayer graphene superlattice. Finite energy Dirac points appear in the energy spectrum due to the application of the vector potential. These extra Dirac points are symmetric about k y = 0 plane for equal barrier and well widths. For different barriers and well widths, one Dirac point shifts away and the second Dirac point shifts towards the k y = 0 plane. The extra Dirac points are not only generated from the original Dirac point but also emerge from the valleys developed in the energy spectrum. The application of both electric and vector potentials with identical barrier and well widths breaks the symmetry of the spectrum about the Fermi level. When the electric and vector potentials are asymmetric with all three layers having the same electric potentials, the energy spectrum becomes asymmetric about the Fermi level, and this asymmetric behavior of both potentials annihilates the original Dirac point from the spectrum. When all the layers have different electric potentials and both electric and vector potentials are asymmetric, the spectrum becomes asymmetric again, but this time the asymmetry of the spectrum occurs across the k y = 0 plane.

Quantum anomalous Hall effect in a three-dimensional topological-insulator–thin-film-ferromagnetic-metal heterostructure

We theoretically show that the three-dimensional (3D) topological insulator (TI)/thin-film ferromagnetic metal (FMM) bilayer structure is possible to be a quantum anomalous Hall (QAH) insulator with a wide global band gap. Studying the band structure and the weight distributions of eigenstates, we demonstrate that the attachment of a metallic thin-film on the 3DTI can shift the topologically non-trivial state into the metal layers due to the hybridization of bands around the original Dirac point. By introducing the magnetic exchange interaction in the thin-film layers, we compute the anomalous Hall conductivity and magnetic anisotropy of the bilayer structure to suggest the appearance of wider gap realizing QAH effect than usual materials, such as magnetically doped thin-films of 3DTI and 3DTI/ferromagnetic insulator heterostructures. Our results indicate that the 3DTI/thin-film FMM bilayer structure may implement the QAH effect even at room temperature, which will pave a way to the experimental realization of other exotic topological quantum phenomena.

Zitterbewegung effect in graphene with spacially modulated potential

The Zitterbewegung (ZB) effect is investigated in graphene with spacially modulated potential near the original Dirac point (ODP) and extra Dirac points (EDPs). Our calculations show that to get the large ZB oscillations, the wave packet center must be at the angle $\theta_0=0$ for EDPs located at zero-energy, or $\theta_0=\pi/2$ for both ODP and EDPs at finite energy $\varepsilon=m\pi$ ($m$ integer). By varying the parameters ($q_2, \mathbb{V}$) of the periodic potential and the initial momentum ($\kappa_0, \theta_0$) of Gaussian wave packet, it is found that the frequency of the ZB oscillations is in the range $[10^{7}~\text{Hz}, 10^{13}~\text{Hz}$] depending on what type of EDP is generated and the amplitude reaches hundreds of angstroms but their attenuation becomes very slow. More analysis of the frequency shows the possibilities in experimentally realizing the ZB effect in our system.

Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: Monodromy matrix approach

We analyze the quasienergy-spectrum and the valence to conduction-band transition probabilities of a tilted anisotropic Dirac material subject to linearly and circularly polarized electromagnetic fields. The quasienergy-spectrum is numerically calculated from the monodromy matrix of the Schr\"odinger equation via the Floquet theorem for arbitrarily intense electromagnetic fields. To asses the valence to conduction-band transition times we deduced a Rabi-like formula in the rotating wave approximation. In the strong-field regime the spectrum as a function of the momentum components divides into two very distinctive regions. In the first, located around the Dirac point, the quasi-spectrum is significantly distorted by the field as the electronic parameters are renormalized by electronic-dressing. In the second, all the characteristics of the free carrier spectrum are retained. Linearly polarized light anisotropically deforms the spectrum according to the field polarization direction. Dirac-like points form around the original Dirac point. The quasi spectrum of circularly polarized light, instead, exhibits a gap formation in the Dirac point and has elliptical symmetry. We show that, in contrast to the single-photon resonant transitions that characterize the weak-field regime, the strong-field regime is dominated by multiphoton resonances.

Gap-like feature observed in the non-magnetic topological insulators

Non-magnetic gap at the Dirac point of topological insulators remains an open question in the field. Here, we present angle-resolved photoemission spectroscopy experiments performed on Cr-doped Bi2Se3 and showed that the Dirac point is progressively buried by the bulk bands and a low spectral weight region in the vicinity of the Dirac point appears. These two mechanisms lead to spectral weight suppression region being mistakenly identified as an energy gap in earlier studies. We further calculated the band structure and found that the original Dirac point splits into two nodes due to the impurity resonant states and the energy separation between the nodes is the low density of state region which appears to be like an energy gap in potoemission experiments. We supported our arguments by presenting photoemission experiments carried out with on- and off- resonant photon energies. Our observation resolves the widely debated questions of apparent energy gap opening at the Dirac point without long range ferromagnetic order in topological insulators.

Chemically Functionalised Graphene FET Biosensor for the Label-free Sensing of Exosomes

A graphene field-effect transistor (gFET) was non-covalently functionalised with 1-pyrenebutyric acid N-hydroxysuccinimide ester and conjugated with anti-CD63 antibodies for the label-free detection of exosomes. Using a microfluidic channel, part of a graphene film was exposed to solution. The change in electrical properties of the exposed graphene created an additional minimum alongside the original Dirac point in the drain-source current (Ids) - back-gate voltage (Vg) curve. When phosphate buffered saline (PBS) was present in the channel, the additional minimum was present at a Vg lower than the original Dirac point and shifted with time when exosomes were introduced into the channel. This shift of the minimum from the PBS reference point reached saturation after 30 minutes and was observed for multiple exosome concentrations. Upon conjugation with an isotype control, sensor response to the highest concentration of exosomes was negligible in comparison to that with anti-CD63 antibody, indicating that the functionalised gFET can specifically detect exosomes at least down to 0.1 μg/mL and is sensitive to concentration. Such a gFET biosensor has not been used before for exosome sensing and could be an effective tool for the liquid-biopsy detection of exosomes as biomarkers for early-stage identification of diseases such as cancer.

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the δk→-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum k→ is independent of the Rashba coupling strength.

Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect

Quantum anomalous Hall effect (QAHE), which generates dissipation-less edge current without external magnetic field, is observed in magnetic-ion doped topological insulators (TIs) such as Cr- and V-doped (Bi,Sb)2Te3. The QAHE emerges when the Fermi level is inside the magnetically induced gap around the original Dirac point of the TI surface state. Although the size of gap is reported to be about 50 meV, the observable temperature of QAHE has been limited below 300 mK. We attempt magnetic-Cr modulation doping into topological insulator (Bi,Sb)2Te3 films to increase the observable temperature of QAHE. By introducing the rich-Cr-doped thin (1 nm) layers at the vicinity of both the surfaces based on non-Cr-doped (Bi,Sb)2Te3 films, we have succeeded in observing the QAHE up to 2 K. The improvement in the observable temperature achieved by this modulation-doping appears to be originating from the suppression of the disorder in the surface state interacting with the rich magnetic moments. Such a superlattice designing of the stabilized QAHE may pave a way to dissipation-less electronics based on the higher-temperature and zero magnetic-field quantum conduction.

Electric and magnetic superlattices in trilayer graphene

The properties of one dimensional Kronig–Penney type of periodic electric and vector potential on ABC-trilayer graphene superlattices are investigated. The energy spectra obtained with periodic vector potentials shows the emergence of extra Dirac points in the energy spectrum with finite energies. For identical barrier and well widths, the original as well as the extra Dirac points are located in the ky=0 plane. An asymmetry between the barrier and well widths causes a shift in the extra Dirac points away from the ky=0 plane. Extra Dirac points having same electron hole crossing energy as that of the original Dirac point as well as finite energy Dirac points are generated in the energy spectrum when periodic electric potential is applied to the system. By applying electric and vector potential together, the symmetry of the energy spectrum about the Fermi level is broken. A tunable band gap is induced in the energy spectrum by applying both electric and vector potential simultaneously with different barrier and well widths.

Band structure of ABC-trilayer graphene superlattice

We investigate the effect of one-dimensional periodic potentials on the low energy band structure of ABC trilayer graphene first by assuming that all the three layers have the same potential. Extra Dirac points having the same electron hole crossing energy as that of the original Dirac point are generated by superlattice potentials with equal well and barrier widths. When the potential height is increased, the numbers of extra Dirac points are increased. The dispersions around the Dirac points are not isotropic. It is noted that the dispersion along the ky direction for kx = 0 oscillates between a non-linear dispersion and a linear dispersion when the potential height is increased. When the well and barrier widths are not identical, the symmetry of the conduction and valence bands is broken. The extra Dirac points are shifted either upward or downward depending on the barrier and well widths from the zero energy, while the position of the central Dirac point oscillates with the superlattice potential height. By considering different potentials for different layers, extra Dirac points are generated not from the original Dirac points but from the valleys formed in the energy spectrum. Two extra Dirac points appear from each pair of touched valleys, so four Dirac points appeared in the spectrum at particular barrier height. By increasing the barrier height of superlattice potential two Dirac points merge into the original Dirac point. This emerging and merging of extra Dirac points is different from the equal potential case.

Epitaxial growth of single-domain graphene on hexagonal boron nitride

Hexagonal boron nitride (h-BN) has recently emerged as an excellent substrate for graphene nanodevices, owing to its atomically flat surface and its potential to engineer graphene's electronic structure. Thus far, graphene/h-BN heterostructures have been obtained only through a transfer process, which introduces structural uncertainties due to the random stacking between graphene and h-BN substrate. Here we report the epitaxial growth of single-domain graphene on h-BN by a plasma-assisted deposition method. Large-area graphene single crystals were successfully grown for the first time on h-BN with a fixed stacking orientation. A two-dimensional (2D) superlattice of trigonal moiré pattern was observed on graphene by atomic force microscopy. Extra sets of Dirac points are produced as a result of the trigonal superlattice potential and the quantum Hall effect is observed with the 2D-superlattice-related feature developed in the fan diagram of longitudinal and Hall resistance, and the Dirac fermion physics near the original Dirac point is unperturbed. The macroscopic epitaxial graphene is in principle limited only by the size of the h-BN substrate and our synthesis method is potentially applicable on other flat surfaces. Our growth approach could thus open new ways of graphene band engineering through epitaxy on different substrates.

Subsurface impurities and vacancies in a three-dimensional topological insulator

Using a three-dimensional microscopic lattice model of a strong topological insulator (TI) we study potential impurities and vacancies in surface, subsurface, and bulk positions. For all impurity locations we find impurity-induced resonance states with energy proportional to the inverse of the impurity strength, although the impurity strength needed for a low-energy resonance state increases with the depth of the impurity. For strong impurities and vacancies as deep as 15 layers into the material, resonance peaks will appear at and around the Dirac point in the surface energy spectrum, splitting the original Dirac point into two nodes located off-center. Furthermore, we study vacancy clusters buried deep inside the bulk and find zero-energy resonance states for both single and multiple-site vacancies. Only fully symmetric multiple-site vacancy clusters show resonance states expelled from the bulk gap.

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.

Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point

Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.

Landau Levels and Quantum Hall Effect in Graphene Superlattices

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling become 4(2N + 1)-fold degenerate (with N = 0, 1, 2, ..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity sigma_{xy} showing a step of size 4(2N + 1)e;{2}/h. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.