Standing waves near the zigzag and armchair edges, and their Berry's phases are investigated. It is suggested that the Berry's phase for the standing wave near the zigzag edge is trivial, while that near the armchair edge is non-trivial. A non-trivial Berry's phase implies the presence of a singularity in parameter space. We have confirmed that the Dirac singularity is absent (present) in the parameter space for the standing wave near the zigzag (armchair) edge. The absence of the Dirac singularity has a direct consequence in the local density of states near the zigzag edge. The transport properties of graphene nanoribbons observed by recent numerical simulations and experiments are discussed from the point of view of the Berry's phases for the standing waves.
Since its discovery, Berry phase has been demonstrated to play an important role in many quantum systems. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2pi, which offers a unique opportunity to explore the tunable Berry phase on the physical phenomena. Here, we report experimental observation of Berry phases-induced valley splitting and crossing in moveable bilayer graphene p-n junction resonators. In our experiment, the bilayer graphene resonators are generated by combining the electric field of scanning tunneling microscope tip with the gap of bila…
Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2pi [K. S. Novoselov et al., "Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene", Nature Phys. 2, 177 (2006)], it has been widely accepted that the low-energy electronic wavefunction in this system is described by a non-trivial Berry phase of 2pi, different from the zero phase of a conventional two-dimensional electron gas. Here, we show that (i) the relevant Berry phase for bilayer graphene is not different from that for a conventional two-dimensional el…
Berry phase plays an important role in determining many physical properties of quantum systems. However, a Berry phase altering energy spectrum of a quantum system is comparatively rare. Here, we report an unusual tunable valley polarized energy spectra induced by continuously tunable Berry phase in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about pi to 2pi by perpendicular magnetic fields. When the Berry phase equals pi or 2pi, the electron states in the two inequivalent valleys are energetically degen…
When a gap of tunable size opens at the conic band intersections of graphene, the Berry phase does not vanish abruptly, but progressively decreases as the gap increases. The phase depends on the reciprocal-space path radius, i.e., for a doped system, the Fermi wave vector. The phase and its observable consequences can thus be tuned continuously via gap opening --by a modulating potential induced by strain, epitaxy, or nanostructuration-- and doping adjustment.
Brillouin zones of graphene systems possess Dirac points, where band degeneracies occur. We study the variety of (and large magnitude) phases that the electronic states can acquire when a uniform time-dependent electric field carries the electrons around one or more Dirac points in a non-concentric fashion. An experimentally accessible determination of excess Berry phases is proposed involving the Zitterbewegung of electronic current near an orthogonality point in adiabatic motion.
Klein tunneling in gapless bilayer graphene, perfect reflection of electrons injecting normal to a pn junction, is expected to disappear in the presence of energy band gap induced by external gates. We theoretically show that the Klein effect still exists in gapped bilayer graphene, provided that the gaps in the n and p regions are balanced such that the polarization of electron pseudospin has the same normal component to the bilayer plane in the regions. We attribute the Klein effect to Berry phase $π$ (rather than the conventional value $2 π$ of bilayer graphene) and to electron-hole and tim…
We have found that the Berry phase of bilayer graphene becomes from 2$π$ estimated by Shubnikov-de Haas oscillations when the A-B stacked pristine bilayer graphene experiences the Li-intercalation and sequential Li-desorption process in ultrahigh vacuum. Furthermore, the mobility of such processed bilayer graphene increases around four times larger, ~ 8,000 cm2/V$\cdot$s, than that of the pristine bilayer graphene. This is mainly due to increment of the scattering time and decrement of the cyclotron mass, which can be interpreted as a result of the change of the stacking structure of bilayer g…
Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of 2π. This nontrival topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties, such as anti-Klein tunneling, unconventional quantum Hall effect, and valley Hall effect1-6. Here we show that the quantum interference due to intervalley scattering induced by atomic defects/impurities provides further insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct v…
Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore of crucial importance for technological applications. While the spectral distribution in energy bands is routinely measured by various techniques, it is more difficult to access the topological properties of band structures such as the Berry phase γ. It is usually thought that measuring the Berry phase requires applying external electromagnetic forces because these allow realizing the adiabatic transport on closed trajectories along which qua…
We consider the anomalous thermoelectric transport in gapped single and bilayer graphene where the gap may be due to broken inversion symmetry. In the presence of the gap, non-trivial Berry phase effects can be shown to mediate a transverse thermoelectric voltage in response to an applied temperature gradient even in the absence of a perpendicular magnetic field. This spontaneous, anomalous Nernst effect is nonzero for non-uniform chemical potential in the two inequivalent valleys in the graphene band structure. Conversely, the Nernst response can be used to create a valley-index polarization …
The electronic dispersion of a graphene bilayer is highly dependent on rotational mismatch between layers and can be further manipulated by electrical gating. This allows for an unprecedented control over electronic properties and opens up the possibility of flexible band structure engineering. Here we present novel magnetotransport data in a twisted bilayer, crossing the energetic border between decoupled monolayers and coupled bilayer. In addition a transition in Berry phase between pi and 2pi is observed at intermediate magnetic fields. Analysis of Fermi velocities and gate induced charge c…
The Berry phase of π in graphene is derived in a pedagogical way. The ambiguity of how to calculate this value properly is clarified. Its connection with the unconventional quantum Hall effect in graphene is discussed.
We study the energy spectrum of a graphene bilayer in the presence of transverse electric and magnetic fields. We find that the resulting Landau levels exhibit a nonmonotonic dependence on the electric field, as well as numerous level crossings. This behavior is explained using quasiclassical quantization rules that properly take into account the pseudospin of the quasiparticles. The pseudospin generates the Berry phase, which leads to a shift in energy quantization and results in a pseudo-Zeeman effect. The latter depends on the electric field, alternates in sign among the two valleys, and al…
Single-layer carbon, or graphene, demonstrates amazing transport properties, such as the minimum conductivity near $\frac{4e^2}{h}$ independent of shapes and mobility of samples. This indicates there exist some unusual effects due to specific Dirac dispersion relation of fermion in two dimensions. By deriving fermion-lattice interaction Hamiltonian we show that Berry phases can be produced in fermion states around two Dirac points by relative rotations of two sublattices. The Berry phases in turn remove the degeneracies of energies for states near the Fermi surface, leading to a dynamical inst…
The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry's phase N pi for N-layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate parts at low energy, reflects Berry's phase N pi. It is particularly prominent in trilayers, N=3, with the Fermi circ…
The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wavefunction may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry-phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a small critical magnetic field is reached. This behavior results from turning on a $π$-Berry phase associated wit…
The Berry phase and the group-velocity-based traversal time have been calculated for an asymmetric non-contacted or contacted graphene structure, and significant differences have been observed compared to semiconductor heterostructures. These differences are related to the specific, Dirac-like evolution law of charge carriers in graphene, which introduces a new type of asymmetry. When contacted with electrodes, the symmetry of the Dirac equation is broken by the Schrodinger-type electrons in contacts, so that the Berry phase and traversal time behavior in contacted and non-contacted graphene d…
We investigate the morphology of quasi-free-standing monolayer graphene (QFMLG) formed at several temperatures by hydrogen intercalation and discuss its relationship with transport properties. Features corresponding to incomplete hydrogen intercalation at the graphene-substrate interface are observed by scanning tunneling microscopy on QFMLG formed at 600 and 800°C. They contribute to carrier scattering as charged impurities. Voids in the SiC substrate and wrinkling of graphene appear at 1000°C, and they decrease the carrier mobility significantly.
In the framework of the non-local dielectric theory the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study image-states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by solving numerically the one-dimensional Schr{ö}dinger equation. We compare with the Rydgberg's series for a perfect metal and with experimental values measured on graphene layers grown on Ir and Ru surfaces. For free standing films, the appearance of states with binding energies in between the clas…
We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, ill…
We show that in gapped bilayer graphene, quasiparticle tunneling and the corresponding Berry phase can be controlled such that it exhibits features of single layer graphene such as Klein tunneling. The Berry phase is detected by a high-quality Fabry-Pérot interferometer based on bilayer graphene. By raising the Fermi energy of the charge carriers, we find that the Berry phase can be continuously tuned from $2π$ down to $0.68π$ in gapped bilayer graphene, in contrast to the constant Berry phase of $2π$ in pristine bilayer graphene. Particularly, we observe a Berry phase of $π$, the standard val…
Hamiltonian and eigenstate problem is formulated for a bilayer graphene in terms of Clifford's geometric algebra \textit{Cl}$_{3,1}$. It is shown that such approach allows to perform analytical calculations in a simple way if geometrical algebra rotors are used. The measured quantities are express through spectrum and rotation half-angle of the pseudospin that appears in geometric algebra rotors. Properties of free charge carriers -- pseudospin, velocity and Berry phase -- in a bilayer graphene are investigated in the presence of the external voltage applied between the two layers.
Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $\sim 0.1 {\rm mV} / μ\rm{m}$. This anomalous Hall effect, due to Berry dipole, is strong…
We have observed the quantum Hall effect (QHE) and Shubnikov-de Haas (SdH) oscillations in highly disordered graphene at magnetic fields up to 65 T. Disorder was introduced by hydrogenation of graphene up to a ratio H/C $\approx 0.1\%$. The analysis of SdH oscillations and QHE indicates that the topological part of the Berry phase, proportional to the pseudo-spin winding number, is robust against introduction of disorder by hydrogenation in large scale graphene.
The magnetic effects in ferromagnetic graphene basically depend on the principle of exchange interaction when ferromagntism is induced by depositing an insulator layer on graphene. Here we deal with the consequences of non-uniformity in the exchange coupling strength of the ferromagnetic graphene. We discuss how the in- homogeneity in the coordinate and momentum of the exchange vector field can provide interesting results in the conductivity analysis of the ferromagnetic graphene. Our analysis is based on the Kubo formalism of quantum transport.
We investigate the magnetotransport properties of quasi-free standing epitaxial graphene bilayer on SiC, grown by atmospheric pressure graphitization in Ar, followed by H$_2$ intercalation. At the charge neutrality point the longitudinal resistance shows an insulating behavior, which follows a temperature dependence consistent with variable range hopping transport in a gapped state. In a perpendicular magnetic field, we observe quantum Hall states (QHSs) both at filling factors ($ν$) multiple of four ($ν=4, 8, 12$), as well as broken valley symmetry QHSs at $ν=0$ and $ν=6$. These results unamb…
High-order terahertz (THz) sideband generation (HSG) in semiconductors is a phenomenon with physics similar to high-order harmonic generation but in a much lower frequency regime. It was found that the electron-hole pairs excited by a weak optical laser can accumulate Berry phases along a cyclic path under the driving of a strong THz field. The Berry phases appear as the Faraday rotation angles of the emission signal under short-pulse excitation in monolayer MoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinear optics is applied to biased bilayer graphene with Bernal stack…
With use of simulated friction force microscopy, we study the effect of varying temperature on the frictional properties of suspended graphene. In contrast with the theory of thermally activated friction on the surfaces of three-dimensional materials, kinetic friction is demonstrated to both locally increase and decrease with increasing temperature, depending on sample size, scanning tip diameter, scanning rate, and the externally applied normal load. We attribute the observed effects to the thermally excited flexural ripples intrinsically present in graphene, demonstrating a unique case of te…
We present a study of quasi-free-standing monolayer graphene obtained by intercalation of Au atoms at the interface between the carbon buffer layer (Bu-L) and the silicon-terminated face (0001) of 4H-silicon carbide. Au intercalation is achieved by deposition of atomically thin Au on the Bu-L followed by annealing at 850 °C in an Argon atmosphere. We explore the intercalation of Au and decoupling of the Bu-L into quasi-free-standing monolayer graphene by surface science characterizations and electron transport in top-gated electronic devices. By gate-dependent magnetotransport we find that the…
It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that trigge…
The electron band structure of manganese-adsorbed graphene on an SiC(0001) substrate has been studied using angle-resolved photoemission spectroscopy. Upon introducing manganese atoms, the conduction band of graphene completely disappears and the valence band maximum is observed at 0.4 eV below Fermi energy. At the same time, the slope of the valence band decreases, approaching the electron band structure calculated using the local density approximation method. While the former provides experimental evidence of the formation of nearly free-standing graphene on an SiC substrate, concomitant wit…
With considering the great success of scanning tunnelling microscopy (STM) studies of graphene in the past few years, it is quite surprising to notice that there is still a fundamental contradiction about the reported tunnelling spectra of quasi-free-standing graphene monolayer. Many groups observed V-shape spectra with linearly vanishing density-of-state (DOS) at the Dirac point, whereas, the others reported spectra with a gap of 60 meV pinned to the Fermi level in the quasi-free-standing graphene monolayer. Here we systematically studied the two contradicted tunnelling spectra of the quasi-f…
Inspired by recent experimental realizations of monolayer Fe membranes in graphene perforations, we perform ab initio calculations of Fe monolayers and membranes embedded in graphene in order to assess their structural stability and magnetization. We demonstrate that monolayer Fe has a larger spin magnetization per atom than bulk Fe and that Fe membranes embedded in graphene exhibit spin magnetization comparable to monolayer Fe. We find that free-standing monolayer Fe is structurally more stable in a triangular lattice compared to both square and honeycomb lattices. This is contradictory to th…
We propose a table-top method to obtain bilayer quasi-free-standing epitaxial-graphene (QFSEG) on SiC(0001). By applying a microwave annealing in air to a monolayer epitaxial graphene (EG) grown on SiC(0001), the buffer layer is decoupled from the SiC substrate and becomes the second EG layer as confirmed by the low energy electron diffraction, high-resolution transmission electron microscopy, Raman scattering spectroscopy, X-ray photoelectron spectroscopy, and angle-resolved photoelectron spectroscopy. The most likely mechanism of the decoupling is given by the oxidation of the SiC surface, w…
We describe a method for measuring the Berry curvature from the wave-packet dynamics in perturbed arrays of evanescently coupled optical waveguides with honeycomb lattice structure. To disentangle the effects of the Berry curvature and the energy dispersion we utilize a difference measurement by propagating the wave packet under the influence of a constant external force back and forth. In this way a non-vanishing Berry curvature is obtained for photonic graphene with small sublattice bias or strain, where the relative error between the exact Berry curvature and the one derived from the semicl…
We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field--theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.
A race is held between ten species of organic gas molecules on a graphene substrate driven by thermal gradients via molecular dynamics. Fast conduction of the molecules is observed with selectivity for aromatic compounds. This selectivity stems from the fact that the planar structure of the aromatic molecule helps keep a shorter distance to the substrate, which is the key to the driving force at the gas-solid interface. The drift velocity monotonically increases with decreasing molecule density, with no ballistic transport observable even for a single molecule. A non-linear regime is discovere…
We study the influence of a magnetic flux tube on the possibility to electrostatically confine electrons in a graphene quantum dot. Without magnetic flux tube, the graphene pseudospin is responsible for a quantization of the total angular momentum to half-integer values. On the other hand, with a flux tube containing half a flux quantum, the Aharonov-Bohm phase and Berry phase precisely cancel, and we find a state at zero angular momentum that cannot be confined electrostatically. In this case, true bound states only exist in regular geometries for which states without zero-angular-momentum co…
Si dangling bonds without H termination at the interface of quasi-free standing monolayer graphene (QFMLG) are known scattering centers that can severely affect carrier mobility. In this report, we study the atomic and electronic structure of Si dangling bonds in QFMLG using low-temperature scanning tunneling microscopy/spectroscopy (STM/STS), atomic force microscopy (AFM), and density functional theory (DFT) calculations. Two types of defects with different contrast were observed on a flat terrace by STM and AFM. Their STM contrast varies with bias voltage. In STS, they showed characteristic …
In a magnetic field few-layer graphene supports, at the lowest Landau level, a multiplet of zero-mode levels nearly degenerate in orbitals as well as in spins and valleys. Those pseudo-zero-mode (PZM) levels are generally sensitive to interactions and external perturbations, and have a crossing among themselves or with other higher Landau levels when an external field is swept over a certain range. A close study is made of how such PZM levels evolve when they are gradually brought from empty to filled levels under many-body interactions. It is pointed out that the level spectra generally avoid…
When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dir…
We investigated the utility of free-standing graphene as a transparent sample carrier for imaging nanometer-sized objects by means of low-energy electron holography. The sample preparation for obtaining contamination-free graphene as well as the experimental setup and findings are discussed. For incoming electrons with 66 eV kinetic energy graphene exhibits 27% opacity per layer. Hence, electron holograms of nanometer-sized objects adsorbed on free-standing graphene can be recorded and numerically reconstructed to reveal the object's shapes and distribution. Furthermore, a Moire effect has bee…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry's phase 2pi affecting their quantum dynamics. The L…
In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an \textit{inhomogeneous} lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us \cite{ber0,ber1,ber2}. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in \cite{niu2} and is the analogue of the spin-Hall effect in semiconductors \cite{MURAKAMI, SINOVA}. Our general expressions …
Valley is a useful degree of freedom for non-dissipative electronics since valley current that can flow even in an insulating material does not accompany electronic current. We use dual-gated bilayer graphene in the Hall bar geometry to electrically control broken inversion symmetry or Berry curvature as well as the carrier density to generate and detect the pure valley current. We find a large nonlocal resistance and a cubic scaling between the nonlocal resistance and the local resistivity in the insulating regime at zero-magnetic field and 70 K as evidence of the pure valley current. The ele…
Non-trivial Berry phase of graphene leads to unusual quantum correction to the conductivity. Berry phase of pi in single layer graphene (SLG) and 2pi in bi-layer graphene (BLG) is expected to reveal weak anti-localization (WAL) and weak localization (WL), respectively. However, experimentally both WAL and WL have been observed in graphene devices depending on the strength of different scattering mechanisms. Graphene superlattice having multiple Dirac cones is expected to exhibit pi to 2pi Berry phase transition from primary Dirac cone (PDC) to cloned Dirac cone (CDC). However, its effect on lo…
We theoretically study the phase of the reflection amplitude of an electron (massive Dirac fermion) at a lateral potential step in Bernal-stacked bilayer graphene. The phase shows anomalous jump of $π$, as the electron incidence angle (relative to the normal direction to the step) varies to pass $\pm π/4$. The jump is attributed to the Berry phase associated with the pseudospin-1/2 of the electron. This Berry-phase effect is robust against the band gap opening due to the external electric gates generating the step. We propose an interferometry setup in which collimated waves can be generated a…
This talk presents a study of massless relativistic Dirac fields in three Euclidean dimensions, at finite temperature and density, in the presence of a uniform electromagnetic background. Apart from explaining the behavior of Hall's conductivity for graphene, our results show a direct relationship between the selection of a phase for the Dirac determinant and the generation (or lack thereof) of Berry's phases and Chern-Simons terms.
We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N. For N = 7 the bands become nearly flat, with a small bandwidth of 3.6 meV. The two nearly flat bands coming from the K and K' valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the band…
