The electron transport of different conical valleys is investigated in graphene with extended line-defects. Intriguingly, the electron with a definite incident angle can be completely modulated into one conical valley by a resonator which consists of several paralleling line-defects. The related incident angle can be controlled easily by tuning the parameters of the resonator. Therefore, a controllable 100% valley polarization, as well as the detection of the valley polarization, can be realized conveniently by tuning the number of line-defects and the distance between two nearest neighbouring line-defects. This fascinating finding opens a way to realize the valley polarization by line-defects. With the advancement of experimental technologies, this resonator is promising to be realized and thus plays a key role in graphene valleytronics.
It is quite easy to control spin polarization and spin direction of a system via magnetic fields. However, there is no such a direct and efficient way to manipulate valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. The pseudomagnetic fields, which are quite different from real magnetic fields, pointing in opposite directions at the two distinct valleys of graphene. Therefore, coexistence of the pseudomagnetic fie…
Valley polarization in graphene breaks inversion symmetry and therefore leads to second-harmonic generation. We present a complete theory of this effect within a single-particle approximation. It is shown that this may be a sensitive tool to measure the valley polarization created, e.g., by polarized light and, thus, can be used for a development of ultrafast valleytronics in graphene.
The valley degeneracy of electron states in graphene stimulates intensive research of valley-related optical and transport phenomena. While many proposals on how to manipulate valley states have been put forward, experimental access to the valley polarization in graphene is still a challenge. Here, we develop a theory of the second optical harmonic generation in graphene and show that this effect can be used to measure the degree and sign of the valley polarization. We show that, at the normal incidence of radiation, the second harmonic generation stems from imbalance of carrier populations in…
The two inequivalent valleys in graphene preclude the protection against inter-valley scattering offered by an odd-number of Dirac cones characteristic of Z2 topological insulator phases. Here we propose a way to engineer a chiral single-valley metallic phase with quadratic crossover in a honeycomb lattice through tailored \sqrt{3}N *\sqrt{3}N or 3N *3N superlattices. The possibility of tuning valley-polarization via pseudo-Zeeman field and the emergence of Dresselhaus-type valley-orbit coupling are proposed in adatom decorated graphene superlattices. Such valley manipulation mechanisms and me…
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…
We investigate physical properties that can be used to distinguish the valley degree of freedom in systems where inversion symmetry is broken, using graphene systems as examples. We show that the pseudospin associated with the valley index of carriers has an intrinsic magnetic moment, in close analogy with the Bohr magneton for the electron spin. There is also a valley dependent Berry phase effect that can result in a valley contrasting Hall transport, with carriers in different valleys turning into opposite directions transverse to an in-plane electric field. These effects can be used to gene…
Silicon has many attractive properties for quantum computing, and the quantum dot architecture is appealing because of its controllability and scalability. However, the multiple valleys in the silicon conduction band are potentially a serious source of decoherence for spin-based quantum dot qubits. Only when these valleys are split by a large energy does one obtain well-defined and long-lived spin states appropriate for quantum computing. Here we show that the small valley splittings observed in previous experiments on Si/SiGe heterostructures result from atomic steps at the quantum well inter…
Atomically precise tailoring of graphene can enable unusual transport pathways and new nanometer-scale functional devices. Here we describe a recipe for the controlled production of highly regular "5-5-8" line defects in graphene by means of simultaneous electron irradiation and Joule heating by applied electric current. High-resolution transmission electron microscopy reveals individual steps of the growth process. Extending earlier theoretical work suggesting valley-discriminating capabilities of a graphene 5-5-8 line defect, we perform first-principles calculations of transport and find a s…
In strained graphene, lattice deformation can create pseudo-magnetic fields and result in zero-field Landau level-like quantization. In the presence of an external magnetic field, valley-polarized Landau levels are predicted to be observed because the pseudo-magnetic fields are of opposite directions in the K and K' valleys of graphene. Here, we present experimental spectroscopic measurements by scanning tunneling microscopy of strained graphene on Rh foil. We direct observed valley splitting of the Landau level induced by the coexistence of the pseudo-magnetic fields and external magnetic fie…
We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic si…
Gapless bilayer graphene is susceptible to a variety of spontaneously gapped states. As predicted by theory and observed by experiment, the ground state is however topologically trivial, because a valley-independent gap is energetically favorable. Here, we show that under the application of interlayer electric field and circularly polarized light, one valley can be selected to exhibit the original interaction instability while the other is frozen out. Tuning this Floquet system stabilizes multiple competing topological ordered states, distinguishable by edge transport and circular dichroism. N…
A system in a quantum superposition of distinct states usually exhibits many peculiar behaviors. Here we show that putting quasiparticles of graphene into superpositions of states in the two valleys can complete change the properties of the massless Dirac fermions. Due to the coexistence of both the quantum and relativistic characteristics, the superposition states exhibit many oddball behaviors in their chiral tunneling process. We further demonstrate that a recently observed line defect in graphene could be used to generate such superposition states. A possible experimental device to detect …
Valley polarized topological kink states, existing broadly in the domain wall of hexagonal lattices systems, are identified in experiments, unfortunately, only very limited physical properties being given. Using an Aharanov-Bohm interferometer composed of domain walls in graphene systems, we study the periodical modulation of pure valley current in a large range by tuning the magnetic field or the Fermi level. For monolayer graphene device, there exists one topological kink state, and the oscillation of transmission coefficients have single period. The $π$ Berry phase and the linear dispersion…
We analyze the problem of electronic transmission through different regions of a graphene sheet that are characterized by different types of connections between the Dirac points. These valley symmetry breaking Hamiltonians might arise from electronic self-interaction mediated by the dielectric environment of distinct parts of the substrate on which the graphene sheet is placed. We show that it is possible to have situations in which we can use these regions to select or filter states of one desired chirality.
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…
Quantum transport calculations describing electron scattering off an extended line defect in graphene are presented. The calculations include potentials from local magnetic moments recently predicted to exist on sites adjacent to the line defect. The transmission probability is derived and expressed as a function of valley, spin, and angle of incidence of an electron at the Fermi level being scattered. It is shown that the previously predicted valley polarization in a beam of transmitted electrons is not significantly influenced by the presence of the magnetic moments. These moments, however, …
We study analytically and numerically the magnetotransport of strained graphene in a Corbino geometry gating in the presence of an external perpendicular magnetic field. The conductance of the Corbino disc of deformed graphene with a uniaxial and an inhomogeneous strain is calculated by using the Landauer-Büttiker method. We show that the oscillation period of the conductance as a function of the magnetic flux depends on uniaxial strain and the conductance sharply drops along the direction of graphene stretching. The conductance amplitude, on the other hand, can be manipulated by induced pseud…
Here we show that twisted graphene trilayer made by misoriented stacking a graphene monolayer on top of a Bernal graphene bilayer can exhibit rich and tailored electronic properties. For the case that the graphene monolayer and bilayer are strongly coupled, both the massless Dirac fermions and massive chiral fermions coexist in the twisted trilayer, leading to unique in-plane chiral tunneling. For a weak coupling between the two graphene systems, the distinct chiralities and pseudospin textures of quasiparticles in monolayer and bilayer enable vertical valley-polarized quantum tunneling betwee…
We analyze universal conductance fluctuations (UCF) in graphene in the framework of diagrammatic perturbation theory in the metallic regime. It is shown that strong inter-valley scattering lifts the valley degeneracy of electronic states, whereas at weak inter-valley scattering two valleys contribute independently such that the variance of UCF would be expected to show sample- and geometry-dependent behavior.
Graphene on hBN (G/hBN) has a long period moiré superstructure owing to the lattice mismatch between two materials. Long periodic potential caused by the moiré superstructure induces modulation of electronic properties of the system. In this paper, we numerically calculate optical conductivity of G/hBN under circularly polarized light irradiation. The lack of spatial inversion symmetry in G/hBN induces the valley polarization. In further, the valley polarization becomes most pronounced in the infrared and terahertz regions if the twist angle between two materials is close to zero for non-dopin…
Spatially varying strained graphene can acquire interesting electronic properties because of the strain-induced valley-dependent gauge (pseudomagnetic) fields1,2. Here we report the realization of strained graphene regions located close to the step edges of Cu(111), obtained by using thermal strain engineering3,4. We study these strained structures with sub-nanometre-resolved scanning tunnelling microscopy and spectroscopy and identify their spatially modulated Dirac points, demonstrating the effect of overlap of Cu and graphene wave functions on the charge transfer between them5. By applying …
The paper addresses boundary electronic properties of graphene with a complex edge structure of the armchair/zigzag/armchair type. It is shown that the finite zigzag region supports edge bound states with discrete equidistant spectrum obtained from the Green's function of the continuum Dirac equation. The energy levels exhibit the coupling between the valley degree of freedom and the orbital quantum number, analogous to a spin-orbit interaction. The characteristic feature of the spectrum is the presence of a zero mode, the bound state of vanishing energy. It resides only in one of the graphene…
When graphene is deformed in a dynamical manner, a time-dependent potential is induced for the electrons. The potential is antisymmetric with respect to valleys, and some straightforward applications are found for Raman spectroscopy. We show that a valley-antisymmetric potential broadens Raman $D$ band but does not affect $2D$ band, which is already observed by recent experiments. The space derivative of the valley antisymmetric potential gives a force field that accelerates intervalley phonons, while it corresponds to the longitudinal component of the previously discussed pseudoelectric field…
We show that the optical excitation of graphene with polarized light leads to the pure valley current where carriers in the valleys counterflow. The current in each valley originates from asymmetry of optical transitions and electron scattering by impurities owing to the warping of electron energy spectrum. The valley current has strong polarization dependence, its direction is opposite for normally incident beams of orthogonal linear polarizations. In undoped graphene on a substrate with high susceptibility, electron-electron scattering leads to an additional contribution to the valley curren…
The conduction properties of a grain boundary junction with Fermi velocity mismatch are analyzed. We provide a generalization of the Dirac Hamiltonian model taking into account the Fermi velocity gradient at the interface. General boundary conditions for the scattering problem are derived within the framework of the matching matrix method. We show that the scattering properties of the interface, as predicted by the theory, strongly depend on the boundary conditions used. We demonstrate that when the valley degeneracy is broken a charge current is established at the grain boundary interface. Th…
Quantum manipulation of valleys in bilayer graphene is investigated. We establish an effective Schrodinger model, and identify two key mechanisms for valley manipulation - band structure warping and generalized valley-orbit interaction. Specifically, we implement valley qubits / FETs in bilayer graphene, as prospective quantum devices to build valley-based quantum / classical information processing.
Van der Waals heterostructures made of graphene and transition metal dichalcogenides (TMD) are an emerging platform for opto-electronic, -spintronic and -valleytronic devices that could benefit from (i) strong light-matter interactions and spin-valley locking in TMDs and (ii) exceptional electron and spin transport in graphene. The operation of such devices requires significant valley polarization and valley coherence, ideally up to room temperature. Here, using a comprehensive Mueller polarimetry analysis, we report \textit{artifact-free} room temperature degrees of valley polarization up to …
We investigate charge, valley, and spin transports in normal/ferromagnetic/normal silicene junc- tion. We show that the charge, valley, and spin conductances in this junction oscillate with the length of the ferromagnetic silicene. It is also found that the current through this junction is valley and spin polarized due to the coupling between valley and spin degrees of freedom, and the valley and spin polarizations can be tuned by local application of a gate voltage. In particular, we find fully valley and spin polarized current by applying the electric field. We also obtain the condition for …
Graphene's outstanding mechanical properties lend to strain engineering, allowing for future valleytronics and nanoelectromechanic applications. In this work, we have found that a Gaussian-shaped strain on a graphene p-n junction results in quantum Hall conductance oscillations due to the rotated angle between valley isospins at the graphene armchair edges. Furthermore, additional Fano resonances were observed as the value of the strain-induced pseudo-magnetic field approaches that of the external magnetic field. The lifted valley degeneracy, stemming from the interplay between the real and ps…
We study intrinsic DC spin and valley Hall conductivity in doped ferromagnetic silicene in the presence of an electric filed applied perpendicular to silicene sheet. By calculating its energy spectrum and wavefunction and by making use of Kubo formalism, we obtain a general relation for the transverse Hall conductivity which can be used to obtain spin- and valley-Hall conductivity. Our results, in the zero limit of the exchange field, reduces to the previous results. Furthermore we discuss electrically tunable spin and valley polarized transport in ferromagnetic silicene and obtain the necessa…
The theoretical results are presented showing that strain-induced anisotropy of graphene spectrum gives rise to the valley currents under the illumination by normally incident light. The currents of the two graphene valleys are mutually compensated providing zero net electric current. The magnitude and direction of the valley currents are determined by the parameters of strain and light polarization. For not too high photon energy strain-induced valley current exceed that due to intrinsic warping of the graphene spectrum which suggests feasibility of strain-mediated valleytronics.
Probing and controlling the valley degree of freedom in graphene systems by transport measurements has been a major challenge to fully exploit the unique properties of this two-dimensional material. In this theoretical work, we show that this goal can be achieved by a quantum-wire geometry made of gapped graphene that acts as a valley filter with the following favorable features: i) all electrical gate control, ii) electrically switchable valley polarity, iii) robustness against configuration fluctuation, and iv) potential for room temperature operation. This valley filtering is accomplished b…
We provide a critical discussion concerning the claim of topological valley currents, driven by a global Berry curvature and valley Hall effect proposed in recent literature. After pointing out a major inconsistency of the theoretical scenario proposed to interpret giant nonlocal resistance, we discuss various possible alternative explanations and open directions of research to solve the mystery of nonlocal transport in graphene superlattices.
An analogue of the Datta-Das spin FET is investigated, which is all-graphene and based on the valley degree of freedom of electrons / holes. The "valley FET" envisioned consists of a quantum wire of gapped graphene (channel) sandwiched between two armchair graphene nanoribbons (source and drain), with the following correspondence to the spin FET: valley (K and K') \leftrightarrow spin (up and down), armchair graphene nanoribbons \leftrightarrow ferromagnetic electrodes, graphene quantum wire \leftrightarrow semiconductor quantum wire, valley-orbit interaction \leftrightarrow Rashba spin-orbit …
In addition to electron charge and spin, novel materials host another degree of freedom, the valley. For a junction composed of valley filter sandwiched by two normal terminals, we focus on the valley efficiency under disorder with two valley filter models based on monolayer and bilayer graphene. Applying the transfer matrix method, valley resolved transmission coefficients are obtained. We find that: i) under weak disorder, when the line defect length is over about $15\rm nm$, it functions as a perfect channel (quantized conductance) and valley filter (totally polarized); ii) in the diffusive…
With its two degenerate valleys at the Fermi level, the band structure of graphene provides the opportunity to develop unconventional electronic applications. Herein, we show that electron and hole quasiparticles in graphene can be filtered according to which valley they occupy without the need to introduce confinement. The proposed valley filter is based on scattering off a recently observed line defect in graphene. Quantum transport calculations show that the line defect is semitransparent and that quasiparticles arriving at the line defect with a high angle of incidence are transmitted with…
It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate vol…
In graphene, the valleys represent spin-like quantities and can act as a physical resource in valley-based electronics to novel quantum computation schemes. Here we demonstrate a direct route to tune and read the valley quantum states of disordered graphene by measuring the mesoscopic conductance fluctuations. We show that the conductance fluctuations in graphene at low temperatures are reduced by a factor of four when valley triplet states are gapped in the presence of short range potential scatterers at high carrier densities. We also show that this implies a gate tunable universal symmetry …
In this work we investigate the effects of a Fermi velocity modulation in a valley filter in graphene created by a combination of a magnetic and electric barrier. With the effective Dirac equation of the system, we use the transfer matrix formalism to obtain the transmittance. We verify that the valley transport in graphene is very sensitive to a Fermi velocity modulation, which is able to choose which valley will be filtered with perfect filtering. Also, it is possible to use a Fermi velocity modulation to filter both valleys or to make the valley filter transparent. It reveals that the Fermi…
Achieving a population imbalance between the two inequivalent valleys is a critical first step for any valleytronic device. A valley-polarization can be induced in biased bilayer graphene using circularly polarized light. In this paper, we present a detailed theoretical study of valley-polarization in biased bilayer graphene. We show that a nearly perfect valley-polarization can be achieved with the proper choices of external bias and pulse frequency. We find that the optimal pulse frequency $ω$ is given by $\hbarω=2a,$ where $2a$ is the potential energy difference between the graphene layers.…
Analogous to charge and spin, electrons in solids endows an additional degree of freedom: the valley pseudospin. Two-dimensional hexagonal materials such as graphene exhibit two valleys, labelled as $\mathbf{K}$ and $\mathbf{K}^{\prime}$. These two valleys have the potential to realise logical operations in two-dimensional materials. Obtaining the desired control over valley polarisation between the two valleys is a prerequisite for the logical operations. Recently, it was shown that two counter-rotating circularly polarised laser pulses can induce a significant valley-polarisation in graphene…
The generation of valley current is a fundamental goal in graphene valleytronics but no practical ways of its realization are known yet. We propose a workable scheme for the generation of bulk valley current in a graphene mechanical resonator through adiabatic cyclic deformations of the strains and chemical potential in the suspended region. The accompanied strain gauge fields can break the spatial mirror symmetry of the problem within each of the two inequivalent valleys, leading to a fnite valley current due to quantum pumping. An all-electrical measurement configuration is designed to detec…
Dirac electrons in graphene have a valley degree of freedom that is being explored as a carrier of information. In that context of "valleytronics" one seeks to coherently manipulate the valley index. Here we show that reflection from a superlattice potential can provide a valley switch: Electrons approaching a pristine-graphene--superlattice-graphene interface near normal incidence are reflected in the opposite valley. We identify the topological origin of this valley switch, by mapping the problem onto that of Andreev reflection from a topological superconductor, with the electron-hole degree…
We study transport in twisted bilayer graphene and show that electrostatic barriers can act as valley splitters, where electrons from the $K$ ($K'$) valley are transmitted only to e.g.\ the top (bottom) layer, leading to valley-layer locked currents. We show that such a valley splitter is obtained when the barrier varies slowly on the moiré scale and induces a Lifshitz transition across the junction, i.e.\ a change in the Fermi surface topology. Furthermore, we show that for a given valley the reflected and transmitted current are transversely deflected, as time-reversal symmetry is effectivel…
We study the non-equilibrium dynamics in a mesoscopic graphene ring excited by picoseconds shaped electromagnetic pulses. We predict an ultrafast buildup of charge polarization, currents and orbital magnetization. Applying the light pulses identified here, non-equilibrium valley currents are generated in a graphene ring threaded by a stationary magnetic flux. We predict a finite graphene ring magnetization even for a vanishing charge current; the magnetization emerges due to the light-induced difference of the valley populations.
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 generation of a fully valley-polarized current (FVPC) in bulk graphene is a fundamental goal in valleytronics. To this end, we investigate valley-dependent transport through a strained graphene modulated by a finite magnetic superlattice. It is found that this device allows a coexistence of insulating transmission gap of one valley and metallic resonant band of the other. Accordingly, a substantial bulk FVPC appears in a wide range of edge orientation and temperature, which can be effectively tuned by structural parameters. A valley-resolved Hall configuration is designed to measure the va…
A pseudo-magnetic field kink can be realized along a graphene nanoribbon using strain engineering. Electron transport along this kink is governed by snake states that are characterized by a single propagation direction. Those pseudo-magnetic fields point towards opposite directions in the K and K' valleys, leading to valley polarized snake states. In a graphene nanoribbon with armchair edges this effect results in a valley filter that is based only on strain engineering. We discuss how to maximize this valley filtering by adjusting the parameters that define the stress distribution along the g…
Considering the difference of energy bands in graphene and silicene, we put forward a new model of the graphene-silicene-graphene (GSG) heterojunction. In the GSG, we study the valley polarization properties in a zigzag nanoribbon in the presence of an external electric field. We find the energy range associated with the bulk gap of silicene has a valley polarization more than 95%. Under the protection of the topological edge states of the silicene, the valley polarization remains even the small non-magnetic disorder is introduced. These results have certain practical significance in applicati…
We demonstrate theoretically how local strains in graphene can be tailored to generate a valley polarized current. By suitable engineering of local strain profiles, we find that electrons in opposite valleys (K or K') show different Brewster-like angles and Goos-Hänchen shifts, exhibiting a close analogy with light propagating behavior. In a strain-induced waveguide, electrons in K and K' valleys have different group velocities, which can be used to construct a valley filter in graphene without the need for any external fields.
We propose a directional switching effect in a metallic device. To such end we exploit a graphene-based device with a three-terminal geometry in the presence of a magnetic field. We show that unidirectional charge and valley currents can be controlled by the Fermi energy and the magnetic field direction in the active device. Interestingly, unidirectional transport of charge and valley is generated between two-terminals at the same bias voltage. Furthermore, we quantify the valley depolarization as a function of disorder concentration. Our results open a way for active graphene-based valleytron…
