We propose an all-electrical setup to generate valley polarization in graphene. A finite graphene sheet is connected to two normal metal electrodes each with two terminals along its zigzag edges, while the armchair edges remain free. When a bias is applied to one terminal and the others are grounded, valley polarization emerges due to transverse momentum matching between the graphene and the metal electrodes. Significant valley polarization is achieved when the Fermi wavevector in the metal exceeds half the separation between the \( K \) and \( K' \) valleys in graphene. We analyze how conductance and valley polarization depend on geometric and electronic parameters. While increasing the width enhances both conductance and polarization, increasing the length introduces Fabry--Pérot oscillations and suppresses valley polarization due to enhanced intervalley mixing. We also examine the effects of disorder: on-site disorder in graphene increases conductance near the Dirac point but reduces valley polarization. Finally, we study the impact of imperfect armchair edges and interface roughness, finding that moderate deviations from ideal conditions still yield substantial valley polarization. Our results demonstrate a viable route to electrically controlling valley degrees of freedom in graphene-based devices.
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…
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…
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…
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.…
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 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…
Intrinsic and extrinsic valley Hall effects are predicted to emerge in graphene systems with uniform or spatially-varying mass terms. Extrinsic mechanisms, mediated by the valley-dependent scattering of electrons at the Fermi surface, can be directly linked to quantum transport simulations. This is a promising route towards more complete experimental investigation of valleytronic phenomena in graphene, but a major obstacle is the difficulty in applying the sublattice-dependent potentials required. Here we show that strongly valley-dependent scattering also emerges from bilayer graphene quantum…
Recent experiments have revealed that novel nonequilibrium states consistent with the hydrodynamic description of electrons are realized in ultrapure graphene, which hosts the valley degrees of freedom. Here, we formulate a theory of electron hydrodynamics including dissipation processes of the valley angular momentum by employing the concept of micropolar fluids. As a result, our theory proposes a novel strategy to generate a valley polarization by the microrotation. We uncover that the rotational viscosity induces longitudinal valley currents which are second order in electric fields.
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experienc…
We study theoretically the electron current across a monolayer graphene/hexagonal boron nitride/bilayer graphene tunnelling junction in an external magnetic field perpendicular to the layers. We show that change in effective tunnelling barrier width for electrons on different graphene layers of bilayer graphene, coupled with the fact that its Landau level wave functions are not equally distributed amongst the layers with a distribution that is reversed between the two valleys, lead to valley polarisation of the tunnelling current. We estimate that valley polarisation $\sim 70\%$ can be achieve…
Valley filtering processes have been explored in different graphene-based configurations and scenarios to control transport responses. Here we propose graphene multi-terminal set-ups properly designed to obtain valley filtered currents in a broad range of energy, besides the possibility of controlling their directions. We explore graphene systems with extended mechanical fold-like deformations as an opportunity to enhance valley filtered transmission. The mixing between the electronic confinement effects due to a magnetic field and strain results in a selective drive of the current components …
We theoretically investigate gate-defined graphene superlattices with broken inversion symmetry as a platform for realizing tunable valley dependent transport. Our analysis is motivated by recent experiments [C. Forsythe et al., Nat. Nanotechnol. 13, 566 (2018)] wherein gate-tunable superlattice potentials have been induced on graphene by nanostructuring a dielectric in the graphene/patterneddielectric/gate structure. We demonstrate how the electronic tight-binding structure of the superlattice system resembles a gapped Dirac model with associated valley dependent transport using an unfolding …
We propose a device in which a sheet of graphene is coupled to a Weyl semimetal, allowing for the physical access to the study of tunneling from two-dimensional to three dimensional massless Dirac fermions. Due to the reconstructed band structure, we find that this device acts as a robust valley filter for electrons in the graphene sheet. We show that, by appropriate alignment, the Weyl semimetal draws away current in one of the two graphene valleys while allowing current in the other to pass unimpeded. In contrast to other proposed valley filters, the mechanism of our proposed device occurs i…
Coherent manipulation of binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid state systems, while exploitation of the valley has only recently been started, yet without control on the single electron level. Here, we show that van-der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunneling microscope and demonstrate valley splitt…
A valley plasmonic crystal for graphene surface plasmons (GSPs) is proposed. We demonstrate that a designer metagate, placed within a few nanometers from graphene, can be used to impose a triangular periodic Fermi energy landscape on the latter. For specific metagate geometries and bias voltages, the combined metagate-graphene structure is shown to produce sufficiently strong Bragg scattering of GSPs to produce complete propagation bandgaps, and to impart the GSPs with nontrivial valley-linked topological properties. Valley-selective kink states supported by a domain wall between differently p…
We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multi-terminal device responses, the presence of a non-uniform local bandgap is shown to give rise to valley-dependent scattering and a finite Fermi surface contribution to the valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These features are robust…
Electrons in graphene have fourfold spin and valley degeneracies owing to the unique bipartite honeycomb lattice and an extremely weak spin-orbit coupling, which can support a series of broken symmetry states. Atomic-scale defects in graphene are expected to lift these degenerate degrees of freedom at the nanoscale, and hence, lead to rich quantum states, highlighting promising directions for spintronics and valleytronics. In this article, we mainly review the recent scanning tunneling microscopy (STM) advances on the spin and/or valley polarized states induced by an individual atomic-scale de…
We develop a theory of the valley Hall effect in high-quality graphene samples, in which strain fluctuation-induced random gauge potentials have been suggested as the dominant source of disorder. We find a near-quantized value of valley Hall conductivity in the band transport regime, which originates from an enhanced side jump of a Dirac electron when it scatters off the gauge potential. By assuming a small residue charge density our theory reproduces qualitatively the temperature- and gap-dependence of the observed valley Hall effect at the charge neutral point. Our study suggests that the va…
Graphene deposited on top of a Copper(111) substrate may develop a Y-shaped Kekulé bond texture (Kekulé-Y), locking the momentum of its Dirac fermions with its valley degree of freedom. As a consequence, the valley degeneracy of its band structure is broken, generating an energy dispersion with two nested Dirac cones with different Fermi velocities. In this work, we investigate the dynamics of electronic wave packets in the Kekulé-Y superlattice. We show that, as a result of the valley-momentum coupling, a valley-driven oscillatory motion of the wave packets ({\it Zitterbewegung}) could appear…
We present electronic structure and quantum transport calculations that predict conducting channels induced in graphene quantum dots by lines of adsorbed hydrogen atoms to function as highly efficient, experimentally realizable valley filters, accumulators and switches. The underlying physics is a novel property of graphene Dirac point resonances (DPRs) that is revealed here, namely, that an electric current passing through a DPR-mediated conducting channel in a given direction is carried by electrons of em only one of the two graphene valleys. Our predictions apply to lines of hydrogen atoms …
Due to their possibility to encode information and realize low-energy-consumption quantum devices, control and manipulation of the valley degree of freedom have been widely studied in electronic systems. In contrast, the phononic counterpart--valley phononics--has been largely unexplored, despite the importance in both fundamental science and practical applications. In this work, we demonstrate that the control of "valleys" is also applicable for phonons in graphene by using a grain boundary. In particular, perfect valley filtering effect is observed at certain energy windows for flexural mode…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
