The existence of nontrivial Berry phases associated with two inequivalent valleys in graphene provides interesting opportunities for investigating the valley-projected topological states. Examples of such studies include observation of anomalous quantum Hall effect in monolayer graphene, demonstration of topological zero modes in molecular graphene assembled by scanning tunneling microscopy, and detection of topological valley transport either in graphene superlattices or at bilayer graphene domain walls. However, all aforementioned experiments involved non-scalable approaches of either mechanically exfoliated flakes or atom-by-atom constructions. Here we report an approach to manipulating the topological states in monolayer graphene via nanoscale strain engineering at room temperature. By placing strain-free monolayer graphene on architected nanostructures to induce global inversion symmetry breaking, we demonstrate the development of giant pseudo-magnetic fields (up to 800 Tesla), valley polarization, and periodic one-dimensional topological channels for protected propagation of chiral modes in strained graphene, thus paving a pathway towards scalable graphene-based valleytronics.
We study a two-dimensional electron system where the electrons occupy two conduction band valleys with anisotropic Fermi contours and strain-tunable occupation. We observe persistent quantum Hall states at filling factors $ν= 1/3$ and 5/3 even at zero strain when the two valleys are degenerate. This is reminiscent of the quantum Hall ferromagnet formed at $ν= 1$ in the same system at zero strain. In the absence of a theory for a system with anisotropic valleys, we compare the energy gaps measured at $ν= 1/3$ and 5/3 to the available theory developed for single-valley, two-spin systems, and fin…
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…
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.
We report measurements of the interaction-induced quantum Hall effect in a spin-polarized AlAs two-dimensional electron system where the electrons occupy two in-plane conduction band valleys. Via the application of in-plane strain, we tune the energies of these valleys and measure the energy gap of the quantum Hall state at filling factor $ν$ = 1. The gap has a finite value even at zero strain and, with strain, rises much faster than expected from a single-particle picture, suggesting that the lowest energy charged excitations at $ν=1$ are "valley Skyrmions".
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 study the effect of the strain on the band structure and the valley-dependent transport property of graphene heterojunctions. It is found that valley-dependent separation of electrons can be achieved by utilizing the strain and on-site energies. In the presence of the strain, the values of the transmission can be effectively adjusted by changing the strengths of the strain, while the transport angle basically keeps unchanged. When an extra on-site energy is simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct tra…
We present a single barrier system to generate pure valley-polarized current in monolayer graphene. A uniaxial strain is applied within the barrier region, which is delineated by localized magnetic field created by ferromagnetic stripes at the regions boundaries. We show that under the condition of matching magnetic field strength, strain potential, and Fermi energy, the transmitted current is composed of only one valley contribution. The desired valley current can transmit with zero reflection while the electrons from the other valley are totally reflected. Thus, the system generates pure val…
The interplay of massive electrons with spin-orbit coupling in bulk graphene results in a spin-valley dependent gap. Thus, a barrier with such properties can act as a filter, transmitting only opposite spins from opposite valleys. In this Letter we show that strain induced pseudomagnetic field in such a barrier will enforce opposite cyclotron trajectories for the filtered valleys, leading to their spatial separation. Since spin is coupled to the valley in the filtered states, this also leads to spin separation, demonstrating a spin-valley filtering effect. The filtering behavior is found to be…
Valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by the deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. We show that valley filtering is most effective with bumps of a certain height and width. Despite the fact that the highest contribution to the polarized current comes from electrons from the lowest sub-band, contributions of other sub-bands are not negligible and can significantly en…
We propose a simple, yet highly efficient and robust device for producing valley polarized current in graphene. The device comprises of two distinct components; a region of uniform uniaxial strain, adjacent to an out-of-plane magnetic barrier configuration formed by patterned ferromagnetic gates. We show that when the amount of strain, magnetic field strength, and Fermi level are properly tuned, the output current can be made to consist of only a single valley contribution. Perfect valley filtering is achievable within experimentally accessible parameters.
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…
We adopt the tight-binding mode-matching method to study the strain effect on silicene heterojunctions. It is found that valley- and spin-dependent separation of electrons cannot be achieved by the electric field only. When a strain and an electric field are simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct transmission lobes in opposite transverse directions, but the up-spin and down-spin electrons will also move in the two opposite transverse directions. Therefore, one can realize an effective modulation of val…
The interplay between topology and valley degree of freedom has attracted much interest because it can realize new phenomena and applications. Here, based on first-principles calculations, we demonstrate intrinsically valley-polarized quantum anomalous Hall effect in monolayer ferrovalley material: Janus VSiGeN4, of which the edge states are chiral-spin-valley locking. Besides, a small tensile or compressive strain can drive phase transition in the material from valley-polarized quantum anomalous Hall state to half-valley-metal state. With the increase of the strain, the material turns into fe…
Strain is extensively used to controllably tailor the electronic properties of materials. In the context of indirect band-gap semiconductors such as silicon, strain lifts the valley degeneracy of the six conduction band minima, and by extension the valley states of electrons bound to phosphorus donors. Here, single phosphorus atoms are embedded in an engineered thin layer of silicon strained to 0.8% and their wave function imaged using spatially resolved spectroscopy. A prevalence of the out-of-plane valleys is confirmed from the real-space images, and a combination of theoretical modelling to…
The valley degrees of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize the valley polarization. Here, we propose a model that the valley polarization transition at different valley points (-K and K points) is produced by biaxial strain. By the first-principle calculations, we illustrate our idea with a concrete example of Janus $\mathrm{GdClF}$ monolayer. The predicted $\mathrm{GdClF}$ monolayer is dynamically, mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor with …
This paper details a complete formalism for calculating electron subband energy and degeneracy in strained multi-valley quantum wells grown along any orientation with explicit results for the AlAs quantum well case. A standardized rotation matrix is defined to transform from the conventional- cubic-cell basis to the quantum-well-transport basis whereby effective mass tensors, valley vectors, strain matrices, anisotropic strain ratios, and scattering vectors are all defined in their respective bases. The specific cases of (001)-, (110)-, and (111)-oriented aluminum arsenide (AlAs) quantum wells…
Previous works on deformed graphene predict the existence of valley-polarized states, however, optimal conditions for their detection remain challenging. We show that in the quantum Hall regime, edge-like states in strained regions can be isolated in energy within Landau gaps. We identify precise conditions for new conducting edges-like states to be valley polarized, with the flexibility of positioning them at chosen locations in the system. A map of local density of states as a function of energy and position reveals a unique braid pattern that serves as a fingerprint to identify valley polar…
Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only pa…
We describe a simple setup generating pure valley currents -- valley transport without charge transport -- in strained graphene nanoribbons with zigzag edges. The crucial ingredient is a uniaxial strain pattern which couples to the low-energy Dirac electrons as a uniform pseudomagnetic field. Remarkably, the resulting pseudo-Landau levels are not flat but disperse linearly from the Dirac points, with an opposite slope in the two valleys. We show how this is a natural consequence of an inhomogeneous Fermi velocity arising in the low-energy theory describing the system, which maps to an exactly-…
We point out a practical way to induce a finite charge Hall conductivity in graphene via an off-diagonal strain. Our conclusions are based on a general analysis and supported by numerical examples. The interplay between a substrate-induced gap and the strain is discussed. We show that the substrate-induced gap itself does not break the symmetry that maps one valley onto the other, and hence does not yield a net charge Hall effect. The net charge Hall conductivity is found to be sizable and should be observable in the presence of both the gap and the strain. The sign of the Hall conductivity ca…
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…
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…
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…
We demonstrate significant modification of the electron-phonon energy loss rate in a many-valley semiconductor system due to lattice mismatch induced strain. We show that the thermal conductance from the electron system to the phonon bath in strained n + Si, at phonon temperatures between 200 mK and 450 mK, is more than an order of magnitude lower than that for a similar unstrained sample.
Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points ($K$ and $K'$) of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points…
Veselago lens focusing in graphene p-n junction is promising for realizations of new generation electron optics devices. However, the effect of the strain-induced Aharonov-Bohm interference in a p-n junction has not been discussed before. We provide an experimentally feasible setup based on the Veselago lens in which the presence of strain can result in both the valley-dependent Lorentz force and Aharonov-Bohm interference. In particular, by employing the Green's function and tight binding methods, we study the strain induced by dislocations and line defects in a p-n junction and show how the …
Measuring degeneracy and broken-symmetry states of a system at nanoscale requires extremely high energy and spatial resolution, which has so far eluded direct observation. Here, we realize measurement of the degeneracy and subtle broken-symmetry states of graphene at nanoscale for the first time. By using edge-free graphene quantum dots, we are able to measure valley splitting and valley-contrasting spin splitting of graphene at the single-electron level. Our experiments detect large valley splitting around atomic defects of graphene due to the coexistence of sublattice symmetry breaking and t…
The magnetoelectric response in inversion-breaking two dimensional Dirac systems induced by strain is analyzed. It is shown that, in the same way that the piezoelectric response in these materials is related to the valley Chern number, the strain-induced magnetoelectric effect is related both to the non trivial Berry curvature and the derivative of the orbital magnetic moment per valley. This phenomenon allows to locally induce and control charge densities by an external magnetic field in strained zones of the sample.
The Berry curvature dipole is a physical quantity that is expected to allow various quantum geometrical phenomena in a range of solid-state systems. Monolayer transition metal dichalcogenides provide an exceptional platform to modulate and investigate the Berry curvature dipole through strain. Here we theoretically demonstrate and experimentally verify for monolayer MoS$_\rm{2}$ the generation of valley orbital magnetization as a response to an in-plane electric field due to the Berry curvature dipole. The measured valley orbital magnetization shows excellent agreement with the calculated Berr…
Mechanical deformations in $α$-$\mathcal{T}_3$ lattices induce local pseudomagnetic fields of opposite directionality for different valleys. When this strain is equipped with a dynamical drive, it generates a complementary valley-asymmetric pseudoelectric field which is expected to accelerate electrons. We propose that by combining these effects by a time-dependent nonuniform strain, tunable valley filtering devices can be engineered that extend beyond the static capabilities. We demonstrate this by implementing an oscillating Gaussian bump centered in a four-terminal Hall bar $α$-$\mathcal{T}…
Strain engineering is a promising approach for suppressing the OFF-state conductance in graphene-based devices that arises from Klein tunnelling. In this work, we derive a comprehensive tight-binding Hamiltonian for strained graphene that incorporates strain-induced effects that have been neglected hitherto, such as the distortion of the unit cell under strain, the effect of strain on the next-nearest neighbor coupling, and the second-order contributions of the strain tensor. We derive the corresponding low-energy effective Hamiltonian about the Dirac points and reformulate the boundary condit…
We test the valley-filtering capabilities of a quantum dot inscribed by locally straining an $α$-$\mathcal{T}_3$ lattice. Specifically, we consider an out-of-plane Gaussian bump in the center of a four-terminal configuration and calculate the generated pseudomagnetic field having an opposite direction for electrons originating from different valleys, the resulting valley-polarized currents, and the conductance between the injector and collector situated opposite one another. Depending on the quantum dot's width and width-to-height ratio, we detect different transport regimes with and without v…
A double peak structure in the magneto-phonon resonance (MPR) spectrum of uniaxial strained graphene, under crossed electric and magnetic fields, is predicted. We focus on the $Γ$ point optical phonon modes coupled to the inter-Landau level transitions $0 \leftrightarrows \pm 1$ where MPR is expected to be more pronounced at high magnetic field. We derive the frequency shifts and the broadenings of the longitudinal (LO) and transverse (TO) optical phonon modes taking into account the effect of the strain modified electronic spectrum on the electron-phonon coupling. We show that the MPR lines a…
We demonstrate tuning of two-dimensional (2D) plasmon spectrum in modulation-doped AlAs quantum wells via the application of in-plane uniaxial strain. We show that dramatic change in the plasma spectrum is caused by strain-induced redistribution of charge carriers between anisotropic $X_x$ and $X_y$ valleys. Discovered piezoplasmonic effect provides a tool to study the band structure of 2D systems. We use piezoplasmonic effect to measure how the inter-valley energy splitting depends on the deformation. This dependency yields the AlAs deformation potential of $E_2 = (5.6 \pm 0.3)$~eV.
We propose a highly efficient silicene device for dual spin and valley filtering. The device consists of two different barrier regions: the first is a region under uniaxial strain, with an exchange field induced by adjacent top and bottom magnetic insulators, while the second comprises of two ferromagnetic stripes which produces a delta-function fringe magnetic field, and a gate electrode to modify the electrochemical potential. For the first region, we investigated the effect of the uniaxial strain in inducing angular separation of the two valley spins in momentum-space, and further spin sepa…
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…
We examine the full static non-linear optical response of uniaxially strained transition metal dichalcogenide monolayers doped with a finite carrier density in the conduction band, in the presence of disorder. We find that the customary shift current is suppressed, yet we identify a strong, valley-dependent non-reciprocal response, which we term a \textit{unidirectional valley-contrasting photo-current} (UVCP). This DC current originates from the combined effect of strain and Kramers symmetry breaking by trigonal warping, while the contributions due to individual valleys can be separated by in…
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 …
Due to its strong bonds graphene can stretch up to 25% of its original size without breaking. Furthermore, mechanical deformations lead to the generation of pseudo-magnetic fields (PMF) that can exceed 300 T. The generated PMF has opposite direction for electrons originating from different valleys. We show that valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by a Gaussian-like deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposi…
The extreme mechanical resilience of graphene and the peculiar coupling it hosts between lattice and electronic degrees of freedom have spawned a strong impetus towards strain-engineered graphene where, on the one hand, strain augments the richness of its phenomenology and makes possible new concepts for electronic devices and, on the other hand, new and extreme physics might take place. Here, we demonstrate that the shape of substrates supporting graphene sheets can be optimized for approachable experiments where strain-induced pseudomagnetic fields (PMF) can be tailored by pressure for direc…
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…
A Kekulé bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekulé-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the…
The valley transport properties of a superlattice of out-of-plane Gaussians deformations are calculated using a Green's function and a Machine Learning approach. Our results show that periodicity significantly improves the valley filter capabilities of a single Gaussian deformation, these manifest themselves in the conductance as a sequence by valley filter plateaus. We establish that the physical effect behind the observed valley notch filter is the coupling between counter-propagating transverse modes; the complex relationship between the design parameters of the superlattice and the valley …
The time evolution of a wavepacket in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudo-magnetic field, on the wave packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K' D…
We systematically study the impact of various electron-acoustic-phonon coupling mechanisms on valley physics in two-dimensional materials. In the static strain limit, we find that Dirac cone tilt and deformation potential have analogous valley Hall response since they fall into the same universality class of pseudospin structure. However, such argument fails for the coupling mechanism with position-dependent Fermi velocity. For the isotropic case, a significant valley Hall effect occurs near charge neutrality similar to the bond-length change, whereas for the anisotropic case, the geometric va…
The low-energy physics of graphene is described by relativistic Dirac fermions with spin and valley degrees of freedom. Mechanical strain can be used to create a pseudo magnetic field pointing to opposite directions in the two valleys. We study interacting electrons in graphene exposed to both an external real magnetic field and a strain-induced pseudo magnetic field. For a certain ratio between these two fields, it is proposed that a fermionic symmetry-protected topological state can be realized. The state is characterized in detail using model wave functions, Chern-Simons field theory, and n…
The polymorph of ${\rm 8-Pmmn}$ borophene is an anisotropic Dirac material with tilted Dirac cones at two valleys. The tilting of the Dirac cones at two valleys are in opposite direction, which manifests itself via valley dependent Landau levels in presence of an in-plane electric field (Hall field). The sensitivity of the Landau levels on valley index causes valley polarized magnetotransport properties in presence of a Hall field, which is in contrast to the monolayer graphene with isotropic non-tilted Dirac cones. The longitudinal conductivity and Hall conductivity are evaluated by using lin…
The electronic, phonon, and thermoelectric properties of a two-dimensional HfS2 monolayer are investigated by using the first-principles calculations combined with the Boltzmann transport theory. The band valleys of the HfS2 monolayer can be effectively tuned by the applied biaxial strain. The Seebeck coefficient and therefore the peak value of the power factor (with the relaxation time inserted) increase when the degeneracy of the band valleys is increased by the strain. When no strain is applied, the HfS2 monolayer is an excellent n-type thermoelectric material, while the thermoelectric perf…
