A kagome lattice is composed of corner-sharing triangles arranged on a honeycomb lattice such that each honeycomb bond hosts a kagome site while each kagome triangle encloses a honeycomb site. Such close relation implies that the two lattices share common features. We predict here that a kagome crystal, similar to the honeycomb lattice graphene, reacts to elastic strain in a unique way that the bulk electronic states in the vicinity of Dirac points are reorganized by the strain-induced pseudomagnetic field into flat Landau levels, while the degenerate edge states in the undeformed crystal become separated in the energy dimension. When the strain is tuned continuously, the resulting scanning pseudomagnetic field gives rise to quantum oscillations in both density of states (DOS) and electric conductivity.
A tight-binding model of 8-Pmmn borophene, a two-dimensional boron crystal, is developed. We confirm that the crystal hosts massless Dirac fermions and the Dirac points are protected by symmetry. Strain is introduced into the model, and it is shown to induce a pseudomagnetic field vector potential and a scalar potential. The dependence of the potentials on the strain tensor is calculated. The physical effects controlled by pseudomagnetic field are discussed.
It is known that Dirac nodes can be present at high-symmetry points of Brillouin zone only for certain space groups. For these cases, the effect of strain is treated by symmetry considerations. The dependence of strain-induced potentials on the strain tensor is found. In all but two cases, the pseudomagnetic field potential is present. It can be used to control valley currents.
Strain fields in graphene giving rise to pseudomagnetic fields have received much attention due to the possibility of mimicking real magnetic fields with magnitudes of greater than 100 Tesla. We examine systems with such strains confined to finite regions ("pseudomagnetic dots") and provide a transparent explanation for the characteristic sublattice polarization occurring in the presence of pseudomagnetic field. In particular, we focus on a triaxial strain leading to a constant field in the central region of the dot. This field causes the formation of pseudo Landau levels, where the zeroth ord…
Gallium nitride nanowire and nanorod substrates with different morphology are prospective platforms allowing to control the local strain distribution in graphene films top of them, resulting in an induction of pseudomagnetic fields. Atomic force microscopy measurements performed in a HybriD mode complemented by scanning electron microscopy allow for a detailed visualization of the strain distribution on graphene surface. Graphene in direct contact with supporting regions is tensile strained, while graphene located in-between is characterized by lower strain. Characteristic tensile strained wri…
We study the effects of strain on the electronic properties and persistent current characteristics of a graphene ring using the Dirac representation. For a slightly deformed graphene ring flake, one obtains sizable pseudomagnetic (gauge) fields that may effectively reduce or enhance locally the applied magnetic flux through the ring. Flux-induced persistent currents in a flat ring have full rotational symmetry throughout the structure; in contrast, we show that currents in the presence of a circularly symmetric deformation are strongly inhomogeneous, due to the underlying symmetries of graphen…
Networks of graphene-based topological domain walls function as nano-scale interferometers of zero-line modes, with magnetic field and(or) scalar potential as the controlling parameters. In the absence of externally applied magnetic or electrical field, strain induces pseudomagnetic field and scalar potential in graphene, which could control the interferometers more efficiently. Two types of strains are considered: (i) Horizontally bending the graphene nanoribbon into circular arc induces nearly uniform pseudomagnetic field; (ii) Helicoidal graphene nanoribbon exhibit nonuniform pseudomagnetic…
Many of the properties of graphene are tied to its lattice structure, allowing for tuning of charge carrier dynamics through mechanical strain. The graphene electro-mechanical coupling yields very large pseudomagnetic fields for small strain fields, up to hundreds of Tesla, which offer new scientific opportunities unattainable with ordinary laboratory magnets. Significant challenges exist in investigation of pseudomagnetic fields, limited by the non-planar graphene geometries in existing demonstrations and the lack of a viable approach to controlling the distribution and intensity of the pseud…
Recent experiments reveal that a scanning tunneling microscopy (STM) probe tip can generate a highly localized strain field in a graphene drumhead, which in turn leads to pseudomagnetic fields in the graphene that can spatially confine graphene charge carriers in a way similar to a lithographically defined quantum dot (QD). While these experimental findings are intriguing, their further implementation in nanoelectronic devices hinges upon the knowledge of key underpinning parameters, which still remain elusive. In this paper, we first summarize the experimental measurements of the deformation …
Realistic relaxed configurations of triaxially strained graphene quantum dots are obtained from unbiased atomistic mechanical simulations. The local electronic structure and quantum transport characteristics of y-junctions based on such dots are studied, revealing that the quasi-uniform pseudomagnetic field induced by strain restricts transport to Landau level- and edge state-assisted resonant tunneling. Valley degeneracy is broken in the presence of an external field, allowing the selective filtering of the valley and chirality of the states assisting in the resonant tunneling. Asymmetric str…
We present a study on the uniformity of the pseudomagnetic field in graphene as a function of the relative orientation between the graphene lattice and straining directions. For this, we strained a regular micron-sized graphene hexagon by deforming it symmetrically by displacing three of its edges. By simulations, we found that the pseudomagnetic field is strongest if the strain is applied perpendicular to the armchair direction of graphene. For a hexagon with a side length of 1 ${\rm μ}$m, the pseudomagnetic field has a maximum of 1.2 T for an applied strain of 3.5% and it is uniform (varianc…
We report on mesoscopic transport fingerprints in disordered graphene caused by strain-field induced pseudomagnetic Landau levels (pLLs). Efficient numerical real space calculations of the Kubo formula are performed for an ordered network of nanobubbles in graphene, creating pseudomagnetic fields up to several hundreds of Tesla, values inaccessible by real magnetic fields. Strain-induced pLLs yield enhanced scattering effects across the energy spectrum resulting in lower mean free path and enhanced localization effects. In the vicinity of the zeroth order pLL, we demonstrate an anomalous trans…
Very recently, the standard description of electrons in strained graphene has been completed by the explicit inclusion of the lattice deformation. Here, the effect of these lattice corrections is taken into account to find the mechanical deformations that generate a uniform pseudomagnetic field inside strained graphene. The main difference when compared with previous proposals in a rectangular geometry, is the need to stretch both zigzag and armchair edges.
The behavior of electrons in strained graphene is usually described using effective pseudomagnetic fields in a Dirac equation. Here we consider the particular case of a spatially constant strain. Our results indicate that lattice corrections are easily understood using a strained reciprocal space, in which the whole energy dispersion is simply shifted and deformed. This leads to a directional dependent Fermi velocity without producing pseudomagnetic fields. The corrections due to atomic wavefunction overlap changes tend to compensate such effects. Also, the analytical expressions for the shift…
A unique attribute of atomically thin quantum materials is the in-situ tunability of their electronic band structure by externally controllable parameters like electrostatic doping, electric field, strain, electron interactions, and displacement or twisting of atomic layers. This unparalleled control of the electronic bands has led to the discovery of a plethora of exotic emergent phenomena. But despite its key role, there is currently no versatile method for mapping the local band structure in advanced 2D materials devices in which the active layer is commonly embedded in various insulating l…
There is a growing effort in creating chiral transport of sound waves. However, most approaches so far are confined to the macroscopic scale. Here, we propose a new approach suitable to the nanoscale which is based on pseudomagnetic fields. These fields are the analogon for sound of the pseudomagnetic field for electrons in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and well-suited for a variety of excitation and readout mecha…
Magnetic effects at optical frequencies are notoriously weak. This is evidenced by the fact that the magnetic permeability of nearly all materials is unity in the optical frequency range, and that magneto-optical devices (such as Faraday isolators) must be large in order to allow for a sufficiently strong effect. In graphene, however, it has been shown that inhomogeneous strains can induce 'pseudomagnetic fields' that behave very similarly to real fields. Here, we show experimentally and theoretically that, by properly structuring a dielectric lattice, it is possible to induce a pseudomagnetic…
In this paper, we investigate the two competing effects of strains and magnetic fields in single-layer graphene to explore its impact on various phenomena of quantum field theory, such as induced charge density, magnetic catalysis, symmetry breaking, dynamical mass generation and magnetization. We show that the interplay between strains and magnetic fields produces not only a breaking of chiral symmetry, as it happens in QED$_{2+1}$, but also parity and time-reversal symmetry breaking. The last two symmetry breakings are related to the dynamical generation of a Haldane mass term. We find that …
Mechanical deformations of graphene induce a term in the Dirac Hamiltonian which is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time dependent oscillating stress applied to a graphene ribbon. The joint Hall-like response to these crossed fields results in a strain-induced charge current along the ribbon. We analyze in detai…
Single-layer graphenes subject to periodic lateral strains are artificial crystals that can support boundary spectra with an intrinsic polarity. These are analyzed by comparing the effects of periodic magnetic fields and strain-induced pseudomagnetic fields that respectively break and preserve time-reversal symmetry. In the former case, a Chern classification of the superlattice minibands with zero total magnetic flux enforces {\it single} counter-propagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counter-propagating modes …
The existence of pseudomagnetic helicons is predicted for strained Dirac and Weyl materials. The corresponding collective modes are reminiscent of the usual helicons in metals in strong magnetic fields but can exist even without a magnetic field due to a strain-induced background pseudomagnetic field. The properties of both pseudomagnetic and magnetic helicons are investigated in Weyl matter using the formalism of the consistent chiral kinetic theory. It is argued that the helicon dispersion relations are affected by the electric and chiral chemical potentials, the chiral shift, and the energy…
In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report a…
We study the effect of a uniform pseudomagnetic field, induced by a strain in a monolayer and double layer of gapped graphene, acting on excitons. For our analysis it is crucial that the pseudomagnetic field acts on the charges of the constituent particles of the excitons, i.e., the electrons and holes, the same way in contrast to a magnetic field. Moreover, using a circularly polarized laser field, the electrons and the holes can be excited only in one valley of the honeycomb lattice of gapped graphene. This breaks the time-reversal symmetry and provides the possibility to observe the various…
It is proposed that strain-induced pseudomagnetic fields in Dirac and Weyl materials could be used as valley and chirality sensitive lenses for beams of Weyl quasiparticles. The study of the (pseudo-)magnetic lenses is performed by using the eikonal approximation for describing the Weyl quasiparticles propagation in magnetic and strain-induced pseudomagnetic fields. Analytical expressions for the locations of the principal foci and the focal lengths are obtained in the paraxial approximation in the models with uniform as well as nonuniform effective magnetic fields inside the lens. The results…
We address the question of the stability of the (fractional) quantum Hall effect (QHE) in presence of pseudomagnetic disorder generated by mechanical deformations of a graphene sheet. Neglecting the potential disorder and taking into account only strain-induced random pseudomagnetic fields, it is possible to write down a Laughlin-like trial ground-state wave function explicitly. Exploiting the Laughlin plasma analogy, we demonstrate that in the case of fluctuating pseudomagnetic fluxes of relatively small amplitude both the integer and fractional quantum Hall effects are always stable upon the…
The electronic behavior in graphene under arbitrary uniaxial deformations, such as foldings or flexural fields is studied by including in the Dirac equation pseudoelectromagnetic fields. General foldings are thus studied by showing that uniaxial deformations can be considered pseudomagnetic fields in the Coulomb gauge norm. This allows to give an expression for the Fermi (zero) energy modes wavefunctions. For random deformations, contact is made with previous works on the quantum Hall effect under random magnetic fields, showing that the density of states has a power law behavior and that the …
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…
The stacking and bending of graphene are trivial but extremely powerful agents of control over graphene's manifold physics. By changing the twist angle, one can drive the system over a plethora of exotic states via strong electron correlation, thanks to the moiré superlattice potentials, while the periodic or triaxial strains induce discretization of the band structure into Landau levels without the need for an external magnetic field. We fabricated a hybrid system comprising both the stacking and bending tuning knobs. We have grown the graphene monolayers by chemical vapor deposition, using $…
Analysis of the strain-induced pseudomagnetic fields (PMFs) generated in graphene nanobulges under three different substrate scenarios shows that, in addition to the shape, the graphene-substrate interaction can crucially determine the overall distribution and magnitude of strain and those fields, in and outside the bulge. We utilize a combination of classical molecular dynamics, continuum mechanics, and tight-binding electronic structure calculations as an unbiased means of studying pressure-induced deformations and the resulting PMF in graphene nanobubbles of various geometries. The interpla…
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 gap equation for Dirac quasiparticles in monolayer graphene in constant magnetic and pseudomagnetic fields, where the latter is due to strain, is studied in a low-energy effective model with contact interactions. Analyzing solutions of the gap equation, the phase diagram of the system in the plane of pseudomagnetic and parallel magnetic fields is obtained in the approximation of the lowest Landau level. The three quantum Hall states, ferromagnetic, antiferromagnetic, and canted antiferromagnetic, are realized in different regions of the phase diagram. It is found that the structure of the …
We study a gapped graphene monolayer in a combination of uniform magnetic field and strain-induced uniform pseudomagnetic field. The presence of two fields completely removes the valley degeneracy. The resulting density of states shows a complicated behaviour that can be tuned by adjusting the strength of the fields. We analyze how these features can be observed in the sublattice, valley and full density of states. The analytical expression for the valley DOS is derived.
The electronic implications of strain in graphene can be captured at low energies by means of pseudovector potentials which can give rise to pseudomagnetic fields. These strain-induced vector potentials arise from the local perturbation to the electronic hopping amplitudes in a tight-binding framework. Here we complete the standard description of the strain-induced vector potential, which accounts only for the hopping perturbation, with the explicit inclusion of the lattice deformations or, equivalently, the deformation of the Brillouin zone. These corrections are linear in strain and are diff…
The superconducting s-wave state in Weyl semimetals in a strong strain-induced pseudomagnetic field is investigated in a model with local four-fermion interaction. It is found that only the inter-node pairing is possible in the lowest pseudo-Landau level approximation. Unlike the case of the lowest Landau level in a conventional magnetic field, the corresponding gap equation has only a trivial solution. Nevertheless, superconductivity can be induced via the proximity effect with a usual s-wave spin-singlet superconductor. Since a pseudomagnetic field is present necessarily at the surface of a …
We examine strain-induced quantized Landau levels in graphene. Specifically, arc-bend strains are found to cause nonuniform pseudomagnetic fields. Using an effective Dirac model which describes the low-energy physics around the nodal points, we show that several of the key qualitative properties of graphene in a strain-induced pseudomagnetic field are different compared to the case of an externally applied physical magnetic field. We discuss how using different strain strengths allows us to spatially separate the two components of the pseudospinor on the different sublattices of graphene. Thes…
We investigate the influence of gauge fields induced by strain on the supercurrent passing through the graphene-based Josephson junctions. We show in the presence of a constant pseudomagnetic field ${\bf B}_S$ originated from an arc-shape elastic deformation, the Josephson current is monotonically enhanced. This is in contrast with the oscillatory behavior of supercurrent (known as Fraunhofer pattern) caused by real magnetic fields passing through the junction. The absence of oscillatory supercurrent originates from the fact that strain-induced gauge fields have opposite directions at the two …
The relevance of the strain-induced Dirac point shift to obtain the appropriate anisotropic Fermi velocity of strained graphene is demonstrated. Then a critical revision of the available effective Dirac Hamiltonians is made by studying in detail the limiting case of a uniform strain. An effective Dirac Hamiltonian for nonuniform strain is thus reported, which takes into account all strain-induced effects: changes in the nearest-neighbor hopping parameters, the reciprocal lattice deformation and the true shift of the Dirac point. Pseudomagnetic fields are thus explained by means of position-dep…
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…
We revise the tight binding approach to strained or curved graphene in the presence of external probes such as Photoemission or Scanning Tunneling Microscopy experiments. We show that extra terms arise in the continuum limit of the tight binding Hamiltonian which can not be accounted for by changes in the hopping parameters due to lattice deformations, encoded in the parameter β. These material independent extra couplings are of the same order of magnitude as the standard ones and have a geometric origin. They include corrections to the position-dependent Fermi velocity and to a new vector fie…
Many intriguing phenomena occur for electrons under strong magnetic fields. Recently, it was proposed that an appropriate strain texture in graphene can induce a synthetic gauge field, in which the electrons behave like in a real magnetic field. This opened the door to control quantum transport by mechanical means and to explore unprecedented physics in high-field regime. Such studies have been achieved in molecular and photonic lattices. Here we report the first experimental realization of giant uniform pseudomagnetic field in acoustics by introducing a simple uniaxial deformation to acoustic…
Graphene is a powerful playground for studying a plethora of quantum phenomena. One of the remarkable properties of graphene arises when it is strained in particular geometries and the electrons behave as if they were under the influence of a magnetic field. Previously, these strain-induced pseudomagnetic fields have been explored on the nano- and micrometer-scale using scanning probe and transport measurements. Heteroepitaxial strain, in contrast, is a wafer-scale engineering method. Here, we show that pseudomagnetic fields can be generated in graphene through wafer-scale epitaxial growth. Sh…
The structural and electronic properties of graphene leads its charge carriers to behave like relativistic particles, which is described by a Dirac-like Hamiltonian. Since graphene is a monolayer of carbon atoms, the strain due to elastic deformations will give rise to so-called `pseudomagnetic fields (PMF)' in graphene sheet, and that has been realized experimentally in strained graphene sample. Here we propose a realistic strained graphene bilayer (SGB) device to detect the pseudo-magnetoexcitons (PME) in the absence of external magnetic field. The carriers in each graphene layer suffer diff…
We show that when the pseudomagnetic fields created by long wavelength deformations are appropriately coupled with a scalar electric potential, a significant energy gap can emerge due to the formation of a Haldane state. Ramifications of this physical effect are examined through the study of various strain geometries commonly seen in experiments, such as strain superlattices and wrinkled suspended graphene. Of particular technological importance, we consider setup where this gap can be tunable through electrostatic gates, allowing for the design of electronic devices not realizable with other …
The degeneracy and spatial support of pseudo-Landau levels (pLLs) in strained honeycomb lattices systematically depends on the geometry -- for instance, in hexagonal and rectangular flakes the 0th pLL displays a twofold increased degeneracy, while the characteristic sublattice polarization of the 0th pLL is only fully realized in a zigzag-terminated triangle. These features are dictated by algebraic constraints in the atomistic theory, and signify a departure from the standard picture in which all qualitative differences between pLLs and Landau levels induced by a magnetic field trace back to …
We propose a quantum electronic device based on strained graphene nanoribbon. Mechanical strain, internal exchange field and spin-orbit couplings (SOCs) have been exploited as principle parameters to tune physical properties of the device. We predict a remarkable zero-field topological quantum phase transition between the time-reversal-symmetry broken quantum spin hall (QSH) and quantum anomalous hall (QAH) states, which was previously thought to take place only in the presence of finite magnetic field. We illustrate as intrinsic SOC is tuned, how two different helicity edge states located in …
