Strain-induced Pseudomagnetic Field Research Articles

Preparation and Modeling of Graphene Bubbles to Obtain Strain-Induced Pseudomagnetic Fields.

It has been both theoretically predicted and experimentally demonstrated that strain can effectively modulate the electronic states of graphene sheets through the creation of a pseudomagnetic field (PMF). Pressurizing graphene sheets into bubble-like structures has been considered a viable approach for the strain engineering of PMFs. However, the bubbling technique currently faces limitations such as long manufacturing time, low durability, and challenges in precise control over the size and shape of the pressurized bubble. Here, we propose a rapid bubbling method based on an oxygen plasma chemical reaction to achieve rapid induction of out-of-plane deflections and in-plane strains in graphene sheets. We introduce a numerical scheme capable of accurately resolving the strain field and resulting PMFs within the pressurized graphene bubbles, even in cases where the bubble shape deviates from perfect spherical symmetry. The results provide not only insights into the strain engineering of PMFs in graphene but also a platform that may facilitate the exploration of the strain-mediated electronic behaviors of a variety of other 2D materials.

Exciton spin Hall effect in arc-shaped strained WSe2

Generating a pure spin current using electrons, which have degrees of freedom beyond spin, such as electric charge and valley index, presents challenges. In response, we propose a mechanism based on intervalley exciton dynamics in strained transition metal dichalcogenides (TMDs) to achieve the in an electrically insulating regime, without the need for an external electric field. The interplay between strain gradients and strain-induced pseudomagnetic fields results in a net Lorentz force on long-lived intervalley excitons in WSe2, carrying nonzero spin angular momentum. This process generates an exciton-mediated pure spin Hall current, resulting in opposite-sign spin accumulations and local magnetization on the two sides of the single-layer arc-shaped TMD. We demonstrate that the magnetic field induced by spin accumulation, at approximately ∼mT, can be detected using techniques such as superconducting quantum interference magnetometry or spatially resolved magneto-optical Faraday and Kerr rotations. Published by the American Physical Society 2024

Valley filtering and valley-polarized collective modes in bulk graphene monolayers

The presence of two sublattices in hexagonal graphene brings two energetically degenerate extremes in the conduction and valence bands, which are identified by the valley quantum number. Recently, this valley degree of freedom has been suggested to encode and process information, which develops a new carbon-based electronics named graphene valleytronics. In this topical review, we present and discuss valley-related transport properties in bulk graphene monolayers, which are due to strain-induced pseudomagnetic fields and associated vector potential, sublattice-stagger potential, and the valley-Zeeman effect. These valley-related interactions can be utilized to obtain valley filtering, valley spatial separation, valley-resolved guiding modes, and valley-polarized collective modes such as edge or surface plasmons. The present challenges and the perspectives on graphene valleytronics are also provided in this review.

Untwisting Moiré Physics: Almost Ideal Bands and Fractional Chern Insulators in Periodically Strained Monolayer Graphene.

Moiré systems have emerged in recent years as a rich platform to study strong correlations. Here, we will propose a simple, experimentally feasible setup based on periodically strained graphene that reproduces several key aspects of twisted moiré heterostructures-but without introducing a twist. We consider a monolayer graphene sheet subject to a C_{2}-breaking periodic strain-induced pseudomagnetic field with period L_{M}≫a, along with a scalar potential of the same period. This system has almost ideal flat bands with valley-resolved Chern number ±1, where the deviation from ideal band geometry is analytically controlled and exponentially small in the dimensionless ratio (L_{M}/l_{B})^{2}, where l_{B} is the magnetic length corresponding to the maximum value of the pseudomagnetic field. Moreover, the scalar potential can tune the bandwidth far below the Coulomb scale, making this a very promising platform for strongly interacting topological phases. Using a combination of strong-coupling theory and self-consistent Hartree-Fock, we find quantum anomalous Hall states at integer fillings. At fractional filling, exact diagonaliztion reveals a fractional Chern insulator at parameters in the experimentally feasible range. Overall, we find that this system has larger interaction-induced gaps, smaller quasiparticle dispersion, and enhanced tunability compared to twisted graphene systems, even in their ideal limit.

Electronic transport in bent carbon nanotubes

We study the electronic transport through uniformly bent carbon nanotubes. For this purpose, we describe the nanotube with the tight-binding model and calculate the local current flow by employing non-equilibrium Green's functions (NEGF) in the Keldysh formalism. In addition, we describe the low-energy excitations using an effective Dirac equation in curved space with a strain-induced pseudo-magnetic field which can be solved analytically for the torus geometry in terms of the Mathieu functions. We obtain a perfect quantitative agreement with the NEGF results. For nanotubes with an armchair edge, already a weak bending of 1% substantially changes the electronic properties. Depending on the valley, the current of the zero mode flows either on the outer or the inner side of the torus and, therefore, can be used as a valley splitter. In contrast, the zigzag nanotubes are largely unaffected by the bending. Our findings are of importance for nanoelectronic applications of carbon nanotubes and open new possibilities for valleytronics.

Compressive strain engineering of strong and sensitive pseudomagnetic fields in buckled graphene nanobubbles

The formation of pseudomagnetic fields is a well-known consequence due to lattice strain, which has considerable effects on the electronic properties of graphene. To this end, strain engineering remains an effective route to enable unconventional electronic properties. Particularly, pseudomagnetic fields due to compressive strain have demonstrated unique advantages such as remarkably high intensities at relatively low magnitude of strains (e.g., 5%) in several experiments. For example, pseudomagnetic fields as high as 300 T have been observed in buckled graphene nanobubbles. Recently, strong pseudomagnetic fields as high as 108 T have been measured in periodically buckled monolayer graphene, responsible for its band flattening and correlated states. Nevertheless, the general features and sensitivities of compressive strain-induced pseudomagnetic fields have been rarely explored, posing challenges for realizing their full potential. In this paper, we carry out large-scale molecular dynamics simulations to explore the properties of pseudomagnetic fields in buckled graphene nanobubbles, which are the basic representative graphene structures under compressive strains. We reveal that compressive strain can induce strong and sensitive pseudomagnetic fields for a variety of nanobubble shapes and boundary relaxation conditions. We also discuss the effect of the microscopy probe tip, which is frequently used to tune the morphologies and strain patterns. These results may offer guidance for designing electronic two-dimensional structures enabled by compressive strain engineering.

Strain-induced pseudo magnetic field in the α−T3 lattice

We investigate the effects of a nonuniform uniaxial strain and a triaxial strain on the $\alpha-{\cal T}_3$ lattice. The analytical expressions of the pseudo-Landau levels (pLLs) are derived based on low-energy Hamiltonians, and are verified by tight-binding calculations. We find the pseudo-magnetic field leads to the oscillating density of states, and the first pLL is sublattice polarized, which is distributed on only two of the three sets of sublattices. For the nonuniform uniaxial strain, we show that pLLs become dispersive due to the renormalization of the Fermi velocity, and a valley polarized current emerges. Our results generalize the study of pseudo-magnetic field to the $\alpha-{\cal T}_3$ lattice, which will not only deepen the understanding of the intriguing effects of mechanical strains, but also provide theoretical foundation for possible experimental studies of the effects of strain on the $\alpha-{\cal T}_3$ lattice.

Phase diagrams and edge-state transitions in graphene with spin-orbit coupling and magnetic and pseudomagnetic fields

The quantum Hall (QH) effect, the quantum spin Hall (QSH) effect, and the quantum valley Hall (QVH) effect are three peculiar topological insulating phases in graphene. They are characterized by three different types of edge states. These three effects are caused by the external magnetic field, the intrinsic spin-orbit coupling (SOC) and the strain-induced pseudomagnetic field, respectively. Here we theoretically study phase diagrams when these effects coexist and analyze how the edge states evolve between the three. We find the real magnetic field and the pseudomagnetic field will compete above the SOC energy gap while the QSH effect is almost unaffected within the SOC energy gap. The edge-state transitions from the QH effect or the QVH effect to the QSH effect directly relies on the arrangement of the zeroth Landau levels. Using edge-state transitions, we raise a device similar to a spin field effect transistor (spin-FET) and also design a spintronics multiple-way switch.

Realizing One-Dimensional Electronic States in Graphene via Coupled Zeroth Pseudo-Landau Levels.

Strain-induced pseudomagnetic fields can mimic real magnetic fields to generate a zero-magnetic-field analog of the Landau levels (LLs), i.e., the pseudo-Landau levels (PLLs), in graphene. The distinct nature of the PLLs enables one to realize novel electronic states beyond what is feasible with real LLs. Here, we show that it is possible to realize exotic electronic states through the coupling of zeroth PLLs in strained graphene. In our experiment, nanoscale strained structures embedded with PLLs are generated along a one-dimensional (1D) channel of suspended graphene monolayer. Our results demonstrate that the zeroth PLLs of the strained structures are coupled together, exhibiting a serpentine pattern that snakes back and forth along the 1D suspended graphene monolayer. These results are verified theoretically by large-scale tight-binding calculations of the strained samples. Our result provides a new approach to realizing novel quantum states and to engineering the electronic properties of graphene by using localized PLLs as building blocks.

Analytic solution to pseudo-Landau levels in strongly bent graphene nanoribbons

Nonuniform elastic strain is known to induce pseudo-Landau levels in Dirac materials. But these pseudo-Landau levels are hardly resolvable in an analytic fashion when the strain is strong because of the emerging complicated space dependence in both the strain-modulated Fermi velocity and the strain-induced pseudomagnetic field. We here analytically characterize the solution to the pseudo-Landau levels in strongly bent graphene nanoribbons by treating the effects of the nonuniform Fermi velocity and pseudomagnetic field on equal footing. The analytic solution is detectable through angle-resolved photoemission spectroscopy and allows quantitative comparison between theories and various experimental signatures of transport, such as the Shubnikov-de Haas oscillation in the complete absence of magnetic fields and the negative strain-resistivity resulting from the valley anomaly. The analytic solution can be generalized to various Dirac materials and will shed light on the related experimental explorations and straintronics applications.

Boundary Modes from Periodic Magnetic and Pseudomagnetic Fields in Graphene.

Single-layer graphene subject to periodic lateral strains is an artificial crystal that can support boundary spectra with an intrinsic polarity. This is 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 single counterpropagating modes traversing each bulk gap on opposite boundaries of a nanoribbon. For the pseudomagnetic field, pairs of counterpropagating modes migrate to the same boundary where they provide well-developed valley-helical transport channels on a single zigzag edge. We discuss possible schemes for implementing this situation and their experimental signatures.

Origami-controlled strain engineering of tunable flat bands and correlated states in folded graphene

Flat electronic bands with tunable structures offer opportunities for the exploitation and manipulation of exotic interacting quantum states. Here, we present a controllable route to construct easily tunable flat bands in folded graphene by nano origami-controlled strain engineering, and we discover correlated states in this system. Via tearing and folding graphene monolayer at arbitrary step edges with scanning tunneling microscope manipulation, we create strain-induced pseudomagnetic fields as well as resulting flat electronic bands in the curved edges of folded graphene. We show that the intensity of the pseudomagnetic field can be readily tuned by changing the width of the folding edge due to the edge-width-dependent lattice deformation, leading to the well adjustability of the geometry of flat bands in folded graphene. Furthermore, by creating expected dispersionless flat bands using this technique, the correlation-induced splits of flat bands are successfully observed in the density of states when these bands are partially filled. Our experiment provides a feasible and effective pathway to engineer the system with tunable flat band structures, and it establishes a platform that can be used to realize devisable strain and interaction-induced quantum phases.

Strain-induced quantum Hall phenomena of excitons in graphene

We study direct and indirect pseudomagnetoexcitons, formed by an electron and a hole in the layers of gapped graphene under strain-induced gauge pseudomagnetic field. Since the strain-induced pseudomagnetic field acts on electrons and holes the same way, it occurs that the properties of single pseudomagnetoexcitons, their collective effects and phase diagram are cardinally different from those of magnetoexcitons in a real magnetic field. We have derived wave functions and energy spectrum of direct in a monolayer and indirect pseudomagnetoexcitons in a double layer of gapped graphene. The quantum Hall effect for direct and indirect excitons was predicted in the monolayers and double layers of gapped graphene under strain-induced gauge pseudomagnetic field, correspondingly.

Anomalous sound attenuation in Weyl semimetals in magnetic and pseudomagnetic fields

We evaluate the sound attenuation in a Weyl semimetal subject to a magnetic field or a pseudomagnetic field associated with a strain. Due to the interplay of intra- and inter-node scattering processes as well as screening, the fields generically reduce the sound absorption. A nontrivial dependence on the relative direction of the magnetic field and the sound wave vector, i.e., the magnetic sound dichroism, can occur in materials with nonsymmetric Weyl nodes (e.g., different Fermi velocities and/or relaxation times). It is found that the sound dichroism in Weyl materials can also be activated by an external strain-induced pseudomagnetic field. In view of the dependence on the field direction, the dichroism may lead to a weak enhancement of the sound attenuation compared with its value at vanishing fields.

The Effects of Pseudomagnetic Fields on Plasmon–Phonon Hybridization in Supported Graphene Probed by a Moving Charged Particle

We analyze the effects of the strain-induced pseudomagnetic field on the subthreshold mechanism of hybridization taking place between the Dirac plasmon in graphene and the surface optical phonon modes in a nearby substrate. It is shown that the pseudomagnetic field exerts quite strong influence on the oscillatory pattern in the total potential in the plane of graphene, as well as on the stopping and the image forces on a charge, which moves parallel to the graphene at a speed below the Fermi velocity, specially for small graphene–substrate gap sizes. One may conclude that the subthreshold mechanism of the plasmon–phonon hybridization can be controlled by varying the pseudomagnetic field strength and the doping density in graphene.

Frequency-tunable terahertz graphene laser enabled by pseudomagnetic fields in strain-engineered graphene.

Graphene-based optoelectronic devices have recently attracted much attention for the next-generation electronic-photonic integrated circuits. However, it remains elusive whether it is feasible to create graphene-based lasers at the chip scale, hindering the realization of such a disruptive technology. In this work, we theoretically propose that Landau-quantized graphene enabled by strain-induced pseudomagnetic field can become an excellent gain medium that supports lasing action without requiring an external magnetic field. Tight-binding theory is employed for calculating electronic states in highly strained graphene while analytical and numerical analyses based on many-particle Hamiltonian allow studying detailed microscopic mechanisms of zero-field graphene Landau level laser dynamics. Our proposed laser presents unique features including a convenient, wide-range tuning of output laser frequency enabled by changing the level of strain in graphene gain media. The chip-scale graphene laser may open new possibilities for graphene-based electronic-photonic integrated circuits.

Graphene gets bent

Graphene gets bent

Graphene under uniaxial inhomogeneous strain and an external electric field: Landau levels, electronic, magnetic and optical properties

We investigate graphene under an inhomogeneous uniaxial strain and an in-plane electric field. We examine in detail the effect of strain and the electric field on relativistic Landau levels, Hall conductivity, de Haas-van Alphen oscillation and optical conductivity. Using Lorentz transformation in combination with supersymmetric quantum mechanics, we examine three different structures of Landau levels induced by three different profiles of inhomogeneous uniaxial strain and external electric fields. It is shown that strain-induced pseudomagnetic field forms Landau levels while electric field opposes formation of these levels. Besides the collapse of strain induced Landau levels, the influences of electric field on the quantization of strain dependent valley Hall conductivity, de Haas-van Alphen quantum oscillation of magnetization as well as optical conductivity have been investigated.

Strain-induced pseudomagnetic field and quantum oscillations in kagome crystals

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.

Superconductivity in Weyl semimetals in a strong pseudomagnetic field

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 Weyl semimetal, the proximity effect is strongly affected by the pseudomagnetic field. The analysis of such an effect showed that while no gap is opened in the spectrum, the degeneracy of energy levels is lifted. The unique character of the proximity effect in Weyl semimetals can be probed via the density of states, the spectral function, and the tunneling current. The density of states does not vanish at small energies and scales linearly with the pseudomagnetic field strength. This scaling is manifested also in the tunneling current.