Pseudomagnetic Field Research Articles

Four-vector optical Dirac equation and spin-orbit interaction of structured light

The spin-orbit interaction of light is a crucial concept for understanding the electromagnetic properties of a material and realizing the spin-controlled manipulation of optical fields. Achieving these goals requires a complete description of spin-dependent optical phenomena in the context of vector-wave mechanics. We develop an extended Dirac theory for optical fields in generic media, which was found to be akin to a non-Hermitian chiral extension of massive fermions with anomalous magnetic momenta moving in an external pseudomagnetic field. This similarity allows us to investigate the optical behaviors of a material by effective field-theory methods and can find wide applications in metamaterials, photonic topological insulators, etc. We demonstrate this method by studying the spin-orbit interaction of structured light in a spin-degenerate medium and inhomogeneous isotropic medium, which leads to both spin-orbital Hall effects and spin-to-orbital angular momentum conversion. Of importance, our approach provides simple and clear physical insight into the spin-orbit interaction of light in generic media, and could potentially bridge our understanding of topological insulators between electronic and photonic systems.

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.

Magnetic-Field-Tunable Valley-Contrasting Pseudomagnetic Confinement in Graphene.

Introducing quantum confinement has uncovered a rich set of interesting quantum phenomena and allows one to directly probe the physics of confined (quasi-)particles. In most experiments, however, an electrostatic potential is the only available method to generate quantum dots in a continuous system to confine (quasi-)particles. Here we demonstrate experimentally that inhomogeneous pseudomagnetic fields in strained graphene can introduce exotic quantum confinement of massless Dirac fermions. The pseudomagnetic fields have opposite directions in the two distinct valleys of graphene. By adding and tuning real magnetic fields, the total effective magnetic fields in the two valleys are imbalanced. By that we realized valley-contrasting spatial confinement, which lifts the valley degeneracy and results in field-tunable valley-polarized confined states in graphene. Our results provide a new avenue to manipulate the valley degree of freedom.

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.

Limits on Axions and Axionlike Particles within the Axion Window Using a Spin-Based Amplifier.

Searches for the axion and axionlike particles may hold the key to unlocking some of the deepest puzzles about our Universe, such as dark matter and dark energy. Here, we use the recently demonstrated spin-based amplifier to constrain such hypothetical particles within the well-motivated "axion window" (10 μeV-1 meV) through searching for an exotic dipole-dipole interaction between polarized electron and neutron spins. The key ingredient is the use of hyperpolarized long-lived ^{129}Xe nuclear spins as an amplifier for the pseudomagnetic field generated by the exotic interaction. Using such a spin sensor, we obtain a direct upper bound on the product of coupling constants g_{p}^{e}g_{p}^{n}. The spin-based amplifier technique can be extended to searches for a wide variety of hypothetical particles beyond the standard model.

Graphene nanoelectromechanical systems as valleytronic devices

We investigate electronic transport in graphene nanoelectromechanical systems, known also as graphene nanodrums or nanomembranes. We demonstrate that these devices, despite their small values of strain between $0.1%$ and $1%$, can be used as efficient and robust valley polarizers and filters. Their working principle is based on the pseudomagnetic field generated by the strain of the graphene membrane. They work for ballistic electron beams as well as for strongly dispersed ones and can be also used as electron beam collimators due to the focusing effect of the pseudomagnetic field. We show additionally that the current flow can be estimated by semiclassical trajectories which represent a computationally efficient tool for predicting the functionality of the devices.

Two-dimensional crystals on adhesive substrates subjected to uniform transverse pressure

In this work we consider bubbles that can form spontaneously when a two-dimensional (2D) crystal is transferred to a substrate with gases or liquids trapped at the crystal–substrate interface. The underlying mechanics may be described by a thin sheet on an adhesive substrate with the trapped fluid applying uniform transverse pressure. What makes this apparently simple problem complex is the rich interplay among geometry, interface, elasticity and instability. Particularly, extensive small-scale experiments have shown that the 2D crystal surrounding a bubble can adhere to and, meanwhile, slide on the substrate. The radially inward sliding causes hoop compression to the 2D crystal which may exploit wrinkling instabilities to relax or partially relax the compression. We present a theoretical model to understand the complex behaviors of even a linearly elastic 2D crystal due to the combination of nonlinear geometry, adhesion, sliding, and wrinkling in bubble systems. We show that this understanding not only successfully predicts the geometry of spontaneous bubbles but also reveals the strain-coupled physics of 2D crystals, e.g., the pseudomagnetic fields in graphene bubbles.

Acoustically Induced Giant Synthetic Hall Voltages in Graphene.

Any departure from graphene's flatness leads to the emergence of artificial gauge fields that act on the motion of the Dirac fermions through an associated pseudomagnetic field. Here, we demonstrate the tunability of strong gauge fields in nonlocal experiments using a large planar graphene sheet that conforms to the deformation of a piezoelectric layer by a surface acoustic wave. The acoustic wave induces a longitudinal and a giant synthetic Hall voltage in the absence of external magnetic fields. The superposition of a synthetic Hall potential and a conventional Hall voltage can annihilate the sample's transverse potential at large external magnetic fields. Surface acoustic waves thus provide a promising and facile avenue for the exploitation of gauge fields in large planar graphene systems.

Electron transport properties of graphene quantum dots with non-centro-symmetric Gaussian deformation

A theoretical investigation on electron transport properties of rectangular graphene quantum dots (GQDs) with non-centro-symmetric out-of-plane Gaussian deformation of elliptic type is presented. Different levels of deformation are explored to estimate system geometry optimal for potential electronic applications. Electronic properties of deformed GQDs are studied in terms of local density of states (LDOS), band-gap opening and equilibrium ballistic conductance. In particular, it was observed that the symmetry of spatial LDOS structure is directly linked with the symmetry of properly defined local strain field (LSF) map, for a wide energy range. The relationship confirms qualitatively predictions obtained on the basis of the concept of a pseudomagnetic field, used in continuum models of graphene, including strain induced effects. The conductance spectra of deformed GQD as a device connected to semi-infinite graphene armchair nanoribbons as reservoirs are studied in a frame of tight-binding (TB) model in combination with non-equilibrium Green’s-functions technique (NEGF).

Quantum Revivals in Curved Graphene Nanoflakes.

Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. We have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.

Magic angles and flat Chern bands in alternating-twist multilayer graphene system

Based on the effective continuum model, we study alternating-twist multilayer graphene system and emergence of magic angles and flat band topology. All the alternating-twist multilayer graphene system (from triple layers to few layers) are found to have flat bands at magic angles where the area of AA stacking equals n-fold (n is an integer) electron cyclotron area. From the pseudo-Landau-level representation, there is always an isolated Dirac band in the alternating-twist graphene system constructed by odd number of layers. Since each pair of flat bands can be perceived as the zeroth pseudo-Landau-levels in two dimensional Dirac fermions, electron in the flat band pair can feel a pseudo-magnetic field with the same magnitude but the opposite sign. Calculated Chern number for each flat band is +1 (or -1) which can be tuned by twisting in the vicinity of magic angles or by gating. The concurrent appearance of strong correlation and band topology of flat bands in the alternating-twist multilayer graphene may pave an avenue for the new understanding of superconductivity observed in triple-layered graphene, and supply a new playground for realizing (quantum) anomalous Hall effect.

Landau levels in curved space realized in strained graphene

The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained graphene realize Dirac fermions in curved space in the presence of a background pseudo-gauge field, providing an ideal playground for this. However, the absence of a direct matching between a numerical, strained tight-binding calculation of an observable and the corresponding curved space prediction has hindered realistic predictions. In this work, we provide this matching by deriving the low-energy Hamiltonian from the tight-binding model analytically to second order in the strain and mapping it to the curved-space Dirac equation. Using a strain profile that produces a constant pseudo-magnetic field and a constant curvature, we compute the Landau level spectrum with real-space numerical tight-binding calculations and find excellent agreement with the prediction of the quantum Hall effect in curved space. We conclude discussing experimental schemes for measuring this effect.

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.

Reverse strain-induced snake states in graphene nanoribbons

Strain can tailor the band structures and properties of graphene nanoribbons (GNRs) with the well-known emergent pseudo-magnetic fields and the corresponding pseudo-Landau levels (pLLs). We design one type of the zigzag GNR (ZGNR) with reverse strains, producing pseudo-magnetic fields with opposite signs in the lower and upper half planes. Therefore, electrons propagate along the interface as "snake states", experiencing opposite Lorentz forces as they cross the zero field border line. By using the Landauer-Buttiker formalism combined with the nonequilibrium Green's function method, the existence and robustness of the reverse strain-induced snake states are further studied. Furthermore, the realization of long-thought pure valley currents in monolayer graphene systems is also proposed in our device.

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.

An atomistic approach for the structural and electronic properties of twisted bilayer graphene-boron nitride heterostructures

Twisted bilayer graphene (TBG) has taken the spotlight in the condensed matter community since the discovery of correlated phases. In this work, we study heterostructures of TBG and hexagonal boron nitride (hBN) using an atomistic tight-binding model together with semi-classical molecular dynamics to consider relaxation effects. The hBN substrate has significant effects on the band structure of TBG even in the case where TBG and hBN are not aligned. Specifically, the substrate induces a large mass gap and strong pseudo-magnetic fields that break the layer degeneracy. Interestingly, such degeneracy can be recovered with a second hBN layer. Finally, we develop a continuum model that describes the tight-binding band structure. Our results show that a real-space tight-binding model in combination with semi-classical molecular dynamics is a powerful tool to study the electronic properties of moiré heterostructures, and to explain experimental results in which the effect of the substrate plays an important role.

Triaxially strained suspended graphene for large-area pseudo-magnetic fields.

Strain-engineered graphene has garnered much attention recently owing to the possibilities of creating substantial energy gaps enabled by pseudo-magnetic fields (PMFs). While theoretical works proposed the possibility of creating large-area PMFs by straining monolayer graphene along three crystallographic directions, clear experimental demonstration of such promising devices remains elusive. Herein, we experimentally demonstrate a triaxially strained suspended graphene structure that has the potential to possess large-scale and quasi-uniform PMFs. Our structure employs uniquely designed metal electrodes that function both as stressors and metal contacts for current injection. Raman characterization and tight-binding simulations suggest the possibility of achieving PMFs over a micrometer-scale area. Current-voltage measurements confirm an efficient current injection into graphene, showing the potential of our devices for a new class of optoelectronic applications. We also theoretically propose a photonic crystal-based laser structure that obtains strongly localized optical fields overlapping with the spatial area under uniform PMFs, thus presenting a practical route toward the realization of graphene lasers.

Cationic vacancies as defects in honeycomb lattices with modular symmetries

Layered materials tend to exhibit intriguing crystalline symmetries and topological characteristics based on their two dimensional (2D) geometries and defects. We consider the diffusion dynamics of positively charged ions (cations) localized in honeycomb lattices within layered materials when an external electric field, non-trivial topologies, curvatures and cationic vacancies are present. The unit (primitive) cell of the honeycomb lattice is characterized by two generators, J_1, J_2 in mathrm{SL}_2({mathbb {Z}}) of modular symmetries in the special linear group with integer entries, corresponding to discrete re-scaling and rotations respectively. Moreover, applying a 2D conformal metric in an idealized model, we can consistently treat cationic vacancies as topological defects in an emergent manifold. The framework can be utilized to elucidate the molecular dynamics of the cations in exemplar honeycomb layered frameworks and the role of quantum geometry and topological defects not only in the diffusion process such as prediction of conductance peaks during cationic (de-)intercalation process, but also pseudo-spin and pseudo-magnetic field degrees of freedom on the cationic honeycomb lattice responsible for bilayers.