Strained Bilayer Graphene Research Articles

Supersymmetry dictated topology in periodic gauge fields and realization in strained and twisted 2D materials

Supersymmetry (SUSY) of a Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum between SPs-with paired zero modes-realized by 2D electrons in zero-flux periodic gauge fields, which can describe twisted or periodically strained 2D materials. We find their low-energy sector containing zero (or threshold) modes must be topologically non-trivial, by proving that Chern numbers of the two SPs have a finite difference dictated by the number of zero modes and energy dispersion in their vicinity. In 30° twisted bilayer (double bilayer) transition metal dichalcogenides subject to periodic strain, we find one SP is topologically trivial in its lowest miniband, while the twin SP of identical dispersion has a Chern number of 1 (2), in stark contrast to time-reversal partners that have to be simultaneously trivial or nontrivial. For systems whose physical Hamiltonian corresponds to the square root of a SUSY Hamiltonian, such as twisted or strained bilayer graphene, we reveal that topological properties of the two SUSY SPs are transferred respectively to the conduction and valence bands, including the contrasted topology in the low-energy sector and identical topology in the high-energy sector. This offers a unified perspective for understanding topological properties in many flat-band systems described by such square-root models. Both types of SUSY systems provide unique opportunities for exploring correlated and topological phases of matter.

Tunable wrinkle patterns in Moiré pattern of interlayer-bonding strained bilayer graphene

Moiré patterns are important structures in two-dimensional (2D) materials, showcasing unique electronic correlated states, which have garnered considerable research interests in recent years. However, current researches on moiré patterns primarily focus on honeycomb patterns induced by lattice mismatches at 2D material hetero-interfaces. In this work, we have demonstrated the ability to generate diverse and tunable wrinkle patterns in interlayer bonding strained bilayer graphene (IB-SBG) through a “stretch-crosslink-release” strategy, facilitated by the interlayer bonding that provides effective in-plane load transfer and interlayer constraint. Three energetically favorable wrinkle patterns are identified, including herringbone, irregular hexagon and honeycomb patterns. In general, wrinkle patterns are determined by two parameters, i.e., pre-strain and the portion of interface with interlayer bonding, and the phase diagram of wrinkle patterns corresponding to the two parameters is provided. Furthermore, strain engineering can be employed in IB-SBG to generate a series of new patterns by precisely adjusting the biaxial strain applied to IB-SBG. The present strategy to achieve tunable wrinkle patterns holds the potential to open new avenues for novel electronic applications based on bilayer graphene systems.

Engineering Transistorlike Optical Gain in Two-Dimensional Materials with Berry Curvature Dipoles.

Transistors are key elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, we use the semiclassical Boltzmann equation approach to characterize the optical conductivity of a two-dimensional material under a static electric bias. Similar to the nonlinear Hall effect, the linear electro-optic (EO) response depends on the Berry curvature dipole and can lead to nonreciprocal optical interactions. Most interestingly, our analysis uncovers a novel non-Hermitian linear EO effect that can lead to optical gain and to a distributed transistor response. We study a possible realization based on strained bilayer graphene. Our analysis reveals that the optical gain for incident light transmitted through the biased system depends on the light polarization, and can be quite large, especially for multilayer configurations.

Erratum: Hydrodynamically enhanced thermal transport due to strong interlayer interactions: A case study of strained bilayer graphene [Phys. Rev. B 105, 125406 (2022)

Erratum: Hydrodynamically enhanced thermal transport due to strong interlayer interactions: A case study of strained bilayer graphene [Phys. Rev. B 105, 125406 (2022)

Strained bilayer graphene, emergent energy scales, and moiré gravity

Twisted bilayer graphene is a rich condensed matter system, which allows one to tune energy scales and electronic correlations. The low-energy physics of the resulting moiré structure can be mathematically described in terms of a diffeomorphism in a continuum formulation. We stress that twisting is just one example of moiré diffeomorphisms. Another particularly simple and experimentally relevant transformation is a homogeneous isomorphic strain of one of the layers, which gives rise to a nearly identical moiré pattern (rotated by 90∘ relative to the twisted structure) and potentially flat bands. We further observe that low-energy physics of the strained bilayer graphene takes the form of a theory of fermions tunneling between two curved space-times. Conformal transformation of the metrics results in emergent “moiré energy scales,” which can be tuned to be much lower than those in the native theory. This observation generalizes to an arbitrary space-time dimension with or without an underlying lattice or periodicity and suggests a family of toy models of “moiré gravity” with low emergent energy scales. Motivated by these analogies, we present an explicit toy construction of moiré gravity, where the effective cosmological constant can be made arbitrarily small. We speculate about possible relevance of this scenario to the fundamental vacuum catastrophe in cosmology.Received 16 September 2021Accepted 14 April 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L022027Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAlternative gravity theoriesBilayersCosmological constantGeneral relativityGravitationQuantum fields in curved spacetimeQuantum theoryPhysical SystemsBilayer filmsGrapheneSuperlatticesCondensed Matter, Materials & Applied PhysicsGravitation, Cosmology & AstrophysicsInterdisciplinary PhysicsGeneral Physics

Hydrodynamically enhanced thermal transport due to strong interlayer interactions: A case study of strained bilayer graphene

Manipulating interlayer interactions in two-dimensional (2D) materials is a widely used and effective method for regulating heat transport, which is important for thermal management of electronics. In this paper, we find that thermal transport can be enhanced by strong interlayer interactions. For instance, 2D bilayer materials with interlayer bonding have larger thermal conductivity than their monolayer counterparts. To further verify the conjecture, we take bilayer graphene (BLG) as a study case to gradually strengthen the interlayer interactions in BLG by applying a series of compressive strains along the out-of-plane direction. It is found that the thermal conductivity of BLG first decreases and then anomalously increases when the strain is larger than the threshold of 12%. For the decreasing trend, it is mainly due to the strain-induced reduction of phonon group velocity and lifetime. While at larger strain (>12%), the anomalous increase of thermal conductivity is found to be caused by hydrodynamic phonon transport and weak phonon anharmonicity. Thus, enhanced interlayer interactions can enhance the hydrodynamic phonon transport and thus improve the heat transfer performance. In this paper, we not only report the hydrodynamic enhancement of thermal transport through enhanced interlayer interactions but also provide solid evidence. These findings will deepen the understanding of thermal transport in layered materials and heterostructures, which will benefit the applications in thermal management.

Rotational Friction Correlated with Moiré Patterns in Strained Bilayer Graphene: Implications for Nanoscale Lubrication

Energy conservation of graphene nanodevices requires frictional dissipation management for their high surface area to volume rates, and rotational motion besides sliding scenarios appear frequently. Here, the rotational friction between graphene layers is investigated by molecular dynamics simulations with a validated graphene-spring model. It shows that the interlayer frictional torque drops an order of magnitude and approaches superlubricity with the emergence of Moiré patterns (MPs). Further analysis reveals that the incommensurate interface of MPs tunes the local energy, which cancels each other out with relative rotation, resulting in ultralow interlayer energy barriers. Accordingly, for bilayer systems with biaxially stretched substrates, a significant torque reduction can be achieved when the size of MPs matches that of the graphene flake. This study would provide new insight into the lubrication of rotatable nanomechanical systems.

Electrically tunable and reversible magnetoelectric coupling in strained bilayer graphene

The valleys in hexagonal two-dimensional systems with broken inversion symmetry carry an intrinsic orbital magnetic moment. Despite this, such systems possess zero net magnetization unless additional symmetries are broken, since the contributions from both valleys cancel. A nonzero net magnetization can be induced through applying both uniaxial strain to break the rotational symmetry of the lattice and an in-plane electric field to break time-reversal symmetry owing to the resulting current. This creates a magnetoelectric effect whose strength is characterized by a magnetoelectric susceptibility, which describes the induced magnetization per unit applied in-plane electric field. Here, we predict the strength of this magnetoelectric susceptibility for Bernal-stacked bilayer graphene as a function of the magnitude and direction of strain, the chemical potential, and the interlayer electric field. We estimate that an orbital magnetization of ~5400 $\mu_{\text{B}}/\mu\text{m}^2$ can be achieved for 1% uniaxial strain and a 10 $\mu\text{A}$ bias current, which is almost three orders of magnitude larger than previously probed experimentally in strained monolayer MoS$_2$. We also identify regimes in which the magnetoelectric susceptibility not only switches sign upon reversal of the interlayer electric field but also in response to small changes in the carrier density. Taking advantage of this reversibility, we further show that it is experimentally feasible to probe the effect using scanning magnetometry.

Triaxial compressive strain in bilayer graphene enabled by nitride stressor layer

A technique that can be used to viably create triaxially strained bilayer graphene on any desirable location by simple patterning was developed. Unlike the conventional graphene strain engineering methods, the photolithographically defined spoke patterns and compressive strained Si3N4 layer deposited by plasma-enhanced chemical vapor deposition (PECVD) system enable the creation of locally confined triaxial strained bilayer graphene at the desire location by forming a unique tristar shaped wrinkle. The tristar shaped wrinkle was investigated with high resolution micro-Raman spectroscopy and atomic force microscopy (AFM) analyses, and confirmed that 0.38% of maximum triaxial compressive strain was created. Mechanical simulation was used to verify the strain distribution and confirm the strain value which was calculated from the Raman spectroscopy and AFM profile. The technique presented here not only provides a practical route to the creation of strained graphene at desired locations but also offers the potential of the creation of multiaxial strain in the graphene for various types of graphene-based electronic and optoelectronic devices.

Piezoelectricity in asymmetrically strained bilayer graphene

We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is very general and can be easily extended to any commensurate graphene-based heterostructure. Here, we consider three cases: (i) twisted bilayer graphene, (ii) bilayer graphene where triaxial stress is applied to one layer and (iii) bilayer graphene where uniaxial stress is applied to one layer. We show that the resulting superstructures can be divided into distinct classes, depending on the twist angle or the magnitude of the induced strain. The different classes are distinguished from each other by the interlayer coupling mechanism, resulting in fundamentally different low-energy physics. For the cases of triaxial and uniaxial stress, the individual graphene layers tend to decouple and we find significant charge transfer between the layers. In addition, this piezoelectric effect can be tuned by applying a perpendicular electric field. Finally, we show how our approach can be generalized to multilayer systems.

Wrinkled bilayer graphene with wafer scale mechanical strain

Wafer-scale strained bilayer graphene is demonstrated by employing a silicon nitride (Si3N4) stressor layer. Different magnitudes of compressive stress up to 840 MPa were engineered by adjusting the Si3N4 deposition recipes, and different strain conditions were analyzed using Raman spectroscopy. The strained graphene displayed significant G peak shifts and G peak splitting with 16.2 cm−1 and 23.0 cm−1 of the G band and two-dimensional band shift, which corresponds to 0.26% of strain. Raman mapping of large regions of the graphene films found that the largest shifts/splitting occurred near the bilayer regions of the graphene films. The significance of our approach lies in the fact that it can be performed in a conventional microfabrication process, i.e., the plasma enhanced chemical vapor deposition system, and thus easily implemented for large scale production.

Anisotropic phonon softening of uniaxially strained bilayer graphene

The effect of strain on the phonon dispersion of bilayer graphene has been studied by polarized Raman spectroscopy on uniaxially strained bilayer graphene. Each of the four peaks that constitute the Raman 2D band splits and redshifts under strain, with the shift rate depending on the strain direction relative to the crystallographic orientation. By comparing the experimental data with first-principles calculation results, it is shown that the splitting and the redshift of the peaks originate from the anisotropic modifications of the phonon dispersion and the electronic band structure of bilayer graphene. The intensity of each peak also depends on the magnitude and direction of strain, which can be explained in terms of the correlation with the momentum of the phonon involved in the Raman scattering path.

Conductance and shot noise in strained bilayer graphene

We explore the effect of trigonal warping and of elastic deformations on the electronic spectrum of bilayer graphene devices, on their ballistic conductance as well as on the shot noise. Uniaxial strain distorts the lattice creating a uniform fictitious gauge field in the electronic Dirac Hamiltonian which ultimately causes a dramatic reconstruction in the trigonally warped electronic spectrum, inducing topological transitions in the Fermi surface. In this paper we present results of ballistic transport in bilayer graphene in the absence and presence of strain, with particular focus on noise and the Fano factor F. The inclusion of trigonal warping preserves the pseudo-diffusive value of F = 1/3 at the Dirac point, as calculated in the absence of trigonal warping terms. However, the range of energies which show pseudo-diffusive transport increases by orders of magnitude compared to the results stemming out of a parabolic spectrum and the applied strain acts to increase this energy range further.

Electronic structure and layer-resolved transmission of bilayer graphene nanoribbon in the presence of vertical fields

Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polarized quantum Hall phase can occur by tuning the interplanar strain. Furthermore, we study the layer-resolved transport properties by calculating the layer polarized quantity by using the recursive Green's function technique and show that the resulting layer polarized value confirms the obtained phases. These predictions can be verified by experiments and our results demonstrate the possibility for exploiting strained bilayer graphene in the presence of external fields for electronics and valleytronics devices.

Merging Dirac points and topological phase transitions in the tight-binding model on the generalized honeycomb lattice

Moving, merging and annihilating Dirac points are studied theoretically in the tight-binding model on honeycomb lattice with up-to third-nearest-neighbor hoppings. We obtain a rich phase diagram of the topological phase transitions in the parameter space of direction-dependent hoppings. We obtain the conditions for the three Dirac points to merge and for the tricritical points. We find that only very small third-nearest-neighbor hoppings are enough for the existence of the merging of three-Dirac-points and the tricritical points, if the system is sufficiently anisotropic. The density of states is obtained to be $D(\epsilon) \propto |\epsilon|^{1/3}$ when three Dirac points merge, and $D(\epsilon) \propto |\epsilon|^{1/4}$ at the tricritical points. It is possible to realize these topological phase transitions in the ultracold atoms on the optical lattice, strained monolayer graphene or strained bilayer graphene.

Conductance anomaly near the Lifshitz transition in strained bilayer graphene

Strain qualitatively changes the low-energy band structure of bilayer graphene, leading to the appearance of a pair of low-energy Dirac cones near each corner of the Brillouin zone, and a Lifshitz transition, (a saddle point in the dispersion relation) at an energy proportional to the strain [M. Mucha-Kruczynski, I.L. Aleiner, and V.I. Fal'ko, Phys. Rev. B 84, 041404 (2011)]. Here, we show that in the vicinity of the Lifshitz transition the conductance of a ballistic n-p and n-p-n junction exhibits an anomaly: a non-monotonic temperature and chemical potential dependence, with the size depending on the crystallographic orientation of the principal axis of the strain tensor. This effect is characteristic for junctions between regions of different polarity (n-p and n-p-n junctions), while there is no anomaly in junctions between regions of the same polarity (n-n' and n-n'-n junctions).

Strain-induced band gaps in bilayer graphene

We present a tight-binding investigation of strained bilayer graphene within linear elasticity theory, focusing on the different environments experienced by the A and B carbon atoms of the different sublattices. We find that the inequivalence of the A and B atoms is enhanced by the application of perpendicular strain $\epsilon_{zz}$, which provides a physical mechanism for opening a band gap, most effectively obtained when pulling the two graphene layers apart. In addition, perpendicular strain introduces electron-hole asymmetry and can result in linear electronic dispersion near the K-point. When applying lateral strain to one layer and keeping the other layer fixed, we find the opening of an indirect band gap for small deformations. Our findings suggest experimental means for strain-engineered band gaps in bilayer graphene.

Strained bilayer graphene: Band structure topology and Landau level spectrum

We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.