14,316 research outputs found
Tall sections from non-minimal transformations
In previous work, we have shown that elliptic fibrations with two sections,
or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass
model of a certain form, namely, the Jacobian of a model.
Most constructions of elliptically fibered Calabi-Yau manifolds with two
sections have been carried out assuming that the image of this birational map
was a "minimal" Weierstrass model. In this paper, we show that for some
elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the
Jacobian of the model is not minimal. Said another way,
starting from a Calabi-Yau Weierstrass model, the total space must be blown up
(thereby destroying the "Calabi-Yau" property) in order to embed the model into
. In particular, we show that the elliptic fibrations studied
recently by Klevers and Taylor fall into this class of models.Comment: 16 page
Highly Deformable Graphene Kirigami
Graphene's exceptional mechanical properties, including its highest-known
stiffness (1 TPa) and strength (100 GPa) have been exploited for various
structural applications. However, graphene is also known to be quite brittle,
with experimentally-measured tensile fracture strains that do not exceed a few
percent. In this work, we introduce the notion of graphene kirigami, where
concepts that have been used almost exclusively for macroscale structures are
applied to dramatically enhance the stretchability of both zigzag and armchair
graphene. Specifically, we show using classical molecular dynamics simulations
that the yield and fracture strains of graphene can be enhanced by about a
factor of three using kirigami as compared to standard monolayer graphene. This
enhanced ductility in graphene should open up interesting opportunities not
only mechanically, but also in coupling to graphene's electronic behavior.Comment: 5 pages, 7 figure
Highly Stretchable MoS Kirigami
We report the results of classical molecular dynamics simulations focused on
studying the mechanical properties of MoS kirigami. Several different
kirigami structures were studied based upon two simple non-dimensional
parameters, which are related to the density of cuts, as well as the ratio of
the overlapping cut length to the nanoribbon length. Our key finding is
significant enhancements in tensile yield (by a factor of four) and fracture
strains (by a factor of six) as compared to pristine MoS nanoribbons.
These results in conjunction with recent results on graphene suggest that the
kirigami approach may be a generally useful one for enhancing the ductility of
two-dimensional nanomaterials
Polarization and valley switching in monolayer group-IV monochalcogenides
Group-IV monochalcogenides are a family of two-dimensional puckered materials
with an orthorhombic structure that is comprised of polar layers. In this
article, we use first principles calculations to show the multistability of
monolayer SnS and GeSe, two prototype materials where the direction of the
puckering can be switched by application of tensile stress or electric field.
Furthermore, the two inequivalent valleys in momentum space, which are dictated
by the puckering orientation, can be excited selectively using linearly
polarized light, and this provides an additional tool to identify the
polarization direction. Our findings suggest that SnS and GeSe monolayers may
have observable ferroelectricity and multistability, with potential
applications in information storage
Accelerated search and design of stretchable graphene kirigami using machine learning
Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ∼4×106 candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.P. Z. H. developed the codes, performed the simulations and data analysis, and wrote the manuscript with input from all authors. P. Z. H. and E. D. C. developed the machine learning methods. P. Z. H., D. K. C. and H. S. P. acknowledge the Hariri Institute Research Incubation Grant No. 2018-02-002 and the Boston University High Performance Shared Computing Cluster. P. Z. H. is grateful for the Hariri Graduate Fellowship. P. Z. H. thank Grace Gu and Adrian Yi for helpful discussions. (2018-02-002 - Hariri Graduate Fellowship)Published versio
Strain-induced gauge and Rashba fields in ferroelectric Rashba lead chalcogenide PbX monolayers (X = S, Se, Te)
One of the exciting features of two-dimensional (2D) materials is their
electronic and optical tunability through strain engineering. Previously, we
found a class of 2D ferroelectric Rashba semiconductors PbX (X = S, Se, Te)
with tunable spin-orbital properties. In this work, based on our previous
tight-binding (TB) results, we derive an effective low-energy Hamiltonian
around the symmetry points that captures the effects of strain on the
electronic properties of PbX. We find that strains induce gauge fields which
shift the Rashba point and modify the Rashba parameter. This effect is
equivalent to the application of in-plane magnetic fields. The out-of-plane
strain, which is proportional to the electric polarization, is also shown to
modify the Rashba parameter. Overall, our theory connects strain and spin
splitting in ferroelectric Rashba materials, which will be important to
understand the strain-induced variations in local Rashba parameters that will
occur in practical applications
Graphene kirigami as a platform for stretchable and tunable quantum dot arrays
The quantum transport properties of a graphene kirigami similar to those
studied in recent experiments are calculated in the regime of elastic,
reversible deformations. Our results show that, at low electronic densities,
the conductance profile of such structures replicates that of a system of
coupled quantum dots, characterized by a sequence of minibands and stop-gaps.
The conductance and I-V curves have different characteristics in the distinct
stages of elastic deformation that characterize the elongation of these
structures. Notably, the effective coupling between localized states is
strongly reduced in the small elongation stage, whereas in the large elongation
regime the development of strong, localized pseudomagnetic field barriers can
reinforce the coupling and reestablish resonant tunneling across the kirigami.
This provides an interesting example of interplay between geometry and
pseudomagnetic field-induced confinement. The alternating miniband and
stop-gaps in the transmission lead to I-V characteristics with negative
differential conductance in well defined energy/doping ranges. These effects
should be stable in a realistic scenario that includes edge roughness and
Coulomb interactions, as these are expected to further promote localization of
states at low energies in narrow segments of graphene nanostructures.Comment: 10 pages, 10 figure
Spin-Orbit Dirac Fermions in 2D Systems
We propose a novel model for including spin-orbit interactions in buckled two
dimensional systems. Our results show that in such systems, intrinsic
spin-orbit coupling leads to a formation of Dirac cones, similar to Rashba
model. We explore the microscopic origins of this behaviour and confirm our
results using DFT calculations
Two-dimensional square buckled Rashba lead chalcogenides
We propose the lead sulphide (PbS) monolayer as a two-dimensional semiconductor with a large Rashba-like spin-orbit effect controlled by the out-of-plane buckling. The buckled PbS conduction band is found to possess Rashba-like dispersion and spin texture at the M and Γ points, with large effective Rashba parameters of λ∼5 eV Å and λ∼1 eV Å, respectively. Using a tight-binding formalism, we show that the Rashba effect originates from the very large spin-orbit interaction and the hopping term that mixes the in-plane and out-of-plane p orbitals of Pb and S atoms. The latter, which depends on the buckling angle, can be controlled by applying strain to vary the spin texture as well as the Rashba parameter at Γ and M. Our density functional theory results together with tight-binding formalism provide a unifying framework for designing Rashba monolayers and for manipulating their spin properties.P.Z.H., H.S.P., and D.K.C. acknowledge the support of the Physics and Mechanical Engineering Department at Boston University. P.Z.H. is grateful for the hospitality of the NUS Centre for Advanced 2D Materials and Graphene Research Centre where this work was initiated. D.K.C. acknowledges the hospitality of the Aspen Center for Physics, which is supported by the US National Science Foundation Grant No. PHY-1607611. A.S.R., A.C.,and A.H.C.N. acknowledge support by the National Research Foundation, Prime Minister Office, Singapore, under its Medium Sized Centre Programme and CRP award "Novel 2D materials with tailored properties: Beyond graphene" (Grant No. R-144-000295-281). (Physics and Mechanical Engineering Department at Boston University; PHY-1607611 - US National Science Foundation; R-144-000295-281 - National Research Foundation, Prime Minister Office, Singapore, under its Medium Sized Centre Programme and CRP award "Novel 2D materials with tailored properties: Beyond graphene")Published versio
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