arXiv subjects

S. Shallcross

Publications and source records attributed to S. Shallcross.

At least 37 records · Page 2Linked to original sources

arXiv2019

Deformation induced pseudo-magnetic fields in complex carbon architectures

We show that the physics of deformation in $α$-, $β$-, and $6,6,12$-graphyne is, despite their significantly more complex lattice structures, remarkably close to that of graphene, with inhomogeneously strained graphyne described at low energies by an emergent Dirac-Weyl equation augmented by strain induced electric and pseudo-magnetic fields. To show this we develop two continuum theories of deformation in these materials: one that describes the low energy degrees of freedom of the conical intersection, and is spinor valued as in graphene, and one describing the full sub-lattice space. The spinor valued continuum theory agrees very well with the full continuum theory at low energies, showing that the remarkable physics of deformation in graphene generalizes to these more complex carbon architectures. In particular, we find that deformation induced pseudospin polarization and valley current loops, key phenomena in the deformation physics of graphene, both have their counterpart in these more complex carbon materials.

cond-mat.mtrl-sci↗

arXiv2019

A complete description of the magnetic ground state in spinel vanadates

Capturing the non-collinear magnetic ground state of the spinel vanadates AV$_2$O$_4$ (A= Mn, Fe and Co) remains an outstanding challenge for state-of-the-art ab-initio methods. We demonstrate that both the non-collinear spin texture, as well as the magnitude of local moments, are captured by a single value of the on-site Hubbard $U$ of 2.7~eV in conjunction with the local spin density approximation (LSDA+$U$), provided the source term (i.e., magnetic monopole term) is removed from the exchange-correlation magnetic field ${\bf B}_{XC}$. We further demonstrate that the magnetic monopole structure in ${\bf B}_{XC}$ is highly sensitive to the value of $U$, to the extent that the interplay between on-site localization and local moment magnitude is qualitatively different depending on whether the source term is removed or not. This suggests that in treating strongly correlated magnetic materials within the LSDA+$U$ formalism, subtraction of the unphysical magnetic monopole term from the exchange-correlation magnetic field is essential to correctly treat the magnetic ground state.

cond-mat.str-el↗

arXiv2019

Moiré quantum well states in tiny angle two dimensional semi-conductors

The valence band edge in tiny angle twist bilayers of MoS$_2$ and phosphorene is shown to consist of highly localized energy levels created by a `moiré quantum well', i.e. trapped by the interlayer moiré potential. These approximately uniformly spaced energy levels exhibit a richly modulated charge density, becoming ultra-localized at the valence band maximum. The number and spacing of such levels is controllable by the twist angle and interlayer interaction strength, suggesting the possibility of `moiré engineering' ordered arrays of quantum dots in 2d twist semi-conductors.

cond-mat.mes-hall↗

arXiv2019

Moiré ordered current loops in the graphene twist bilayer

While a typical material exhibits field induced currents only at the boundary, a uniform out-of-plane magnetic field applied to two mutually rotated layers of graphene is shown to result in an ordered array of permanent current loops throughout the material. Each current loop consists of an interlayer current flowing through the open AA stacked regions of the moiré created by rotation, which then flows back through the neighboring AB regions to form a circuit, with significant current strength even at small fields. Similar moiré ordered arrays of current loops are also shown to exist in non-equilibrium transport states, where they manifest as current back flowing against the applied bias in the device. Such current loops thus represent an intrinsic feature of the twist bilayer in conditions of broken time reversal symmetry, and exist both as a low field imprint of the moiré lattice on Landau physics, and as measurable moiré scale current configurations in transport states.

cond-mat.mes-hall↗

arXiv2019

A non-perturbative theory of effective Hamiltonians: example of moiré materials

We demonstrate that there exists a continuum Hamiltonian $H(\bf{r},\bf{p})$ that is formally the operator equivalent of the general tight-binding method, inheriting the associativity and Hermiticity of the latter operator. This provides a powerful and controlled method of obtaining effective Hamiltonians via Taylor expansion with respect to momentum and, optionally, deformation fields. In particular, for fundamentally non-perturbative defects, such as twist faults and partial dislocations, the method allows the deformation field to be retained to all orders, providing an efficient scheme for the generation of transparent and compact Hamiltonians for such defects. We apply the method to a survey of incommensurate physics in twist bilayers of graphene, graphdiyne, MoS$_2$, and phosphorene. For graphene we are able to reproduce the `reflected Dirac cones' of the $30^\circ$ quasi-crystalline bilayer found in a recent ARPES experiment, and show it is an example of a more general phenomena of coupling by the moiré momentum. We show that incommensurate physics is governed by the decay of the interlayer interaction on the scale of the single layer reciprocal lattices, and demonstrate that if this is slow incommensurate scattering effects lead to very rapid broadening of band manifolds as the twist angle is tuned through commensurate values.

cond-mat.mtrl-sci↗

arXiv2018

Dislocation and node states in bilayer graphene systems

We investigate the electronic structure of realistic partial dislocation networks in bilayer graphene that feature annihilating, wandering, and intersecting partial lines. We find charge accumulation states at partials that are sensitive to Fermi energy and partial Burgers vector but not to the screw versus edge character of the partial. These states are shown to be current carrying, with the current density executing a spiral motion along the dislocation line with a strong interlayer component to the current. Close to the Dirac point localization on partials switches to localization on intersections of partials, with a corresponding complex current flow around the nodes.

cond-mat.mes-hall↗

arXiv2018

Straintronics beyond homogeneous deformation

We present a continuum theory of graphene treating on an equal footing both homogeneous Cauchy-Born (CB) deformation, as well as the microscopic degrees of freedom associated with the two sublattices. While our theory recovers all extant results from homogeneous continuum theory, the Dirac-Weyl equation is found to be augmented by new pseudo-gauge and chiral fields fundamentally different from those that result from homogeneous deformation. We elucidate three striking electronic consequences: (i) non-CB deformations allow for the transport of valley polarized charge over arbitrarily long distances e.g. along a designed ridge; (ii) the triaxial deformations required to generate an approximately uniform magnetic field are unnecessary with non-CB deformation; and finally (iii) the vanishing of the effects of a one dimensional corrugation seen in \emph{ab-initio} calculation upon lattice relaxation are explained as a compensation of CB and non-CB deformation.

cond-mat.mes-hall↗

arXiv2018

Moiré edge states in twisted graphene nanoribbons

The edge physics of graphene based systems is well known to be highly sensitive to the atomic structure at the boundary, with localized zero mode edge states found only on the zigzag type termination of the lattice. Here we demonstrate that the graphene twist bilayer supports an additional class of edge states, that (i) are found for all edge geometries and thus are robust against edge roughness, (ii) occur at energies coinciding with twist induced van Hove singularities in the bulk and (iii) possess an electron density strongly modulated by the moiré lattice. Interestingly, these "moiré edge states" exist only for certain lattice commensurations and thus the edge physics of the twist bilayer is, in dramatic contrast to that of the bulk, not uniquely determined by the twist angle.

cond-mat.mes-hall↗

arXiv2017

Tuning topological surface magnetism by bulk alloying

Deploying an analytical atomistic model of the bulk band structure of the IV-VI semiconductors we connect the spin structure of the topological surface state to the crystal field and spin orbit coupling parameters of the bulk material. While the Dirac-Weyl (or equivalently, Rashba) type topological surface state is often assumed universal, we show that the physics of the surface state is strikingly non-universal. To see this explicitly we calculate the RKKY interaction, which may be viewed as a probe of this surface state spin structure, finding its \emph{qualitative form} depends on the values the bulk spin-orbit and crystal field parameters take. This opens the way to tune the spin interaction on the surface of a IV-VI topological insulator by, for instance varying the composition of the IV-VI ternary compounds, as well as highlighting the importance of the connection between bulk and surface physics in topological insulators.

cond-mat.mes-hall↗

arXiv2017

Bulk physics entwined with a topological surface state

For the IV-VI semiconductor family we derive an exact relation between the microscopic gap edge wave functions of the bulk insulator and the Dirac-Weyl topological surface state wave function, thus obtaining a fully microscopic surface state. We find that the balance of spin-orbit interaction and crystal field in the bulk, and the band bending at the surface, can profoundly influence the surface state spin-momentum locking. As a manifestation of this we predict that the spin texture of the $M$-point Dirac cones of SnTe can be tuned through an unexpectedly rich sequence of spin textures -- warped helical with winding number $\pm 1$, $k_x$ linear, hyperbolic, and $k_y$ linear -- e.g. by tuning the band bending at the surface.

cond-mat.mtrl-sci↗

arXiv2017

Large magnetocrystalline anisotropy in tetragonally distorted Heuslers: a systematic study

With a view to the design of hard magnets without rare earths we explore the possibility of large magnetocrystalline anisotropy energies in Heusler compounds that are unstable with respect to a tetragonal distortion. We consider the Heusler compounds Fe$_2$YZ with Y = (Ni, Co, Pt), and Co$_2$YZ with Y = (Ni, Fe, Pt) where, in both cases, Z = (Al, Ga, Ge, In, Sn). We find that for the Co$_2$NiZ, Co$_2$PtZ, and Fe$_2$PtZ families the cubic phase is always, at $T=0$, unstable with respect to a tetragonal distortion, while, in contrast, for the Fe$_2$NiZ and Fe$_2$CoZ families this is the case for only 2 compounds -- Fe$_2$CoGe and Fe$_2$CoSn. For all compounds in which a tetragonal distortion occurs we calculate the MAE finding remarkably large values for the Pt containing Heuslers, but also large values for a number of the other compounds (e.g. Co$_2$NiGa has an MAE of -2.11~MJ/m$^3$). The tendency to a tetragonal distortion we find to be strongly correlated with a high density of states at the Fermi level in the cubic phase. As a corollary to this fact we observe that upon doping compounds for which the cubic structure is stable such that the Fermi level enters a region of high DOS, a tetragonal distortion is induced and a correspondingly large value of the MAE is then observed.

cond-mat.mtrl-sci↗

arXiv2016

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula and applications to the graphene-type systems

We have extended the semi-classical theory to include a general account of matrix valued Hamiltonians, i.e. those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a $n\times n$ dimensional Hamiltonian $H(\hat{\boldsymbol p},\hat{\boldsymbol q})$. The classical dynamics is governed by $n$ Hamilton-Jacobi (HJ) equations, that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of $H(\hat{\boldsymbol p}\to\boldsymbol p,\hat{\boldsymbol q}\to\boldsymbol q)$, which describe the internal structure of the semi-classical particles. This Berry curvature is a fully classical object and is, in that sense, as fundamental to the semi-classical theory of matrix Hamiltonians as the Hamilton-Jacobi equations. At the $\mathcal{O}(\hbar^1)$ level, it results in an additional semi-classical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semi-classical phase will, generally, only be zero only for the case in which the Berry phase is topological (i.e. depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally we apply our method to an inhomogeneous system consisting of a strain engineered one dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semi-classical moiré potential. The semi-classical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

cond-mat.mes-hall↗

arXiv2016

Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene

We have surveyed the in-plane transport properties of the graphene twist bilayer using (i) a low-energy effective Hamiltonian for the underlying electronic structure, (ii) an isotropic elastic phonon model, and (iii) the linear Boltzmann equation for elastic electron-phonon scattering. We find that transport in the twist bilayer is profoundly sensitive to the rotation angle of the constituent layers. Similar to the electronic structure of the twist bilayer the transport is qualitatively different in three distinct angle regimes. At large angles ($θ> \,\approx\!\!10^\circ$) and at temperatures below an interlayer Bloch-Grüneisen temperature of $\approx 10$~K the conductivity is independent of the twist angle i.e. the layers are fully decoupled. Above this temperature the layers, even though decoupled in the ground state, are re-coupled by electron-phonon scattering and the transport is different both from single layer graphene as well as the Bernal bilayer. In the small angle regime $θ<\,\approx\!\!2^\circ$ the conductivity drops by two orders of magnitude and develops a rich energy dependence, reflecting the complexity of the underlying topological changes (Lifshitz transitions) of the Fermi surface. At intermediate angles the conductivity decreases continuously as the twist angle is reduced, while the energy dependence of the conductivity presents two sharp transitions, that occur at specific angle dependent energies, and that may be related to (i) the well studied van Hove singularity of the twist bilayer and (ii) a Lifshitz transition that occurs when trigonally placed electron pockets decorate the strongly warped Dirac cone. We examine the role of a layer perpendicular electric field finding that it affects the conductivity strongly at low temperatures whereas this effect is washed out by Fermi smearing at room temperatures.

cond-mat.mes-hall↗

arXiv2016

Going beyond k.p theory: a general method for obtaining effective Hamiltonians in both high and low symmetry situations

We provide a method for the generation of effective continuum Hamiltonians that goes beyond the well known k.p method in being equally effective in both high, and low (or no) symmetry situations. Our approach is based on a surprising exact map of the two-centre tight-binding method onto a compact continuum Hamiltonian, with a precise condition given for the hermiticity of the latter object. We apply this method to a broad range of low dimensional systems of both high and low symmetry: graphene, graphdiyne, γ-graphyne, 6,6,12-graphyne, twist bilayer graphene, and partial dislocation networks in Bernal stacked bilayer graphene. For the single layer systems the method yields Hamiltonians for the ideal lattices, as well as a systematic theory for corrections due to deformation. In the case of bilayer graphene we provide a compact expression for an effective field capable of describing any stacking deformation of the bilayer; twist bilayer graphene, as well as the partial dislocation network in AB stacked graphene, emerge as special cases of this field. For the latter system we find (i) charge pooling on the mosaic of AB and AC segments near the Dirac point and (ii) localized current carrying states on the partials with the current density characterized by both intralayer and interlayer components.

cond-mat.mes-hall↗

arXiv2015

Spectrum for non-magnetic Mott insulators from power functional within Reduced Density Matrix Functional Theory

A fully first principles theory capable of treating strongly correlated solids remains the outstanding challenge of modern day materials science. This is exemplified by the transition metal oxides, prototypical Mott insulators, that remain insulating even in the absence of long range magnetic order. Capturing the non-magnetic insulating state of these materials presents a difficult challenge for any modern electronic structure theory. In this paper we demonstrate that reduced density matrix functional theory, in conjunction with the power functional, can successfully treat the non-magnetic insulating state of the transition metal oxides NiO and MnO. We show that the electronic spectrum retains a gap even in the absence of spin order. We further discuss the detailed way in which RDMFT performs for Mott insulators and band insulators, finding that for the latter occupation number minimization alone is required, but for the former full minimization over both occupation numbers and natural orbitals is essential.

cond-mat.str-el↗

arXiv2015

Doping induced metal-insulator phase transition in NiO

The insulator to metal phase transition in NiO is studied within the framework of reduced density matrix functional theory and density functional theory. We find that the spectral density obtained using reduced density matrix functional theory is in good agreement with experiments both undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition \emph{qualitatively differs} depending on whether NiO is calculated within density functional theory or reduced density matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.

cond-mat.str-el↗

arXiv2012

Spectral density and metal-insulator phase transition in Mott insulators within RDMFT

We present a method for calculating the spectrum of periodic solids within reduced density matrix functional theory. This method is validated by a detailed comparison of the angular momentum projected spectral density with that of well established many-body techniques, in all cases finding an excellent agreement. The physics behind the pressure induced insulator-metal phase transition in MnO is investigated. The driving mechanism of this transition is identified as increased crystal field splitting with pressure, resulting in a charge redistribution between the Mn $e_g$ and $t_2g$ symmetry projected states.

cond-mat.str-el↗

arXiv2012

Spectrum of extended systems from Reduced Density Matrix Functional Theory

We present a method for calculating the spectrum of extended solids within reduced density matrix functional theory. An application of this method to the strongly correlated transition metal oxide series demonstrates that (i) an insulating state is found in the absence of magnetic order and, in addition, (ii) the interplay between the change transfer and Mott-Hubbard correlation is correctly described. In this respect we find that while NiO has a strong charge transfer character to the electronic gap, with substantial hybridization between $t_{2g}$ and oxygen-$p$ states in the lower Hubbard band, for MnO this is almost entirely absent. As a validation of our method we also calculate the spectra for a variety of weakly correlated materials, finding good agreement with experiment and other techniques.

cond-mat.str-el↗