arXiv subjects

Perry T. Mahon

Publications and source records attributed to Perry T. Mahon.

10 recordsLinked to original sources

arXiv2024

Moir\'{e} band theory for M-valley twisted transition metal dichalcogenides

We propose twisted bilayers of certain group IV and IVB trigonal transition metal dichalcogenides (TMDs) MX$_{2}$ (M$=$Zr, Hf, Sn and X$=$S, Se) as moir\'{e} materials. In monolayer form these TMDs have conduction band minima near the three inequivalent Brillouin zone $M$ points and negligible spin-orbit coupling, implying six flavors of low-energy conduction band states. The flavor sectors decouple at the single-particle level and in twisted bilayers are accurately described by emergent moir\'e-periodic Hamiltonians that we derive from small-unit-cell density functional theory calculations. Because the valley-projected Hamiltonians have large valley-dependent mass anisotropies and are time-reversal invariant, spontaneous valley polarization is signaled in transport by anisotropy instead of by the anomalous Hall and magnetic circular dichroism signals commonly observed in graphene and $K$-valley TMD-based moir\'{e} multilayers.

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arXiv2024

Capacitive scheme to detect the topological magnetoelectric effect

The topological magnetoelectric effect (TME) is a defining property of three-dimensional $\mathbb{Z}_{2}$ topological insulators that was predicted on theoretical grounds more than a decade ago, but has still not been directly measured. In this Letter we propose a strategy for direct measurement of the TME and discuss the precision of the effect in real devices with charge and spin disorder.

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arXiv2023

Bulk versus surface: Nonuniversal partitioning of the topological magnetoelectric effect

The electronic ground state of a three-dimensional (3D) band insulator with time-reversal ($\Theta$) symmetry or time-reversal times a discrete translation ($\Theta T_{1/2}$) symmetry is classified by a $\mathbb{Z}_{2}$-valued topological invariant and characterized by quantized magnetoelectric response. Here we demonstrate by explicit calculation in model $\mathbb{Z}_{2}$ topological insulator thin-films that whereas the magnetoelectric response is localized at the surface in the $\Theta$ symmetry (nonmagnetic) case, it is nonuniversally partitioned between surface and interior contributions in the $\Theta T_{1/2}$ (antiferromagnetic) case, while remaining quantized. Within our model the magnetic field induced polarization arises entirely from an anomalous $\mathscr{N}=0$ Landau level subspace within which the projected Hamiltonian is a generalized Su-Schrieffer-Heeger model whose topological properties are consistent with those of the starting 3D model. We identify a new connection between the ground-state geometry of that 3D model and surface-interior partitioning in thin films.

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arXiv2023

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) $\mathbb{Z}_2$ topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular $\mathbb{Z}_2$ topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear response calculations in non-magnetic $\mathbb{Z}_2$ TIs that is more plainly consistent with TRS, and use this interpretation to discuss the effect's observation - still absent over a decade after its prediction. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in non-magnetic $\mathbb{Z}_2$ TIs the TME is activated by magnetic surface dopants, that the charge density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect.

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arXiv2023

Polarization and orbital magnetization in Chern insulators: A microscopic perspective

We derive macroscopic expressions for the polarization and orbital magnetization of a Chern insulator in its zero-temperature ground state using a previously developed formalism for treating microscopic polarization and magnetization fields in extended media. In the limit of a topologically trivial insulator, our results reduce to those of the "modern theories of polarization and magnetization." In a Chern insulator, however, we find a generically nonvanishing microscopic free current density, the macroscopic average of which vanishes. Moreover, the expression that we obtain for the polarization is qualitatively similar to that of the "modern theory," while the expressions for the orbital magnetization fundamentally differ; the manner in which they differ elucidates the distinct philosophies of these theoretical frameworks.

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arXiv2023

Electric polarization and magnetization in metals

A feature of the "modern theory" is that electric polarization is not well-defined in a metallic ground state. A different approach invokes the general existence of a complete set of exponentially localized Wannier functions, with respect to which general definitions of microscopic electronic polarization and magnetization fields, and free charge and current densities are always admitted. These definitions assume no particular initial electronic state of the crystal, and the set of microscopic fields satisfy the usual relations of classical electrodynamics. Notably, when applied to a trivial insulator initially occupying its $T=0$ ground state, the expressions for the unperturbed polarization and orbital magnetization, and for the orbital magnetoelectric polarizability tensor obtained from these different approaches can agree. However, the "modern theory of magnetization" has been extended via thermodynamic arguments to include metals and Chern insulators. We here compare with that generalization and find disagreement; the manner in which the expressions differ elucidates the distinct philosophies of these approaches. Our approach leads to the usual electrical conductivity tensor in the long-wavelength limit; in the absence of any scattering mechanisms, the dc divergence of that tensor is due to the free current density and the finite-frequency generalization of the anomalous Hall contribution arises from a combination of bound and free current densities. As well, in the limit that the electronic ground state is that of a trivial insulator, our expressions reduce to those expected for the unperturbed polarization and magnetization, and the electric susceptibility.

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arXiv2021

From magnetoelectric response to optical activity

We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into "site" polarization and magnetization fields, from which "site multipole moments" can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them; for electromagnetic fields varying little over a lattice constant these are the electric and magnetic dipole moments per unit volume, and the electric quadrupole moment per unit volume. A description of optical activity and related magneto-optical phenomena follows from the response of these macroscopic quantities to the electromagnetic field and, while in this paper we work within the independent particle and frozen-ion approximations, both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.

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arXiv2020

Magnetoelectric polarizability: A microscopic perspective

We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric and magnetic fields at zero temperature. To first-order in the applied fields, the free charge and current densities vanish; thus the response of the system is characterized by the first-order modifications to the microscopic polarization and magnetization fields. Associated with the dipole moment of the microscopic polarization (magnetization) field is a macroscopic polarization (magnetization), for which we extract various response tensors. We focus on the orbital magnetoelectric polarizability (OMP) tensor, and find the accepted expression as derived from the "modern theory of polarization and magnetization." Since our results are based on the spatial averages of microscopic fields, we can identify the distinct contributions to the OMP tensor from the perspective of this microscopic theory, and we establish the general framework in which extensions to finite frequency can be made.

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arXiv2019

Quantum Interference Control of Localized Carrier Distributions in the Brillouin Zone

Using transition-metal dichalcogenides as an example, we show that the quantum interference arising in two- and three-photon absorption processes can lead to controllable, highly localized carrier distributions in the Brillouin zone. We contrast this with the previously studied one- and two-photon absorption, and find qualitatively different features, including changes in the relevance of interband and intraband processes according to the excitation energy. Thus, the distribution of excitations arising under certain circumstances in two- and three-photon absorption can facilitate the study of far-from-equilibrium states that are initially well localized in crystal momentum space.

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arXiv2019

Microscopic polarization and magnetization fields in extended systems

We introduce microscopic polarization and magnetization fields at each site of an extended system, as well as free charge and current density fields associated with charge movement from site to site, by employing a lattice gauge approach based on a set of orthogonal orbitals associated with each site. These microscopic fields are defined using a single-particle electron Green function, and the equations governing its evolution under excitation by an electromagnetic field at arbitrary frequency involve the electric and magnetic fields rather than the scalar and vector potentials. If the sites are taken to be far from each other, we recover the limit of isolated atoms. For an infinite crystal we choose the orbitals to be maximally-localized Wannier functions, and in the long wavelength limit we recover the expected linear response of an insulator, including the zero frequency transverse conductivity of a topologically nontrivial insulator. For a topologically trivial insulator we recover the expected expressions for the macroscopic polarization and magnetization in the ground state, and find that the linear response to excitation at arbitrary frequency is described solely by the microscopic polarization and magnetization fields. For very general optical response calculations the microscopic fields necessarily satisfy charge conservation, even under basis truncation, and do not suffer from the false divergences at zero frequency that can plague response calculations using other approaches.

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