arXiv subjects

Alistair H. Duff

Publications and source records attributed to Alistair H. Duff.

6 recordsLinked to original sources

arXiv2026

Multi-photon schemes for mid-infrared detection : Comparative study of bulk GaAs and Ge$_{1-x}$Sn$_x$

We calculate the theoretical non-degenerate two photon absorption and three color injected current response tensors for bulk GaAs and Ge$_{1-x}$Sn$_x$ for a range of alloy compositions. In particular, by including a ''pump'' beam we compare two ''schemes'' that are sensitive to mid-infrared photons. In ''scheme I'' we consider GaAs and a pump photon with energy greater than half the band gap, and in ''scheme II'' we consider Ge$_{1-x}$Sn$_x$ with a pump photon with energy less than half the band gap. We find that for certain pump and alloy concentrations Ge$_{1-x}$Sn$_x$ has a substantially larger nonlinear response and three-color injected current than GaAs in the mid-infrared frequency window where both materials can absorb photons via non-degenerate two-photon absorption.

cond-mat.mtrl-sci↗

arXiv2025

Frequency Dependent Magnetic Susceptibility and the $q^2$ effective conductivity tensor

We apply a microscopic formalism for the calculation of material response properties to the problem of the generalization of a first-principles, i.e based on the energy spectrum and geometric properties of the Bloch functions, derivation of the AC magnetic susceptibility. We find that the AC susceptibility forms only a part of the $q^2$ -- where $q$ is the wavevector of the applied field -- effective conductivity tensor, and many additional response tensors characterizing both electric and magnetic multipole moments response to electromagnetic fields and their derivatives must be included to create the full gauge-invariant response. As was seen with the DC magnetic susceptibility and optical activity (characterized by the linear in $q$ contribution to the conductivity) one must be careful with the diagonal elements of the Berry connection. To our knowledge this is the only derivation of such a result general for crystalline insulators, with both `atomic like' contributions and `itinerant contributions' due to overlap of atomic orbitals and non-flat bands. Additionally, quantities familiar from quantum geometry like the Berry connection, curvature, and quantum metric appear extensively.

cond-mat.mes-hall↗

arXiv2025

Linear response of a Chern insulator to finite-frequency electric fields

We derive the macroscopic charge and current densities of a Chern insulator initially occupying its electronic ground state as it responds to a finite-frequency electric field; we use a previously developed formalism based on microscopic polarization and magnetization fields in extended media. In a topologically trivial insulator, our result reduces to the familiar expression for the induced current density in linear response obtained from a Kubo analysis. But for a Chern insulator we find an extra "topological" term involving the (first) Chern number associated with the occupied bands, encoding the quantum anomalous Hall effect in the presence of a frequency-dependent electric field. While an analogous term has been introduced in the "modern theories of polarization and magnetization" for the linear response of finite-sized systems to static electric fields, our expression is valid for bulk Chern insulators in the presence of both static and finite-frequency electric fields, being derived analytically from a microscopic treatment of the electronic degrees of freedom, and can be generalized in a straightforward way to describe the response of a Chern insulator to electromagnetic fields that are not only frequency-dependent but also spatially inhomogeneous.

cond-mat.mes-hall↗

arXiv2023

Proof of Gauge-Invariance of Magnetic Susceptibility of Topologically Trivial Insulators in the Independent Particle Approximation

We have derived an expression for the magnetic susceptibility of topologically trivial insulators, however an important consideration for any response tensor is whether it is gauge-invariant. By this we refer to the gauge-freedom in choosing the Bloch functions one uses in a computation since multiplication by an arbitrary $\textbf{k}$-dependent complex phase produces equally valid Bloch functions. Additionally Wannier functions, which can be constructed by a unitary mixing of the Bloch functions, are a useful basis for computation due to their localized properties, but are strongly non-unique. Therefore, we show that the theoretical expression we derived is independent of the choice of Bloch functions or Wannier functions used, and thus is gauge-invariant in this sense.

cond-mat.mes-hall↗

arXiv2023

Microscopic Theory of the Magnetic Susceptibility of Insulators

We present a general theory of the magnetic susceptibility of insulators that can be extended to treat spatially varying and finite frequency fields. While there are existing results in the literature for the zero frequency response that appear to be in disagreement with each other, we show that the apparent differences between them vanish with the use of various sum rules, and that our result is in agreement with them. Although our strategy is based on the use of Wannier functions, we show that our result can be written in a ``gauge invariant" form involving Bloch functions. We can write it as the sum of terms that involve the diagonal elements of the Berry connection, and this decomposition is particularly useful in considering the limit of isolated molecules. But these contributions can be repackaged to give a form independent of those diagonal elements, which is thus generally more suitable for numerical computation. We consider an h-BN model to demonstrate the practical considerations in building a model and making calculations within this formalism.

cond-mat.mes-hall↗

arXiv2023

Magnetoelectric polarizability and optical activity: spin and frequency dependence

We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons, introducing a general spin orbit coupling and Zeeman interaction term in the Hamiltonian. At finite frequencies and including spin, the magnetoelectric polarizability tensor is replaced by two separate tensors, one that relates the polarization \textbf{P} to the magnetic field \textbf{B} and a separate tensor that relates the magnetization \textbf{M} to the electric field \textbf{E}. When combined with other relevant response tensors a third rank tensor that relates the induced current density to gradients in the electric field can be introduced; it is gauge invariant, in a form suitable for numerical calculations, and describes optical activity -- including spin effects -- even in materials that may lack time reversal symmetry.

cond-mat.mes-hall↗