arXiv subjects

Matthew Albert

Publications and source records attributed to Matthew Albert.

5 recordsLinked to original sources

arXiv2026

A new perspective on the anomalous Hall effect

We revisit the anomalous Hall effect in magnetic conductors, and its generalization to finite frequencies, using a formalism based on microscopic notions of polarization, magnetization, and free charges and currents. The electronic degrees of freedom are treated within second-quantized field theory, where the Hamiltonian features a static and cell-periodic magnetic field that encodes the magnetic order in the crystal and breaks time-reversal symmetry. We study the dynamics of bound and free charge carriers at the microscopic level as they respond to a spatially uniform electric field at finite frequency. The conductivity tensor describing the long-wavelength response is a sum of three terms, including a Kubo term associated with the polarization response, along with the metallic Drude term and the anomalous Hall conductivity that are associated with the longitudinal and transverse parts of the free current response, respectively. We also present numerical calculations of these contributions for the ferromagnetic body-centered cubic phase of iron.

cond-mat.mes-hall↗

arXiv2026

Linear response of the Chern insulator MnBi$_2$Te$_4$: A Wannier function approach

Recent work demonstrated that in the long wavelength limit the linear response of a Chern insulator to finite-frequency electric fields is the sum of two terms: A general frequency-dependent Kubo contribution that is present irrespective of band topology, and a topological Hall term that vanishes for topologically trivial insulators. Motivated by recent experiments and theoretical predictions, we use these expressions to calculate the optical conductivity and susceptibility of intrinsically magnetic MnBi$_2$Te$_4$ thin films with one, four, five, and eleven septuple layers by combining density functional theory with "single-shot" Wannier functions. To characterize the underlying topology of these systems, we compute the two-dimensional Chern number of these films using recently derived global expressions formulated in terms of Bloch energies and velocity matrix elements; the use of these expressions allows us to circumvent numerical issues at band crossings. Films with eleven septuple layers are of particular interest. We find that they have the same Chern number as five septuple layer films, in contrast to the reported "higher Chern-number phase" of these systems in other studies; we discuss a few possible reasons for the discrepancy. We also identify spin-orbit coupling-driven band inversions as a possible indicator of these topological phases.

cond-mat.mes-hall↗

arXiv2024

Optical Properties of Gated Bilayer Graphene Quantum Dots with Trigonal Warping

We determine the optical properties of gated bilayer graphene quantum dots with trigonal warping (TW) of single-particle energy spectra. The lateral structure of metallic gates confines electrons and holes in a quantum dot (QD) electrostatically. The gated bilayer graphene energy spectrum is characterized by two K-valleys surrounded by three minivalleys with energies depending on the applied vertical electric field. Employing an atomistic tight-binding model, we compute the single-particle QD states and analyze the influence of TW on the energy spectrum as the lateral confining potential depth varies. We find a regime where the QD levels are dominated by the presence of three minivalleys around each K-valley. Next, we compute dipole matrix elements and analyze the oscillator strengths and optical selection rules for optical valence to conduction band transitions. We then include electron-electron interactions by first computing the microscopic Coulomb matrix elements, electron self-energy, and solving the Bethe-Salpeter equation to obtain the excitonic spectrum. Finally, we obtain the absorption spectrum for a shallow confining potential depth, which further amplifies the effects of TW on the optical properties. Our results predict the existence of two degenerate bright exciton states, each built of the three minivalley states that do not exist in the deep confinement regime, where the effects of TW are negligible.

cond-mat.mes-hall↗

arXiv2023

Electrically Tunable Fine Structure of Negatively Charged Excitons in Gated Bilayer Graphene Quantum Dots

We predict here the fine structure of an electrically tunable negatively charged exciton (trion) composed of two electrons and a hole confined in a gated bilayer graphene quantum dot (QD). We start with an atomistic approach, allowing us to compute confined electron and confined hole QD states for a structure containing over one million atoms. Using atomistic wavefunctions we compute Coulomb matrix elements and self-energies. In the next step, by solving the Bethe-Salpeter-like equation for trions, we describe a negatively charged exciton, built as a strongly interacting interlayer complex of two electrons in the conduction band and one hole in the valence band. Unlike in conventional semiconducting QDs, we show that the trion contains a fine structure composed of ten states arising from the valley and spin degrees of freedom. Finally, we obtain absorption into and emission from the trion states. We predict the existence of bright low-energy states and propose to extract the fine structure of the trion using the temperature dependence of emission spectra.

cond-mat.mes-hall↗

arXiv2023

Complex quantum momentum due to correlation

Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism of quantum mechanics integrates complex numbers within its fundamental principles, and whether this arises out of necessity or not is an important question that many have attempted to answer. Here, we will consider two electrons in a one-dimensional quantum well where the interaction potential between the two electrons is attractive as opposed to the usual repulsive coulomb potential. Pairs of electrons exhibiting such effective attraction towards each other occur in other settings, namely within superconductivity. We will demonstrate that this attractive interaction leads to the necessity of complex momentum solutions, which further emphasizes the significance of complex numbers in quantum theory. The complex momentum solutions are solved using a perturbative analysis approach in tandem with Newton's method. The probability densities arising from these complex momentum solutions allow for a comparison with the probability densities of the typical real momentum solutions occurring from the standard repulsive interaction potential.

quant-ph↗