arXiv subjects

Jason G. Kattan

Publications and source records attributed to Jason G. Kattan.

7 recordsLinked to original sources

arXiv2026

Ferroelectric superconductivity in noncentrosymmetric metals

It has recently been shown in experiments that certain materials can display both superconductivity and ferroelectricity, contrary to a long-standing conjecture that these two phenomena are incompatible, or at least unrelated. In this work we study superconductivity in ferroelectric metals, using a formalism of ionic polarization fields coupled to itinerant electrons, both of which are treated at the microscopic level. The ferroelectric order manifests as a spontaneous polarization that may be uniform or spatially modulated, and fluctuations of the polarization mediate interactions between the electrons. The polarization fluctuations give rise to attractive interactions that can lead to Cooper pairing in certain lattice configurations, analogous to the nonpolar phonons in conventional BCS theory. Working with a simplified BCS model, we derive conditions under which superconductivity can coexist with and even emerge from ferroelectricity.

cond-mat.supr-con↗

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↗

arXiv2026

Chern insulators in two and three dimensions: A global perspective

We introduce a second-quantized field theory for Chern insulators in which the Hamiltonian features a static vector potential that has the periodicity of the crystal's lattice and spontaneously breaks time-reversal symmetry in the system's ground state. Such a vector potential generates a magnetic field at the microscopic level that may be thought of as arising from local moments associated with one or more magnetic ions in each unit cell. Considering spinor electrons, we study the Chern invariants characterizing the topology of the occupied valence bands of Chern insulators in both two and three dimensions - the Chern number and the Chern vector, respectively - and we derive novel expressions for these topological invariants that are globally defined across the Brillouin zone and involve the full band structure of the system. We also study the long-wavelength response of a Chern insulator to electromagnetic fields at finite frequency, generalizing the quantum anomalous Hall effect in the static limit to the optical regime.

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

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.

cond-mat.mes-hall↗

arXiv2023

Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization

We formulate a non-relativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and magnetization field operators whose moments are identified with the multipole moments of the charge-current distribution. The multipolar Hamiltonian is obtained from the minimal coupling Hamiltonian through a unitary transformation, often referred to as the Power-Zienau-Woolley transformation; we renormalize this Hamiltonian using perturbation theory, the result of which is used to compute the leading-order radiative corrections to the electronic energy levels due to interactions between the electrons and quantum vacuum fluctuations in the electromagnetic field. Our renormalized energy shift constitutes a generalization of the Lamb shift in atomic hydrogen, valid for general localized assemblies of atoms and molecules, possibly with net charge but absent free current. By expanding the fields in a series of multipole moments, our results can be used to study contributions to this energy shift coming from specific multipole moments of arbitrary order.

physics.atom-ph↗