arXiv subjects

Todd Van Mechelen

Publications and source records attributed to Todd Van Mechelen.

13 recordsLinked to original sources

arXiv2023

Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity

Edge states occurring in Chern and quantum spin-Hall phases are signatures of the topological electronic band structure in two-dimensional (2D) materials. Recently, a new topological electromagnetic phase of graphene characterized by the optical N-invariant has been proposed. Optical N-invariant arises from repulsive Hall viscosity in hydrodynamic many-body electron systems, fundamentally different from the Chern and Z2 invariants. In this paper, we introduce the topologically protected edge excitation -- optical N-plasmon of interacting many-body electron systems in the topological optical N-phase. These optical N-plasmons are signatures of the topological plasmonic band structure in 2D materials. We demonstrate that optical N-plasmons exhibit fundamentally different dispersion relations, stability, and edge profiles from the topologically trivial edge magneto plasmons. Based on the optical N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic circulator, which is a chiral quantum radio-frequency circuit component crucial for information routing and interfacing quantum-classical computing systems. Furthermore, we reveal that optical N-plasmons can be effectively tuned by the neighboring dielectric environment without breaking the topological properties. Our work provides a smoking gun signature of repulsive Hall viscosity and opens practical applications of topological electromagnetic phases of two-dimensional materials.

cond-mat.mes-hall↗

arXiv2022

Pico-photonics: Anomalous Atomistic Waves in Silicon

The concept of photonic frequency $(ω)$ - momentum $(q)$ dispersion has been extensively studied in artificial dielectric structures such as photonic crystals and metamaterials. However, the $ω-q$ dispersion of electrodynamic excitations hosted in natural materials at the atomistic level is far less explored. Here, we develop a Maxwell Hamiltonian theory of matter combined with the quantum theory of atomistic polarization to obtain the electrodynamic dispersion of natural materials interacting with the photon field. We apply this theory to silicon and discover the existence of anomalous atomistic waves. These waves occur in the spectral region where propagating waves are conventionally forbidden in a macroscopic theory. Our findings demonstrate that natural media can host a variety of yet to be discovered waves with sub-nano-meter effective wavelengths in the pico-photonics regime.

physics.optics↗

arXiv2021

Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor

A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect time-reversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space group symmetries. In this article, we introduce a new class of two-dimensional topological materials known as optical $N$-insulators that possess obstructions to constructing localized molecular polarizabilities. The optical $N$-invariant $N\in\mathbb{Z}$ is the winding number of the atomistic susceptibility tensor $χ$ and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the optical band structure of the material -- the eigenvectors of the susceptibility tensor -- which constitutes the collection of optical Bloch functions. The localized basis of these eigenvectors are optical Wannier functions which represent the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical phase $N\neq 0$, such a localized polarization basis is impossible to construct. Utilizing the mathematical machinery of $K$-theory, these optical $N$-phases are refined further to account for the underlying crystalline symmetries of the material, generating a classification of the topological electromagnetic phase of matter.

cond-mat.mes-hall↗

arXiv2020

Optical $N$-invariant of graphene's viscous Hall fluid

Over the past three decades, graphene has become the prototypical platform for discovering unique phases of topological matter. Both the Chern insulator $C\in\mathbb{Z}$ and the quantum spin Hall insulator $ν\in\mathbb{Z}_2$ were first predicted in graphene, which led to a veritable explosion of research in topological materials. Here, we introduce a new topological classification of two-dimensional matter -- the optical $N$-phases $N\in\mathbb{Z}$. The $C$ and $ν$ phases are related to charge and spin transport respectively, whereas the $N$-phases are connected to polarization transport. In all three cases, transportation of charge/spin/polarization quanta is forbidden in the bulk but permitted on the edge. One fundamental difference is that the $N$-invariant is defined for dynamical electromagnetic waves over all Matsubara frequencies and wavevectors. We show this topological quantum number is captured solely by the spatiotemporal dispersion of the susceptibility tensor $χ(ω,\mathbf{q})$. We also prove $N\neq 0$ is nontrivial in graphene's viscous Hall fluid with the underlying physical mechanism being Hall viscosity $η_H$. In the nontrivial phase, we discover a deep sub-wavelength phenomenon reminiscent of the Meissner effect: at a particularly large photon momentum $q=D_H^{-1}$ defined by the Hall diffusion length $D_H$, the magnetic field is completely expelled from the viscous Hall fluid. We propose a new probe of topological matter, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, to unravel this novel optical $N$-invariant and verify the magnetic field expulsion. Our work indicates that graphene with Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.

cond-mat.mes-hall↗

arXiv2019

Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter

We present the fundamental model of a topological electromagnetic phase of matter: viscous Maxwell-Chern-Simons theory. Our model applies to a quantum Hall fluids with viscosity. We solve both continuum and lattice regularized systems to demonstrate that this is the minimal (exactly solvable) gauge theory with a nontrivial photonic Chern number ($C\neq 0$) for electromagnetic waves coupled to a quantum Hall fluid. The interplay of symmetry and topology is also captured by the spin-1 representations of a photonic skyrmion at high-symmetry points in the Brillouin zone. To rigorously analyze the topological physics, we introduce the viscous Maxwell-Chern-Simons Lagrangian and derive the equations of motion, as well as the boundary conditions, from the principle of least action. We discover topologically-protected chiral (unidirectional) edge states which minimize the surface variation and correspond to massless photonic excitations costing an infinitesimal amount of energy. Physically, our predicted electromagnetic phases are connected to a dynamical photonic mass in the integer quantum Hall fluid. This arises from viscous (nonlocal) Hall conductivity and we identify the nonlocal Chern-Simons coupling with the Hall viscosity. The electromagnetic phase is topologically nontrivial $C\neq 0$ when the Hall viscosity inhibits the total bulk Hall response. Our work bridges the gap between electromagnetic and condensed matter topological physics while also demonstrating the central role of spin-1 quantization in nontrivial photonic phases.

cond-mat.mes-hall↗

arXiv2019

Electron g-factor engineering for non-reciprocal spin photonics

We study the interplay of electron and photon spin in non-reciprocal materials. Traditionally, the primary mechanism to design non-reciprocal photonic devices has been magnetic fields in conjunction with magnetic oxides, such as iron garnets. In this work, we present an alternative paradigm that allows tunability and reconfigurability of the non-reciprocity through spintronic approaches. The proposed design uses the high-spin-orbit coupling of a narrow-band gap semiconductor (InSb) with ferromagnetic dopants. A combination of the intrinsic and a gate-applied electric field gives rise to a strong external Rashba spin-orbit coupling (RSOC) in a magnetically doped InSb film. The RSOC which is gate alterable is shown to adjust the magnetic permeability tensor via the electron g-factor of the medium. We use electronic band structure calculations (k$\cdot$p theory) to show the gate-adjustable RSOC manifest itself in the non-reciprocal coefficient of photon fields via shifts in the Kerr and Faraday rotations. In addition, we show that photon spin properties of dipolar emitters placed in the vicinity of a non-reciprocal electromagnetic environment is distinct from reciprocal counterparts. The Purcell factor (F$_{p}$) of a spin-polarized emitter (right-handed circular dipole) is significantly enhanced due to a larger g-factor while a left-handed dipole remains essentially unaffected. Our work can lead to electron spin controlled reconfigurable non-reciprocal photonic devices.

physics.app-ph↗

arXiv2019

Dirac Wire

The interplay of photon spin and orbital angular momentum (OAM) in the optical fiber (1D waveguide) has recently risen to the forefront of quantum nanophotonics. Here, we introduce the fermionic dual of the optical fiber, the Dirac wire, which exhibits unique electronic spin and OAM properties arising from confined solutions of the Dirac equation. The Dirac wires analyzed here represent cylindrical generalizations of the Jackiw-Rebbi domain wall and the minimal topological insulator, which are of significant interest in spintronics. We show the unique longitudinal spin arising from electrons confined to propagation in a wire, an effect which is fundamentally prohibited in planar geometries. Our work sheds light on the universal spatial dynamics of electron spin in confined geometries and the duality between electronic and photonic spin.

quant-ph↗

arXiv2019

Unidirectional Maxwellian Spin Waves

We develop a unified perspective of unidirectional topological edge waves in non-reciprocal media. We focus on the inherent role of photonic spin in non-reciprocal gyroelectric media, ie. magnetized metals or magnetized insulators. We first review the concept of a Maxwell Hamiltonian in non-reciprocal media, which immediately reveals that the gyrotropic coefficient behaves as a photon mass in two dimensions. Similar to the Dirac mass, this photonic mass opens bandgaps in the energy dispersion of bulk propagating waves. Within these bulk photonic bandgaps, three distinct classes of Maxwellian edge waves exist - each arising from subtle differences in boundary conditions. On one hand, the edge wave solutions are rigorous photonic analogs of Jackiw-Rebbi electronic edge states. On the other hand, for the exact same system, they can be high frequency photonic counterparts of the integer quantum Hall effect, familiar at zero frequency. Our Hamiltonian approach also predicts the existence of a third distinct class of Maxwellian edge wave exhibiting topological protection. The Maxwellian edge state in this unique \textit{quantum gyroelectric phase of matter} necessarily requires a sign change in gyrotropy arising from non-locality (spatial dispersion). A signature property of these topological electromagnetic edge states is that they are oblivious to the contacting medium, ie. they occur at the interface of the quantum gyroelectric phase and any medium (even vacuum). Furthermore, the Maxwellian spin waves exhibit photonic spin-1 quantization in exact analogy with their supersymmetric spin-\sfrac{1}{2} counterparts. The goal of this paper is to discuss these three foundational classes of edge waves in a unified perspective while providing in-depth derivations, taking into account non-locality and various boundary conditions.

physics.optics↗

arXiv2018

Non-local topological electromagnetic phases of matter

In 2+1D, topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries. Additionally, they support topologically protected spin-1 edge states, which are fundamentally different than spin-1/2 and pseudo-spin-1/2 edge states arising in fermionic and pseudo-fermionic systems. The striking feature of the edge state is that all electric and magnetic field components vanish at the boundary. This surprising open boundary solution of Maxwell's equations, dubbed the quantum gyroelectric effect [Phys. Rev. A 98, 023842 (2018)], only occurs in the presence of temporal as well as spatial dispersion (nonlocality) and is the supersymmetric partner of the topological Dirac edge state where the spinor wave function completely vanishes at the boundary. In this paper, we generalize these topological electromagnetic phases beyond the continuum approximation to the exact lattice field theory of a periodic atomic crystal. To accomplish this, we put forth the concept of microscopic (nonlocal) photonic band structure of solids, analogous to the traditional theory of electronic band structure. Our definition of topological invariants and topological phases uses optical Bloch modes and can be applied to naturally occurring crystalline materials. For the photon propagating within a crystal, our theory shows that besides the Chern invariant $\mathfrak{C}\in\mathbb{Z}$, there are also symmetry-protected topological (SPT) invariants $ν\in\mathbb{Z}_N$ which are related to the cyclic point group $C_N$ of the crystal $ν=\mathfrak{C}\mod N$. Due to the rotational symmetries of light $\mathcal{R}(2π)=+1$, these SPT phases are manifestly bosonic and behave very differently from their fermionic counterparts $\mathcal{R}(2π)=-1$ encountered in conventional condensed matter systems.

cond-mat.str-el↗

arXiv2018

Photonic Dirac monopoles and skyrmions: spin-1 quantization

We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring vacuum where the reciprocal momentum space of both Maxwell's equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity - i.e. a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-1/2 skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-1/2 helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases.

physics.optics↗

arXiv2018

Quantum gyro-electric effect: Photon spin-1 quantization in continuum topological bosonic phases

Topological phases of matter arise in distinct fermionic and bosonic flavors. The fundamental differences between them are encapsulated in their rotational symmetries - the spin. Although spin quantization is routinely encountered in fermionic topological edge states, analogous quantization for bosons has proven elusive. To this end, we develop the complete electromagnetic continuum theory characterizing 2+1D topological bosons, taking into account their intrinsic spin and orbital angular momentum degrees of freedom. We demonstrate that spatiotemporal dispersion (momentum and frequency dependence of linear response) captures the matter-mediated interactions between bosons and is a necessary ingredient for topological phases. We prove that the bulk topology of these 2+1D phases is manifested in transverse spin-1 quantization of the photon. From this insight, we predict two unique bosonic phases - one with even parity $C=\pm 2$ and one with odd $C=\pm 1$. To understand the even parity phase $C=\pm 2$, we introduce an exactly solvable model utilizing non-local optical Hall conductivity and reveal a single gapless photon at the edge. This unidirectional photon is spin-1 helically quantized, immune to backscattering, defects, and exists at the boundary of the $C=\pm 2$ bosonic phase and any interface - even vacuum. The contrasting phenomena of transverse quantization in the bulk, but longitudinal (helical) quantization on the edge is addressed as the quantum gyro-electric effect (QGEE). We also validate our bosonic Maxwell theory by direct comparison with the supersymmetric Dirac theory of fermions. To accelerate the discovery of such bosonic phases, we suggest two new probes of topological matter with broken time-reversal symmetry: momentum-resolved electron energy loss spectroscopy and cold atom near-field measurement of non-local optical Hall conductivity.

cond-mat.mes-hall↗

arXiv2018

Dirac-Maxwell correspondence: Spin-1 bosonic topological insulator for light

Fundamental differences between fermions and bosons are revealed in their spin and distribution statistics as well as the discrete symmetries they obey (charge, parity and time). While significant progress has been made on fermionic topological phases of matter with time-reversal symmetry, the bosonic counterpart still remains elusive. We present here a spin-1 bosonic topological insulator for light by utilizing a Dirac-Maxwell correspondence. Departing from structural photonic approaches which mimic the pseudo-spin-\textonehalf{} behavior of electrons, we exploit the integer spin and discrete symmetries of the photon to formulate a distinct bosonic topological phase of matter. We introduce a bosonic Kramers theorem and the photonic equivalent of topological quantization, which arises solely from photon spin. Our continuum field theory predicts that photons acquire a mass in the presence of a spatio-temporally dispersive degenerate chirality, a unique form of magneto-electric coupling inside matter fundamentally different from well-known chirality, magneto-electricity, gyrotropy or bi-anisotropy. We predict that this unique dispersive (non-local) degenerate chiral medium has anomalous parity and time-reversal symmetries and if found in nature will exhibit a gapped Quantum spin-1 Hall bosonic phase. Photons do not possess a conductivity transport parameter which can be quantized (unlike electronic systems), but we predict that photon spin quantization of symmetry-protected edge states is amenable to experimental isolation leading to a new bosonic phase of matter.

cond-mat.mes-hall↗

arXiv2015

Universal spin-momentum locking of evanescent waves

We show the existence of an inherent property of evanescent electromagnetic waves: spin-momentum locking, where the direction of momentum fundamentally locks the polarization of the wave. We trace the ultimate origin of this phenomenon to complex dispersion and causality requirements on evanescent waves. We demonstrate that every case of evanescent waves in total internal reflection, surface states and optical fibers/waveguides possesses this intrinsic spin-momentum locking. We also introduce a universal right-handed triplet consisting of momentum, decay and spin for evanescent waves. We derive the Stokes parameters for evanescent waves which reveal an intriguing result - every fast decaying evanescent wave is inherently circularly polarized with its handedness tied to the direction of propagation. We also show the existence of a fundamental angle associated with total internal reflection (TIR) such that propagating waves locally inherit perfect circular polarized characteristics from the evanescent wave. This circular TIR condition occurs if and only if the ratio of permittivities of the two dielectric media exceeds the golden ratio. Our work leads to a unified understanding of this spin-momentum locking in various nanophotonic experiments and sheds light on the electromagnetic analogy with the quantum spin hall state for electrons.

physics.optics↗