# Optical Properties of Magnetic Monopole Excitons

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## Abstract

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## 1. Introduction

**E**,

**v**,

**B**represents the external electric field, velocity of the charge, and magnetic induction intensity. Using the duality of electrons and monopoles, one can write the expression for a monopole having magnetic charges g, with replacing

**B**by $\mathbf{E}/c$,

**E**by -$c\mathbf{B}$. The elementary charge g of a magnetic monopole is defined as $g=\frac{2\pi \hslash}{e{\mu}_{0}}$ using the Ampere’s form of Dirac quantization [7]. h is the Planck’s constant and ${\mu}_{0}$ the vacuum magnetic permeability. Then, the electromagnetic force of a magnetic monopole is represented as the following:

_{2}[10,11,12,13]. Moreover, a magnetic monopole phase transition was reported in the spin ice [14,15,16,17]. The elementary excitation of the spin ice material may generate the quasiparticles resembling the magnetic monopole-antimonopole pairs, which in principle may provide a opportunity for scientists to study the quasiparticles behaving like the magnetic monopoles. Here, we consider the monopole quasiparticles that constitute the collective modes of a medium composed by billions of particles. Initially, the centers of opposite magnetic charges of monopole excitons coincide; therefore, the system is magnetically neutral. By applying the magnetic field to the system, charges will be pulled away from the original position. Hence, a non-zero magnetic dipole moment will be generated. This toy model would apply for a one-dimensional magnetic crystal material, where energy bands may be introduced for magnetic monopoles and antimonopoles in the same way as they are introduced for electrons and holes in a semiconductor.

## 2. One-Dimensional Magnetic Susceptibility

## 3. Single Magnetic Monopole in Periodic Triangle Magnetic Potential Field

## 4. The Energy Spectrum of a Magnetic Monopole Exciton

## 5. Magnetic Wave Equation of Monopole Exciton Polariton

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Magnetic field is parallel to the magnetic monopole dipole moment, displacement from equilibrium center is

**x**.

**Figure 3.**Numerical solution of the wave function of the monopole in one period of the magnetic field. The pseudo-wavevector is $k=0.48\pi $. The wave function is divided into barrier and well regions and shown in blue color, while the red vertical dashed line indicates the boundary where the sign of the magnetic field flips, and the green vertical dashed lines are the boundaries of barrier and well regions depending on the relationship between energy of the monopole and local potential of the magnetic field.

**Figure 5.**The coupled oscillator model of a magnetic monopole polariton in a microcavity system. Solid lines: dispersion curves of exciton-polariton. Dashed lines: non-coupled exciton (yellow) and cavity mode (purple).

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**MDPI and ACS Style**

Cao, J.; Kavokin, A.
Optical Properties of Magnetic Monopole Excitons. *Condens. Matter* **2023**, *8*, 43.
https://doi.org/10.3390/condmat8020043

**AMA Style**

Cao J, Kavokin A.
Optical Properties of Magnetic Monopole Excitons. *Condensed Matter*. 2023; 8(2):43.
https://doi.org/10.3390/condmat8020043

**Chicago/Turabian Style**

Cao, Junhui, and Alexey Kavokin.
2023. "Optical Properties of Magnetic Monopole Excitons" *Condensed Matter* 8, no. 2: 43.
https://doi.org/10.3390/condmat8020043