# Magnetic Monopoles, Dyons and Confinement in Quantum Matter

## Abstract

**:**

## 1. Magnetic Monopoles

## 2. Effective Electromagnetic Action for Quantum Materials

## 3. Compact Effective Action of Granular Insulators

## 4. Quantum Wires and Josephson Junction Chains

## 5. The Superconductor-to-Superinsulator Transition in Quantum Films

## 6. Confinement and Superinsulation

## 7. Dyons, Oblique Confinement and the Pseudogap State

## 8. The Role of Disorder

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A magnetic monopole with its Dirac string, an infinitely thin and long solenoid bringing in the magnetic flux from infinity. The Dirac string is a coordinate singularity and can be displaced to another position by a gauge transformation.

**Figure 4.**A (non-relativistic) magnetic monopole instanton tunnelling between the one-vortex sector and the zero-vortex sector in a 2D quantum film.

**Figure 5.**Short magnetic dipoles when the vortices have tension, panel (

**a**); free magnetic monopoles when the vortices become tensionless Dirac strings, panel (

**b**).

**Figure 6.**Logarithmic plot of the sheet resistance of a NbTiN film as a function of $1/T$. The dashed straight line corresponds to the usual activated behaviour of an insulator. The data show a hyperactivated behaviour fitting the divergent BKT behaviour [10], with ${T}_{c}=0.062{\phantom{\rule{4pt}{0ex}}}^{\circ}K$ without an applied magnetic field and with ${T}_{c}=0.175{\phantom{\rule{4pt}{0ex}}}^{\circ}K$ at $B=0.3$ T. From [17], ©Elsevier (2013).

**Figure 7.**The I(V) curves of a superinsulating NbTiN quantum film at 50 mK, clearly showing the two kinks and three regimes corresponding to the electric Meissner state, the mixed state and the normal insulating state. From [24], Creative Commons Attribution 4.0.

**Figure 8.**The transition from hyperactivated to metallic behaviour of superinsulators as the sample size is decreased, showing asymptotic freedom in the electric pion interior. From [24], Creative Commons Attribution 4.0.

**Figure 9.**Dynamic response of a NbTiN quantum film. Panel (

**a**): the difference between the normal insulator at 300 mK and the superinsulator at 20 mK. Panel (

**b**): the scaling of the shift time ${t}_{\mathrm{sh}}$ as a function of the reduced voltage $(V-{V}_{\mathrm{c}1})$ (with ${V}_{\mathrm{c}1}$ denoted by ${V}_{p}$ here). The two different critical exponents correspond to jumps from the Meissner state to the mixed state and from the Meissner state to the normal insulator, respectively. From [25], Creative Commons Attribution 4.0.

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**MDPI and ACS Style**

Trugenberger, C.A.
Magnetic Monopoles, Dyons and Confinement in Quantum Matter. *Condens. Matter* **2023**, *8*, 2.
https://doi.org/10.3390/condmat8010002

**AMA Style**

Trugenberger CA.
Magnetic Monopoles, Dyons and Confinement in Quantum Matter. *Condensed Matter*. 2023; 8(1):2.
https://doi.org/10.3390/condmat8010002

**Chicago/Turabian Style**

Trugenberger, Carlo A.
2023. "Magnetic Monopoles, Dyons and Confinement in Quantum Matter" *Condensed Matter* 8, no. 1: 2.
https://doi.org/10.3390/condmat8010002