This document discusses how antiferromagnetic magnons can enhance superconductivity by mediating attractive interactions between electrons. It explains that while phonons typically mediate superconductivity, magnons from a magnetic material can also induce electron pairing. The key points are that antiferromagnetic magnons have a squeezed ground state with large net spins on each sublattice, and coupling electrons to only one of these sublattices results in a dramatically amplified electron interaction strength and higher critical temperature for superconductivity.

1. Enhancement of superconductivity mediated by
antiferromagnetic squeezed magnons
Eirik Erlandsen, Akashdeep Kamra, Arne Brataas, and Asle Sudbø
Phys. Rev. B 100, 100503(R) (2019)

2. 2
Superconductivity
• Interaction between electrons mediated by phonons
• Attractive interaction in a thin shell around the Fermi surface
• Leads to formation of Cooper pairs below a critical temperature
Bardeen et al., Phys. Rev. 108, 1175-1204 (1957)
: Depends on the strength of theattractive
interactionand the densityofstates at the Fermi level
: Cutoffon phonon spectrum

3. 3
Magnon-mediated superconductivity
• Electron-magnon interactions can arise from interfacial coupling to a magnetic material
• Different magnet/conductor heterostructures have been investigated
• Predicted:
• Interaction between electrons mediated by magnons
• Leads to formation of Cooper pairs below a critical temperature
Rohling et al., Phys. Rev. B 97, 115401 (2018)
Fjærbu et al., Phys. Rev. B 100, 125432 (2019)
Kargarian et al., Phys. Rev. Lett. 117, 076806 (2016)
Hugdal et al., Phys. Rev. B 97, 195438 (2018)
Gong et al., Science Advances 3, e1602579 (2017)

4. 4
The ferromagneticground state
• Excitations: magnons = delocalized spin flips
Ground state
State with one magnon
State with two magnons

5. 5
The antiferromagnetic ground state
• Spin-flip magnon on sublattice A
• Spin-flip magnon on sublattice B
A A AB B
• State with no sublattice magnons (Néel state)
• This is not the quantum ground state of an antiferromagnet
• The sublattice spin-flip magnons are not the eigen-excitations of an antiferromagnet

6. 6
The antiferromagnetic ground state
Spin-flip magnon on sublattice A
Spin-flip magnon on sublattice B
• The ground state can, however, be expressed in
term of the sublattice spin-flip magnons
• The result is a two-mode squeezed state, familiar
from quantum optics
Kamra et al., Phys. Rev. B 100, 174407 (2019)
Ground state
State with one spin-up
antiferromagneticmagnon
Néel state

7. 7
Coupling enhancement
• The net spin on each sublattice associated
with an antiferromagnetic magnon is typically
much larger than one
Kamra et al., Phys. Rev. B 100, 174407 (2019)
• Asymmetric coupling achievable through an
uncompensated antiferromagnetic interface
• Coupling to only one sublattice involves
coupling to a large spin

8. 8
System
Erlandsen et al., Phys. Rev. B 100, 100503(R) (2019)
• Compensated and uncompensated
antiferromagnetic interfaces can be
realized in experiments
• The model allows us to tune between
these two cases
• We derive effective electron-electron
interactions mediated by magnons
• Attractive interactions in the spin-triplet
, p-wave channel
Compensated UncompensatedModel

9. 9
Result
Erlandsen et al., Phys. Rev. B 100, 100503(R) (2019)
• Dramatically amplified interaction strength
and critical temperature when coupling to
an uncompensated antiferromagnetic
interface