Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -- so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the exploitation of fermionic duality for a quantum dot with strong interaction -- covering both the repulsive and attractive case -- proximized by contact with a large-gap superconductor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong interaction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analytically in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.Comment: Submission to SciPos

Magnon dispersion in bilayers of two-dimensional ferromagnets

We determine magnon spectra of an atomic bilayer magnet with ferromagnetic intra- and both ferro- and anti- ferromagnetic interlayer coupling. Analytic expressions for the full magnon band of the latter case reveal that both exchange interactions govern the fundamental magnon gap. The inter and intralayer magnetic ordering are not independent: the intralayer ferromagnetism stabilizes antiferromagnetic inter-layer order. The topology of these exchange-anisotropy spin models without spin-orbit interaction turns out to be trivial

Magnon dispersion in bilayers of two-dimensional ferromagnets

We determine magnon spectra of an atomic bilayer magnet with ferromagnetic intra- and both ferro- and antiferromagnetic interlayer coupling. Analytic expressions for the full magnon band of the latter case reveal that both exchange interactions govern the fundamental magnon gap. The inter- and intralayer magnetic ordering are not independent: a stronger ferromagnetic intralayer coupling effectively strengthens the antiferromagnetic interlayer coupling as we see from comparison of two bilayer systems. The trivial topology of these exchange-anisotropy spin models without spin-orbit interaction excludes a magnon thermal Hall effect.</p