Quantum magnetism in systems with SU(N) symmetry and magnetic impurities in superconductors

PhD Program

Speaker

Chen-How Huang
DIPC

When

2025/04/09
14:30

Place

Auditorium CFM (Donostia / San Sebastián)

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PhD Thesis defense by Chen-How Huang

Supervisors: Miguel Angel Cazalilla Gutierrez (Ikerbasque Research Professor)

Quantum Systems and Technologies

Magnetic phenomena in systems exhibiting superconductivity, quantum impurity interactions, and exotic phase transitions present a rich domain for theoretical exploration. This thesis synthesizes insights from several studies investigating these areas.

* The interplay between superconductors (SC) and ferromagnetic insulators (FMI) reveals novel correlations, where the FMI induces spin polarization at the SC surface through the magnetic proximity effect.
This effect is further examined via Kondo coupling to magnetic impurities, demonstrating energy splitting in fermion-parity states linked to Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interactions and spin-triplet correlations. Numerical renormalization group (NRG) and perturbative analyses establish a scaling relationship between this splitting and the Kondo temperature relative to the superconducting gap.

* Quantum spin- 1/2 impurities coupled to s-wave superconductors are analyzed using large-N mean-field theory, which proves effective in the strong-coupling regime (TK ≳ ∆). This method accurately predicts Yu-Shiba-Rusinov subgap states, their spectral properties, and local density profiles, complementing NRG techniques and extending to more complex impurity models.

* We propose to utilize two spin-1/2 imputiries on a superconducting bath as a quantum qubit. This can be realized with either quantum dots or triangulene spin-1 Heisenberg chain on superconducting surface. An effective two level model is proposed to describe the dynamics and validated by time-dependent NRG.

* In SU(N > 2)-symmetric Fermi gases, the ferromagnetic phase transition is shown to be first-order, in line with Landau's mean-field predictions. Unrestricted Hartree-Fock calculations and beyond-mean-field corrections illustrate the role of magnetic fluctuations, which amplify the abruptness of the transition and enhance full polarization tendencies in the gas.

* Investigating lightly-doped multilayer graphene with a generalized four-component spin model reveals density-driven phase transitions.
While Hartree-Fock methods predict cascading transitions, incorporation of correlation energies via the random- phase approximation simplifies these to a single transition governed by the interplay iii iv of exchange and correlation energies. These findings elucidate the phase behavior of multilayer graphene and extend to similar symmetry-broken electron gas systems.

This amalgamation highlights the universality and diversity of magnetic transitions and interactions, spanning superconductors, Fermi gases, and layered graphene systems, thereby offering a foundation for future theoretical and experimental studies.