Time Evolution in Superconducting Nanostructures

• Název práce v češtině: Časový vývoj v supravodivých nanostrukturách
• Název v anglickém jazyce: Time Evolution in Superconducting Nanostructures
• Klíčová slova: kvantové tečky|supravodivost|Josephsonův jev|časový vývoj|náhlá změna
• Klíčová slova anglicky: quantum dots|superconductivity|Josephson Junction|time evolution|quench
• Akademický rok vypsání: 2024/2025
• Typ práce: bakalářská práce
• Jazyk práce: angličtina
• Ústav: Katedra fyziky kondenzovaných látek (32-KFKL)
• Vedoucí / školitel: RNDr. Martin Žonda, Ph.D.
• Řešitel: skrytý - zadáno a potvrzeno stud. odd.
• Datum přihlášení: 10.05.2025
• Datum zadání: 11.05.2025
• Datum potvrzení stud. oddělením: 12.05.2025
• Datum odevzdání elektronické podoby: 17.07.2025
• Oponenti: doc. RNDr. Tomáš Novotný, Ph.D.
• Konzultanti: Mgr. Daniel Bobok

Zásady pro vypracování

Over the past decades, significant progress has been made in experimental techniques that enable the coupling of nanodevice, often containing only a few active orbital, with superconducting (SC) reservoirs. These hybrid systems are promising components for superconducting electronics, advanced sensing applications, and both topological and quantum technologies.

While the equilibrium properties of simple systems, such as a single quantum dot coupled to one or two BCS leads, are now well understood, more complex geometries and out-of-equilibrium scenarios still present considerable theoretical challenges. To address these, our group has recently developed scalable, effective models that allow for an efficient investigation of dynamical properties in such systems.

The aim of this thesis is to explore the transient dynamics following sudden change, known as quenches, in system parameters. The research will focus on two central questions:

1.How is the proximity effect established when a quantum dot is suddenly coupled to superconducting leads?
2.Can the recently discovered symmetry that maps a multi-lead system to two symmetrically coupled leads be generalized to systems under finite voltage bias?


The student will develop a strong foundation in the physics of hybrid superconducting nanostructures, with a particular focus on the superconducting Anderson Impurity Model in its various formulations. This involves working with the formalism of second quantization, understanding the fundamentals of Green’s functions, and deriving effective low-energy models.

Utilizing the recently introduced chain mapping technique for representing leads, the work will emphasize the time evolution of large non-interacting electron systems via the Liouville-von Neumann equation for the density matrix. This approach is expected to pave the way for future generalizations that incorporate magnetic dynamics, modeled by a classical spin coupled to the quantum dot.

Seznam odborné literatury

[1] J. Klíma, B. Velický, Kvantová Mechanika I., Karolinum
[2] V. Meden; The Anderson–Josephson quantum dot—a theory perspective; J. Phys.: Condens. Matter 31 163001 (2019)
[3] A. Kadlecova et al.; Practical Guide to Quantum Phase Transitions in Quantum-Dot-Based Tunable Josephson Junctions. Phys. Rev. Applied 11, 044094 (2019)
[4] J. Cheng et al.; Quasiparticle trapping in quench dynamics of superconductor / quantum dot / superconductor Josephson junctions; Phys. Rev. B 110, 125417 (2024)
[5] R. Seoane Souto et al.Transient dynamics of a magnetic impurity coupled to superconducting electrodes: Exact numerics versus perturbation theory, Phys. Rev. B 104, 214506 (2021)
[6] K. Wrześniewski et al., B. Baran, R. Taranko, T. Domański, and I. Weymann, Quench dynamics of a correlated quantum dot sandwiched between normal-metal and superconducting leads, Phys. Rev. B 103, 155420 (2021).