Quantum geometric phases in systems with spin-orbit coupling

Medic, Luka (avtor), Ramšak, Anton (mentor)

This Thesis explores the interplay between quantum geometric phases, spin-orbit interaction (SOI), topology, and quantum dynamics in three distinct systems: open quantum spin-boson models, nonlinear optical response in topological semimetals, and synthetic topological phases in Josephson junctions. In the first part, we consider the spectral and initial value problem for the Lindblad-Gorini-Kossakowski-Sudarshan master equation describing an open quantum system of bosons and spins, where the bosonic parts of the Hamiltonian and Lindblad jump operators are quadratic and linear respectively, while the spins couple to bosons via mutually commuting spin operators. As a concrete example, we examine a spin qubit that is confined in a driven harmonic trap, influenced by Rashba SOI, and coupled to a thermal bath. In the band theory, SOI lifts band degeneracy, a crucial factor in the search for topological states of matter, including Weyl semimetals (WSMs). In the second part of this Thesis, we investigate anomalous high-harmonic generation in a model undergoing a transition from a time-reversal symmetry-broken WSM to a semi-Dirac regime. The latter is a gapless semimetal with a dispersion that is parabolic in one direction and conical in the other two. We demonstrate that the intensity of the induced anomalous high harmonics is significantly enhanced in the semi-Dirac regime. In WSMs, we show that anomalous high harmonics primarily originate from excitations at momenta where the dispersion deviates from strict linearity. Furthermore, we establish that within the linearized low-energy theory, the anomalous response remains purely harmonic, highlighting the role of nonlinear band dispersion in driving higher-order harmonics. In the third part, we study a two-terminal Josephson junction with conventional superconductors and a normal region with Rashba SOI, characterized by two Aharonov-Casher (AC) fluxes. When the superconducting phase difference equals $\pi$, the Andreev subgap spectrum may host zero-energy Weyl singularities associated with a vanishing normal-state reflection eigenvalue. With one of the AC fluxes playing the role of a quasimomentum, the junction can be viewed as an artificial one-dimensional chiral topological insulator. Its topological phase can be tuned by crossing a Weyl singularity by means of varying the remaining AC flux. By associating an additional component of the quasimomentum with the superconducting phase difference, an artificial Chern insulator is realized. Lastly, we devise a driving protocol to determine the enclosed topological charge by measuring superconducting and spin currents through the system.

• Jezik: Angleški jezik
• Ključne besede: geometric phase, spin-orbit interaction, third quantization, high harmonic generation, Weyl semimetal, Berry curvature, topological invariant, Josephson junction, Andreev bound state, Aharonov-Casher effect, kinematic curvature
• Vrsta gradiva: Doktorsko delo/naloga
• Tipologija: 2.08 - Doktorska disertacija
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2025
• PID: 20.500.12556/RUL-168421
• COBISS.SI-ID: 229429251
• Datum objave v RUL: 12.04.2025

Sekundarni jezik

• Jezik: Slovenski jezik
• Naslov: Kvantne geometrijske faze v sistemih s sklopitvijo spin-tir

Izvleček

V tej disertaciji obravnavamo kvantne geometrijske faze, interakcijo spin-tir, topologijo in kvantno dinamiko v treh različnih sistemih: odprti kvantni spin-bozonski modeli, nelinearen optični odziv v topoloških polkovinah in sintetične topološke faze v Josephsonovih stikih. V prvem delu obravnavamo spektralni problem lastnih vrednosti in problem začetnih vrednosti za Lindblad-Gorini-Kossakowski-Sudarshanovo enačbo, ki opisuje odprti kvantni sistem bozonov in spinov, kjer so Hamiltonijan in Lindbladovi operatorji kvadratični oziroma linearni v bozonskih operatorjih, spini pa se z bozoni sklapljajo preko medsebojno komutirajočih spinskih operatorjev. Podrobneje obravnavamo primer odprtega spin-bozonskega modela, ki opisuje spinski kubit v prisotnosti Rashbove sklopitve spin-tir, pri čemer je kubit ujet v gnano harmonično past in sklopljen s termalno kopeljo. V teoriji elektronskih pasov interakcija spin-tir odpravlja degeneracijo energijskih pasov. Slednje je pomemben dejavnik pri iskanju topoloških materialov, kar vključuje Weylove polkovine. V drugem delu disertacije raziskujemo generiranje anomalnih višjih harmonikov v modelu, ki vključuje prehod iz Weylove polkovine z zlomljeno simetrijo na obrat časa v semi-Diracov režim, tj. polkovino brez energijske reže in z disperzijo, ki je v eni smeri parabolična in v drugih dveh linearna. Predstavimo, da je intenziteta induciranih anomalnih višjih harmonikov visoka v semi-Diracovem režimu. Za Weylove polkovine pokažemo, da so anomalni višji harmoniki posledica vzbujanj pri momentih, kjer disperzija ni strogo linearna, in da je v linearizirani nizkoenergijski teoriji anomalni odziv le harmoničen. V tretjem delu preučujemo dvoterminalni Josephsonov stik s konvencionalnimi superprevodniki in normalnim območjem z Rashbovo sklopitvijo spin-tir, ki jo karakterizirata dve neodvisni Aharonov-Casherjevi (AC) fazi. Ko je superprevodna fazna razlika enaka $\pi$, lahko spekter vezanih stanj Andrejeva vsebuje Weylove singularnosti z ničelno energijo, ki so hkrati povezane z ničelno refleksivnostjo v nesuperprevodnem stanju sistema. Z eno od AC faz, ki igra vlogo kvazimomenta, lahko stik obravnavamo kot sintetični enodimenzionalni kiralni topološki izolator. Topološko fazo lahko spreminjamo s prehodom skozi Weylovo singularnost s spreminjanjem preostale AC faze. Če obravnavamo superprevodno fazno razliko kot dodatno komponento kvazimomenta, realiziramo sintetični Chernov izolator. Na koncu predlagamo protokol za določitev zaobjetega topološkega naboja z merjenjem superprevodnih in spinskih tokov skozi sistem.

• Ključne besede: geometrijska faza, sklopitev spin-tir, tretja kvantizacija, generiranje visokih harmonikov, Weylova polkovina, Berryjeva ukrivljenost, topološka invarianta, Josephsonov stik, vezano stanje Andrejeva, Aharonov-Casherjev pojav, kinematična ukrivljenost