Abstract
In this thesis, superconductivity of fermions in twodimensional Hubbard lattice models is theoretically studied. Each of the studied lattice structures features intriguing properties that provide valuable insight to understand superconductivity in general. While real condensed matter systems are too complicated to tackle with theoretical tools, the Hubbard model is one of the simplest quantum manybody models to possess a wide spectrum of physically relevant phenomena, from superconductivity to magnetism and topological order. Hubbard models are also interesting as they can be experimentally realized and accurately controlled by utilizing ultracold gases. The first part of the thesis explains the required theoretical background of superconductivity in the level of meanfield and linear response theories. Specifically, we primarily focus on the superfluid weight which implies the existence of the Meissner effect and dissipationless current, defining properties of superconductors. We further discuss how the BerezinskiiKosterlitzThouless (BKT) transition, related to the loss of superconductivity due to the thermal fluctuations of the superconducting order parameter in high enough temperatures, can be accessed via the superfluid weight. In the second part, the main results are discussed. We show how the superconductivity of lattice models featuring dispersionless Bloch bands, socalled flat bands, can be large and originating from the quantum geometric properties of the Bloch states of the flat bands. This is in contrast to conventional dispersive bands where superconductivity is determined by the effective mass of the particles, i.e. by the dispersion relation of the Bloch bands alone and not by the Bloch states. This is well demonstrated in the Lieb lattice geometry, studied in Publication I, which features both a strictly flat and two dispersive Bloch bands, allowing direct comparison of superconductivity in dispersive and flat bands. We show how the superconductivity of the flat band is more robust than that of the dispersive bands and how the superfluid weight behaves nonmonotonically as a function of the interaction strength. This nonmonotonic behavior should be experimentally accessible. Flat band superconductivity is also the topic of Publication III, where the experimentally realized twisted bilayer graphene (TBG) is studied with local and nonlocal attractive interactions. We predict qualitative differences between local and nonlocal interaction schemes which could be distinguished experimentally and reveal the quantum geometric origin of superconductivity in TBG systems in case of both the assumed interaction schemes. Exotic FuldeFerrell (FF) superfluid phases, characterized by the nonzero momentum of Cooper pairs, were explored in Publication II. We show how the FF phases can be stabilized against thermal fluctuations in the presence of spinorbit coupling (SOC) and that topologically nontrivial FF states, created with SOC and Zeeman fields, can be found at finite temperatures.
Original language  English 

Qualification  Doctor's degree 
Awarding Institution 

Supervisors/Advisors 

Publisher  
Print ISBNs  9789526088549 
Electronic ISBNs  9789526088556 
Publication status  Published  2019 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 superconductivity
 Hubbard model
 topology
 lattice
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Julku, A. (2019). Superconductivity in geometrically and topologically nontrivial lattice models. Aalto University.