arXiv subjects

Florian Simon

Publications and source records attributed to Florian Simon.

5 recordsLinked to original sources

arXiv2026

Composite quantum geometry of superconductors

The interplay of superconductivity and the quantum geometry of the normal state has recently been the subject of an array of studies, especially regarding the superfluid weight. In this work, we turn our attention to the quantum geometry of the superconducting state itself, set by the Bogoliubov-de Gennes (BdG) Hamiltonian, which dictates the geometric and topological properties of superconductivity. We show that under three general conditions, namely superconducting fitness, orbital uniformity of the superconducting pairing, and absence of normal-state spin-flip terms, the BdG quantum geometry exactly separates into a sum of the normal-state quantum geometry and an additional pairing quantum geometry, thereby displaying a simple composite structure. We show that this separation holds for all spin-singlet and -triplet pairings, including nonunitary spin-triplet pairing. We further provide explicit analytical formulas for the pairing quantum geometry for all these cases. These results establish how superconducting pairing alone easily drives both topology and a finite quantum metric, thus being present even in topological trivial or flat band superconductors, with no normal state quantum geometry. To complement these results, we also derive the BdG quantum geometry of a general two-orbital spin-singlet superconductor with non-uniform pairing and finite superconducting fitness. Here, our explicit analytical results establish a non-separable composite BdG quantum geometry, with the normal state and pairing contributions generally intertwining, thereby producing even more possibilities for finite quantum geometry. Our results provide design rules for creating superconductors and superconducting hybrid structures with nontrivial topology and finite quantum metric and will additionally help in the experimental diagnosis of unconventional superconductivity.

cond-mat.supr-con↗

arXiv2025

Normal state quantum geometry, non-locality and superconductivity

We investigate aspects of the relation between the quantum geometry of the normal state (NS) and the superconducting phase, through the lens of non-locality. By relating band theory to quantum estimation theory, we derive a direct momentum-dependent relation between quantum geometry and the quantum fluctuations of the position operator. We then investigate two effects of the NS quantum geometry on superconductivity. On the one hand, we present a physical interpretation of the conventional and geometric contributions to the superfluid weight in terms of two different movements of the normal state charge carriers forming the Cooper pairs. The first contribution stems from their center-of-mass motion while the second stems from their zero-point motion, thereby explaining its persistence in flat-band systems. On the other hand, we phenomenologically derive an emergent Darwin term driven by the NS quantum metric. We show its form in one and two-body problems, derive the effective pairing potential in $s$-wave superconductors, and explicit its form in the case of two-dimensional massive Dirac fermions. We thus show that the NS quantum metric screens the pairing interaction and weakens superconductivity, which could be tested experimentally by doping a superconductor. Our work reveals the ambivalent relationship between non-interacting quantum geometry and superconductivity, and possibly in other correlated phases.

cond-mat.supr-con↗

arXiv2025

$\mathbb{Z}_2$ topological invariants from the Green's function diagonal zeros

We investigate the relationship between the analytical properties of the Green's function and $\mathbb{Z}_2$ topological insulators, focusing on three-dimensional inversion-symmetric systems. We show that the diagonal zeros of the Green's function in the orbital basis provide a direct and visual way to calculate the strong and weak $\mathbb{Z}_2$ topological invariants. We introduce the surface of crossings of diagonal zeros in the Brillouin zone, and show that it separates time-reversal invariant momenta (TRIMs) of opposite parity in two-band models, enabling the visual computation of the $\mathbb{Z}_2$ invariants by counting the relevant TRIMs on either side. In three-band systems, a similar property holds in every case except when a trivial band is added in the band gap of a non-trivial two-band system, reminiscent of the band topology of fragile topological insulators.

cond-mat.mes-hall↗

arXiv2023

Normal state quantum geometry and superconducting domes in (111) oxide interfaces

We theoretically investigate the influence of the normal state quantum geometry on the superconducting phase in (111) oriented oxide interfaces and discuss some of the implications for the $\text{LaAlO}_3/\text{SrTiO}_3$ (LAO/STO) heterostructure. From a tight-binding modeling of the interface, we derive a two-band low-energy model, allowing us to analytically compute the quantum geometry and giving us access to the superfluid weight, as well as to showcase the role of two particular relevant energy scales. One is given by the trigonal crystal field which stems from the local trigonal symmetry at the interface, and the other one is due to orbital mixing at the interface. Our calculations indicate that the variation of the superfluid weight with the chemical potential $\mu$ is controlled by the quantum geometry in the low-$\mu$ limit where it presents a dome. At higher values of $\mu$ the conventional contribution dominates. In order to make quantitative comparisons between our results and experimental findings, we rely on an experimentally observed global reduction of the superfluid weight that we apply to both the conventional and geometric contributions. Furthermore, an experimentally measured non-monotonic variation of $\mu$ with the gate voltage $V_g$ is taken into account and yields a two-dome scenario for the superconducting critical temperature as a function of $V_g$. The observed dome in the low-$V_g$ regime is explained by the non-monotonic evolution of a dominant conventional part of the superfluid density. In contrast, the expected second dome at larger values of $V_g$ limit would be due to a dominant quantum-geometric contribution.

cond-mat.supr-con↗

arXiv2022

Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials

We theoretically investigate how the Berry curvature, which arises in multi-band structures when the electrons can be described by an effective single-band Hamiltonian, affects the superconducting properties of two-dimensional electronic systems. Generically the Berry curvature is coupled to electric fields beyond those created by the periodic crystal potential. A potential source of such electric fields, which vary slowly on the lattice scale, is the mutual interaction between the electrons. We show that the Berry curvature provides additional terms in the Hamiltonian describing interacting electrons within a single band. When these terms are taken into account in the framework of the usual BCS weak-coupling treatment of a generic attractive interaction that allows for the formation of Cooper pairs, the coupling constant is modified. In pure singlet and triplet superconductors, we find that the Berry curvature generally lowers the coupling constant and thus the superconducting gap and the critical temperature as a function of doping. From an experimental point of view, a measured deviation from the expected BCS critical temperature upon doping, e.g. in doped two-dimensional transition-metal dichalcogenides, may unveil the strength of the Berry curvature.

cond-mat.mes-hall↗