# Superconducting surfaces, solitons and skyrmions

**Time: **
Mon 2024-05-13 15.00

**Location: **
FA31, Roslagstullsbacken 21, Stockholm

**Language: **
English

**Doctoral student: **
Mats Barkman
, Kondenserade materiens teori

**Opponent: **
Professor Leo Radzihovsky, University of Colorado Boulder

**Supervisor: **
Egor Babaev, Kondenserade materiens teori

QC 2024-04-29

## Abstract

This thesis focuses on superconductivity, a field within condensed matter physics which since its experimental discovery roughly a century ago, not only has lead to significant contributions revealing the fundamental theories of physics, but also to practical applications. This includes for example quantum vortices, which play paramount roles both in other condensed matter settings, but also in high-energy physics. The dissipationless currents in superconductors are essential to achieve the strong magnetic fields necessary when performing Magnetic Resonant Imaging (MRI).

My research on superconductors spans across three topics: superconducting surfaces, multiband superconductivity and inhomogeneous states formed in imbalanced superfluids. A brief introduction and summary of the scientific contribution of this thesis to each of these topics is given below.

Bardeen-Cooper-Schrieffer (BCS) theory tells us that from a microscopic perspective, superconductivity is the phenomenon of condensation of bound electron pairs, so-called Cooper pairs. The superconducting state is described by a complex-valued field known as the superconducting gap parameter. In the most simple superconducting materials, where there is only one electronic band, only one complex field is necessary to describe the superconducting state, which spontaneously breaks U(1)-symmetry. In other superconducting materials, such as the iron-based superconductor Ba_{1−x}K* _{x}*Fe

_{2}As

_{2}, the band structure is more complicated and multiple electronic bands are present. Such multiband superconductors may require multiple complex fields to describe the superconducting state, which can spontaneously break other symmetries, such as time-reversal symmetry, in addition to U(1)-symmetry.

Two proposed pairing symmetries for spontaneous time-reversal symmetry breaking (TRSB) spin-singlet superconductors are *s*+i*s* and *s*+i*d*. In Paper IV, we demonstrate how magnetic features of pinned domain walls in anisotropic TRSB superconductors can be used to distinguish between *s*+i*s* and *s*+i*d* pairing.

Classifying topological excitations in superconductors is crucial to understand the superconducting state. For example, quantum vortices are key in understanding the magnetic response of type-II superconductors, and the thermal fluctuations-induced phase transitions in superconductors and superfluids. It has been hypothesized that multiband superconductors, which are described by multiple complex fields, can host topological excitations which are different from the ordinary quantum vortices. Understanding the properties of these new topological excitations carries similar importance to that of ordinary quantum vortices. In Paper VII and Paper VIII, we provide the first microscopic demonstration of multiband fractional vortices and **C**P^{2}-skyrmions using fully self-consistent Bogoliubov-de Gennes (BdG) theory. Previous demonstrations of such topological excitations have been done using classical field theory approaches, such as Ginzburg-Landau (GL) theory. Our BdG calculations maintain microscopic degrees of freedom which are neglected using GL and quasiclassical theories of superconductivity.

The most well-known inhomogeneous superconducting phase is the Abrikosov vortex lattice, which forms in the presence of an external magnetic field in type-II superconductors. Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) proposed another type of inhomogeneous superconducting state, which may form in the presence of a suﬀiciently large population imbalance between spin up and spin down electrons. The origin of this supersolid state is the formation of Cooper pairs with non-zero net momentum due to spin-dependent Fermi surfaces. In Paper V, we show that spin-imbalanced superfluids can host a unique type of solitons, even before the FFLO regime is entered. These solitons are not present in ordinary uniform superconducting states, and can therefore act as identifiable traces of the FFLO state.

The Fulde-Ferrell state and the Larkin-Ovchinnikov state are characterized respectively by modulation in the phase and the density of the superconducting gap parameter. In Paper II, we explored the possibility of other types of inhomogeneous states caused by imbalance in multiband superconductors. Using GL theory, we demonstrated two new types of inhomogeneous states, characterized by spatially alternating chirality and nematicity.

Understanding the superconducting properties of surfaces and boundaries is important, both fundamentally to the theory of superconductivity and practically in the construction of superconducting devices. In Paper I and Paper III we demonstrate using both GL and BdG theory that pair-density-wave superconductors support superconducting surface states with critical temperatures larger than the bulk critical temperature. In Paper VI we show increased critical temperatures of superconductor-insulator interfaces. The increase in critical temperature occurs without locally increasing the superconducting pairing strength near the boundaries, or without the introduction of modified surface phonons.