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Transport theory and finite element methods for mesoscopic superconducting devices
Doctoral thesis, 2022

This thesis investigates superconductors that are brought out of equilibrium through injection of charge and heat from normal-metal reservoirs. In particular for unconventional superconductors, where the pairing correlations have a non-trivial orbital symmetry, the resulting non-equilibrium is thus far only partially explored. A better understanding is desirable both from a fundamental point of view as well as for applications in superconducting devices.

As a step in this direction, we study transport in mesoscopic superconducting hybrid structures with arbitrary mean free path using the quasiclassical theory of superconductivity. In order for fundamental conservation laws to be satisfied, a description of the non-equilibrium state requires a fully self-consistent solution of the underlying equations. We present strategies on how such a self-consistent solution can be achieved. Using these techniques, we investigate the non-linear steady-state response of both conventional and unconventional superconductors to an external voltage- or temperature-bias. Specifically, we study charge transport in a conventional s-wave and an unconventional d-wave superconductor under voltage bias, the thermoelectric effect due to elastic impurity scattering in both systems, and the influence of spectral rearrangements on a suggested sub-dominant s-wave order-parameter component in d-wave superconductors. Lastly, we introduce a finite element method for the quasiclassical theory. It can be used to study transport in two or more dimensions where geometric effects such as current focussing and dilution can occur. We present exemplary results based on this method for equilibrium transport in two dimensions.

unconventional superconductors

quasiclassical theory

transport theory

non-equilibrium superconductivity

finite element methods

## Author

### Kevin Marc Seja

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

### Quasiclassical theory of charge transport across mesoscopic normal-metal-superconducting heterostructures with current conservation

PHYSICAL REVIEW B,; Vol. 104(2021)

**Journal article**

### Thermopower and thermophase in a d -wave superconductor

Physical Review B,; Vol. 105(2022)

**Journal article**

### Seja, K.M. & Löfwander, T.: Self-consistent theory of current injection into d and d + is superconductors

### Seja, K.M. & Löfwander, T. : A finite element method for the quasiclassical theory of superconductivity

**Non-equilibrium superconductivity in mesoscopic unconventional superconductors**

At low temperatures, electrons in metals can show peculiar electromagnetic properties such as the flow of lossless charge currents and expelling of external magnetic field. This is called conventional superconductivity and was discovered already in 1911.

Later, in 1987, it was discovered that one specific group of copper-oxide materials exhibit superconductivity at much higher temperatures. These high-temperature superconductors have different properties from the metallic superconductors and are called unconventional. This makes them interesting objects for basic research on unconventional mechanisms of superconductivity.

At the same time, their high critical temperatures make them prime candidates for superconducting device applications. Examples include magnetic field sensors, light detectors, and more. This thesis studies the steady-state non-equilibrium response of such high-temperature superconductors to an applied external bias. This is relevant from a basic research point of view, as well as to improve the understanding of device functionalities based on such materials.

### Collective Modes and Quantum Transport in Quantum Materials

Swedish Research Council (VR) (2019-05274), 2020-01-01 -- 2023-12-31.

### Areas of Advance

Nanoscience and Nanotechnology (SO 2010-2017, EI 2018-)

### Subject Categories

Physical Sciences

### Roots

Basic sciences

### Infrastructure

C3SE (Chalmers Centre for Computational Science and Engineering)

### ISBN

978-91-7905-670-4

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 5136

### Publisher

Chalmers

Kollektorn (A423), 4th floor, MC2, Kemivägen 9, Göteborg

Opponent: Professor Juan Carlos Cuevas, Universidad Autonoma de Madrid, Spain