Superconducting Vortices in Half-Metals

When the impurity mean free path is short, only spin-polarized Cooper pairs which are non-locally and antisymmetrically correlated in time may exist in a half-metallic ferromagnet. As a consequence, the half-metal acts as an odd-frequency superconducting condensate. We demonstrate both analytically and numerically that quantum vortices can emerge in half-metals despite the complete absence of conventional superconducting correlations. Because these metals are conducting in only one spin band, we show that a circulating spin supercurrent accompanies these vortices. Moreover, we demonstrate that magnetic disorder at the interfaces with the superconductor influences the position at which the vortices nucleate. This insight can be used to help determine the effective interfacial misalignment angles for the magnetization in hybrid structures, since the vortex position is experimentally observable via STM-measurements. We also give a brief discussion regarding which superconducting order parameter to use for odd-frequency triplet Cooper pairs in the quasiclassical theory.Comment: 9 pages, 8 figure

Exotic Vortex Structures in Diffusive Superconducting Systems

Selv vanligvis ikke-superledende materialer kan oppføre seg superledende dersom de blir plassert inntil en superleder. Dette fenometet kalles the proximity effect på engelsk, og når to materialer plasseres inntil hverandre på denne måten kan det oppstå ny fysikk som ikke finnes i materialene hver for seg. Studien av slike heterogene mesoskopiske strukturer tilbyr gode muligheter, både for grunnleggende og anvendt forskning innen mange ulike felt innen fysikk, slik som kvantedata- maskiner, spinntronikk, interferometri og superledning. Likevel er det fortsatt mye som ukjent, og mange problemer er fortsatt uløste. Denne oppgaven tar for seg to slike problemer. Den første handler om dannelsen av superledende vortekser i superledende kondensater som er odd-frekvens og triplett-spinn. Den andre dreier seg om dannelsen av lukkede vorteksløkker i superledende systemer. Kvantiserte vortekser kan dannes når vanlige superledere eksponeres for et magnetfelt. Dette er et grunnleggende kjennetegn ved superledning, men likevel er lite kjent om hvis og hvordan vortekser kan oppstå i odd-frekvens superledere. Oddfrekvens superledning har aldri blitt observert å oppstå i et materiale spontant, men rene odd-frekvente superledende korrelasjoner kan oppstå i diffusive fullpolariserte ferromagneter dersom de plasseres i nærheten av konvensjonelle superledere. I denne oppgaven studerer jeg slike systemer og finner at superledende vortekser også kan danne seg i rene odd-frekvens triplett-spinn superledende kondensater. Jeg finner at vorteksene i halvmetaller har ekstra dynamikk sammenlignet med vorteksene i normale proksimitetssystemer. Denne dynamikken kan brukes til å avgjøre magnetiseringsvinkler ved grensesjikt som ellers kan være vanskelig å måle. I visse tilfeller antas det at kvantiserte vortkeser kan danne lukkede løkker. Disse superledende vorteksløkkene har vært fokus i mye teoretisk arbeid, men hittil har man ikke klart å detektere dem eksperimentelt. I den andre delen av denne oppgaven studerer jeg et system som jeg viser at gir vorteksløkker med størrelser som enkelt kan kontrolleres. Disse vorteks-løkkene kan gjøres vilkårlig store, og kan dermed justeres så de treffer overflaten. Dette betyr at de kan bli observert direkte, ettersom skanning-tunnelering-mikroskop allerede har blitt brukt til å se superledende vortekser på overflaten av proksimitetssystemer. Resultatene i denne oppgaven antyder også at man kan kontrollere vortekssløkker i andre systemer som er det ikke er like åpenbart at man kan kontrollere, men som det er enklere å lage eksperimentelt. Funnene som presenteres i denne oppgaven har gitt to innsendinger til tidsskriftet Physical Review Letters. Disse ligger vedlagt.When otherwise non-superconducting materials are placed in close proximity to a superconductor, superconducting correlations can leak through their shared boundary. This phenomenon is known as the proximity effect and when two materials are placed adjacent to each other in this way it can lead to new physics not seen in either material on their own. The study of these heterogenic mesoscopic structures offer great opportunities for fundamental as well as applied research in various fields in physics, including quantum computation, spintronics, interferometry and superconductivity. Still, much remains unknown and many problems remains unsolved. This thesis tackles two such problems. The first is regarding the formation of superconducting vortices in pure triplet-spin odd-frequency superconducting condensates and the latter is about the formation of vortex loops in superconducting systems. Quantized vortices can form when ordinary superconductors are exposed to a magnetic field. This is a basic characteristic of superconductivity, but little is known about if and how vortices appear in odd-frequency superconductors. Odd-frequency superconductivity has never been observed to arise spontaneously in a material, but purely odd-frequency superconducting correlations do in fact occur in diffusive fully-polarized ferromagnets when they are placed in proximity to conventional superconductors. In this thesis I study such systems and find that superconducting vortices can also form in purely odd-frequency triplet-spin superconducting condensates. I find that, compared to vortices in normal proximity systems, the vortices in half-metals exhibit extra dynamics. This finding can possibly be used to determine interfacial magnetization angles which are difficult to find directly. In certain situations these quantized vortices are believed to form closed loops. These superconducting vortex loops have so far avoided experimental detection despite being the focus of much theoretical work. In the second part of this thesis I propose a system which host controllable superconducting vortex loops. Because the size of the loops in this system can be controlled and be made arbitrary large, they can be tuned so as to hit the surface. This makes them directly detectable through the method of scanning tunneling microscopy, a method which has already been used successfully to observe superconducting vortices. The findings in this thesis also suggest that vortex loops in systems which are less obviously controllable but more easy to create experimentally can be controlled in a similar fashion. The findings presented in this thesis has yielded two submissions to the journal Physical Review Letters. Preprints are attached in the appendix

Temporarily enhanced superconductivity from magnetic fields

Contrary to the expected detrimental influence on superconductivity when applying a magnetic field, we predict that the abrupt onset of such a field can temporarily strongly enhance the superconducting order parameter. Specifically, we find that the supercurrent in a Josephson junction with a normal metal weak link can increase more than twentyfold in this way. The effect can be understood from the interplay between the energy dependence of Andreev reflection and the abrupt spin-dependent shift in the distribution functions for excitations in the system. The duration of the increase depends on the inelastic scattering rate in the system and is estimated to be in the range of nanoseconds. We demonstrate this by developing a method which solves the Usadel equation for an arbitrary time dependence. This enables the study of ultrafast time-dependent physics in heterostructures combining superconductors with different types of materials.publishedVersio

Temporarily enhanced superconductivity from magnetic fields

Contrary to the expected detrimental influence on superconductivity when applying a magnetic field, we predict that the abrupt onset of such a field can temporarily strongly enhance the superconducting order parameter. Specifically, we find that the supercurrent in a Josephson junction with a normal metal weak link can increase more than twentyfold in this way. The effect can be understood from the interplay between the energy-dependence of Andreev reflection and the abrupt spin-dependent shift in the distribution functions for excitations in the system. The duration of the increase depends on the inelastic scattering rate in the system and is estimated to be in the range of nanoseconds. We demonstrate this by developing a method which solves the Usadel equation for an arbitrary time-dependence. This enables the study of ultrafast time-dependent physics in heterostructures combining superconductors with different types of materials.Comment: 5 (10) pages, 1 (2) figure

Controllable Vortex Loops in Superconducting Proximity Systems

Superconducting vortex loops have so far avoided experimental detection despite being the focus of much theoretical work. We here propose a method of creating controllable vortex loops in the superconducting condensate arising in a normal metal through the proximity effect. We demonstrate both analytically and numerically that superconducting vortex loops emerge when the junction is pierced by a current-carrying insulated wire and give an analytical expression for their radii. The vortex loops can readily be tuned big enough to hit the sample surface, making them directly observable through scanning tunneling microscopy.Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:1904.0484

Spin-orbit pumping

We study theoretically the effect of a rotating electric field on a diffusive nanowire and find an effect that is analogous to spin pumping, which refers to the generation of spin through a rotating magnetic field. The electron spin couples to an external electric field because the particle motion induces an effective magnetic field in its rest frame. In a diffusive system the velocity of the particle, and therefore also its effecive magnetic field, rapidly and randomly changes direction. Nevertheless, we demonstrate analytically and via a physical argument why the combination of the two effects described above produces a finite magnetization along the axis of rotation. This manifests as a measurable spin-voltage in the range of tens of microvolts.Comment: 4 (+3) pages, 3 figure

Barrier and finite size effects on the extension of topological surface-states into magnetic insulators

The interplay between magnetic and topological order can give rise to phenomena such as the quantum anomalous Hall effect. The extension of topological surface states into magnetic insulators (MIs) has been proposed as an alternative to using intrinsically magnetic topological insulators (TIs). Here, we theoretically study how this extension of surface states into a magnetic insulator are influenced both by the interface barrier potential separating a topological insulator and a magnetic insulator and by finite size effects in such structures. We find that the the gap in the surface states depends non-monotonically on the barrier strength. A small, but finite, barrier potential turns out to be advantageous as it permits the surface states to penetrate even further into the MI. Moreover, we find that due to finite size effects in thin samples, increasing the spin-splitting in the MI can actually decrease the gap of the surface states, in contrast to the usual expectation that the gap opens as the spin-splitting increases.Comment: 5 pages, 5 figure

Superconducting proximity effect and long-ranged triplets in dirty metallic antiferromagnets

Antiferromagnets have no net spin-splitting on the scale of the superconducting coherence length. Despite this, antiferromagnets have been observed to suppress superconductivity in a similar way as ferromagnets, a phenomenon that still lacks a clear understanding. We find that this effect can be explained by the role of impurities in antiferromagnets. Using quasiclassical Green's functions, we study the proximity effect and critical temperature in diffusive superconductor-metallic antiferromagnet bilayers. The non-magnetic impurities acquire an effective magnetic component in the antiferromagnet. This not only reduces the critical temperature but also separates the superconducting correlations into short-ranged and long-ranged components, similar to ferromagnetic proximity systems.Comment: 5 pages, 4 figure

Quasiclassical theory for antiferromagnetic metals

Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of of the magnetic moments. The quasiclassical framework is useful because it separates the quantum effects occurring at length scales comparable to the Fermi wavelength from other length scales, and has successfully been used to study a wide range of phenomena involving both superconductivity and ferromagnetism. Starting from a tight-binding Hamiltonian, we develop general quasiclassical equations of motion and boundary conditions, which can be used to describe two-sublattice metallic antiferromagnets in the dirty limit. The boundary conditions are applicable also for spin-active boundaries that can be either compensated or uncompensated. Additionally, we show how nonuniform or dynamic magnetic textures influence the equations and we derive a general expression for observables within this framework.Quasiclassical theory for antiferromagnetic metalsacceptedVersio

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer shallow water equations. So far, it has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions for the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly captures the behaviour of shocks and contact discontinuities without any additional closure relations. The proof yields a novel formulation of an effective one-layer shallow water model. The result shows that simplification to an effective one-layer model is well justified mathematically and can be made without additional knowledge of the shock behaviour. The shock speed in the proposed model is consistent with empirical models and identical to the front conditions that have been found theoretically by e.g. von K\'arm\'an and by Benjamin. This suggests that the breakdown of the shallow-water equations in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the shallow water framework to shocks by studying shocks in one-dimensional lock-exchange/lock-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. We then solve the equations numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer shallow-water equations. We also compare numerical results using our model with results from dam break experiments. Predictions from the one-layer model are found to be in good agreement with experiments.Comment: 23 pages, 17 figure