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A study of proximity-induced and magnon-mediated superconductivity on the surface of topological insulators
Full text linkSummary:
This thesis presents a study of superconducting phases in different effectively two-dimensional (2D) systems with spin-orbit coupling, with particular emphasis on systems consisting topological insulators (TIs) in proximity to superconductors (S) and magnetic insulators. The research has led to five papers.
The first paper examines the possible superconducting phases in a 2D repulsive Hubbard model with Zeeman splitting and Rashba spin-orbit coupling, showing that the Kohn-Luttinger mechanism is responsible for the effective attractive pairing. The spin-orbit coupling, however, indirectly affects the symmetry of the order parameter, leading to a chiral p ± ip or p state depending on the orientation of the Zeeman field.
Two papers consider the proximity effect between a superconductor and topological insulator, and the interplay with exchange fields. When a spin valve is placed on top of a TI Josephson junction, we find that vortices can be induced on the surface of the TI depending on the spin valve configuration. We also study the possibility of a strong inverse proximity effect — a significant reduction in the superconducting gap — in an S-TI bilayer, finding that this is unlikely for a conventional s-wave superconductor, but might occur in unconventional superconductors with low Fermi energies.
The final two papers examine superconductivity mediated by magnons on the surface of a TI coupled to a magnetic insulator. When neglecting the frequency dependence of the magnons we find that, depending on the coupling between the magnons, both BCS type and Amperean p-wave pairing is possible. Including the magnon frequency dependence, we also find the possibility of odd-frequency s-wave Amperean pairing.Sammendrag — Superledning i topologiske isolatorer
En superleder er et materiale som kan lede strøm uten motstand, og som derfor ikke utvikler varme. Med tanke på hvor mye energitap som skyldes motstanden i ledninger og elektriske komponenter, høres dette helt fantastisk ut. Problemet er at de fleste superledere må kjøles ned til minst minus 140 grader Celsius, noe som naturligvis setter begrensninger for praktisk bruk.
De siste årene har det blitt forsket på om superledere kan brukes i store datasentre. Datasentrene bruker nemlig allerede enorme mengder energi på kjøling, og det kan derfor faktisk lønne seg å bruke superledende komponenter. Spørsmålet blir da hvordan man kan sende og lagre informasjon ved hjelp av superledere, og hvilke andre materialer som skal inngå i slike systemer.
Et foreslått materiale er topologiske isolatorer. Disse materialene leder strøm kun på overflatene – det indre av materialet er isolerende og leder dermed ikke strøm. De metalliske tilstandene på overflaten av topologiske isolatorer er også robuste mot urenheter, noe som kan gjøre dem godt egnet til teknologiske anvendelser. Ved å plassere en superleder inntil en topologiske isolator smitter noen av de superledende egenskapene over på den topologiske isolatoren, og teoretiske beregninger har vist at dette kan gi en helt spesiell type partikler som kan brukes i kvantedatamaskiner.
I mitt doktorgradsarbeid har jeg gjort teoretiske undersøkelser av ulike typer superledning på overflaten av topologiske isolatorer. Superledningen kan enten arves fra en nærliggende superleder, eller oppstå grunnet vekselvirkninger med en magnet som gjør selve den topologiske isolatoren superledende.
Håpet er at stadig ny kunnskap om superledning etterhvert skal føre til teknologiske fremskritt som både bidrar til å redusere energibruk, og å lage mer effektive datamaskiner
Colossal enhancement of photomagnonic coupling in antiferromagnet-topological insulator heterostructures
Full text linkStudien av Magnon-foton interaksjonar som følgje av Zeeman-kopling i elektromagnetiske holrom er eit veksande felt som har vore gjenstand for granskning innan forskning på kvantematerie og elektronspinn-manipulasjon i magnetiske materialar for spinntroniske applikasjonar. Nylege teoretiske undersøkingar viser at ein kan forvente ei fotomagnonisk vekselverknad som er ti gongar sterkare enn vanleg i overgangen mellom ein topologisk isolator og ein ferromagnet. Der Zeeman-koplinga gir vekselverknad mellom elektronspinnet og den magnetiske komponenten til fotonet, gir den topologiske isolatoren opphav til ein effektiv kopling til fotonet sin elektriske komponent. I denne oppgåva utvidar vi dette resultatet til tilfelle der ein istadenfor brukar ein antiferromagnet, og viser korleis dette gir ei ytterlegare tidobling av vekselverknaden. Jamført den vanlege fotomagnoniske Zeeman-koplinga i antiferromagnetiske materialar, er dette ei auking på minst to størrelsesordner. For å vise dette, utleies ein effektiv teori for magnon-foton-systemet ved hjelp av Feynman's løypeintegralformalisme ved å integrere ut det fermioniske elektronfeltet sine fridomsgrader. Vidare granskes korleis den resulterande vekselverknad avhenger av temperatur og den antiferromagnetiske elektronspinnordninga i overgangen, før dei fotoniske og magnoniske Green-funksjonane utleies. Vi finn uttrykk for den spektroskopiske splittinga og spreiingsoppførselen til fotonar som vekselverkar med heterostrukturen som følgje av den fotomagnoniske koplinga ved å studere systemet sin spektralfunksjon. Til slutt forslår vi at den allereie eksisterande heterostrukturen MnSe/Bi₂Se₃ er ein framifrå kandidat for å realisere den foreslåtte koplinga i eksperiment.The study of strong magnon-photon interactions due to Zeeman coupling in electromagnetic cavities is an emerging field within the study of quantum matter and the manipulation of spin states in magnetic materials for spintronic applications. Recent theoretical work predicts that the photomagnonic interaction is enhanced by an order of magnitude at the interface between an appropriately chosen combination of a topological insulator material and a ferromagnet. Unlike the Zeeman interaction, which couples the electron spin to the photon's magnetic field component, the topological insulator mediates a coupling to the electric field-component of the photon. Here, we expand this result to the case of antiferromagnet-topological insulator heterostructures, and show that the interaction strength can be enhanced by an order of magnitude relative to its ferromagnetic counterpart. This further constitutes an enhancement of at least two orders of magnitude relative to the conventional Zeeman-based photomagnonic interaction in antiferromagnets. To do so, we derive an effective photomagnonic theory for a model system using the Feynman path integral formalism to integrate out the interacting topological insulator's electronic degrees of freedom. The resulting interaction's dependence on temperature and the antiferromagnet's interfacial spin ordering is studied, before deriving the Green's functions for the magnonic and photonic fields. Expressions for the resulting polarization dependent spectroscopic splitting and anticrossing behaviour of the resulting photon dispersion is derived using the system's spectral function. Finally, we propose that the existing MnSe/Bi₂Se₃ heterostructure is an excellent candidate for realizing the interaction in experiment
Diffusive Curved Superconductor-Ferromagnet Proximity Systems in and out of Equilibrium
Full text linkI strukturer med superledere og ferromagneter kan superledende korrelasjoner lekke et lite stykke inn i ferromagneten; dette er den superledende proksimitetseffekten. Hybridsystemer hvor denne effekten er signifikant kan ved de rette omstendighetene gi opphav til spinn-polariserte superledende korrelasjoner som penetrerer et langt stykke inn i ferromagneten. Dette er lik-spinn triplett korrelasjoner. Superstrømmer av disse lik-spinn triplettene har netto spinn, slik at de kan la oss manipulere den magnetiske strukturen til materialer uten varmetapet fra konvensjonell elektronikk.
Å krumme disse hybridstrukturene kan være en måte å generere lik-spinn triplett korrelasjoner. Krumning har fordelen at den i prinsippet er dynamisk justerbar, og ikke avhengig av iboende egenskaper i materalet.
I denne avhandlingen undersøkes egenskapene til krummede superleder-ferromgnet hybridstrukturer i regimet med diffusiv transport. Vi reformulerer Usadel-likningen med et endelig spin-bane juster-felt for en-dimensjonale kurver i planet, i tillegg til kvante-kinetiske likninger for å undersøke ikke-likevektsegenskapene til systemet. Videre introduserer vi en buelengde parametrisering av en klasse kurver, slik av vi kan studere effekten av ikke-uniform krumning.
Analyse av likevekt-superstrømmene viser en forsterkning av den totale ladningsstrømmen dersom systemet krummes. Avhengig av den geometriske symmetrien på systemet kan overgangen gjennomgå en 0-π overgang. Denne 0-π overgangen skjer ved forskjellige krumningsamplituder avhengig av symmetrien på den krummede regionen. En krumningsindusert 0-π overgang er i prinsippet dynamisk justerbar, og dermed lovende for anvendelser i spintronikk .
Analyse av spinn-akkumulering i en krummet ledning indikerer krummingsavhengige spinn-akkumuleringsprofiler, disse kan videre manipuleres ved å sette en spenning på systemet. Dette kan gi flere frihetsgrader for å manipulere kretselementer i spintronikk-systemer. Rammeverket kan også fasilitere videre undersøkelser av ikke-likevektseffekter i hybridstrukturer med superledere.In junctions between superconductors and ferromagnets, superconducting correlations may penetrate a short distance into the ferromagnet; this is the superconducting proximity effect. Heterostructures exhibiting the superconducting proximity effect may under the right conditions generate spin-polarized superconducting correlations that penetrate far into the ferromagnet; these are the long range triplet correlations. Supercurrents carried by long range triplets carry net spin, and may allow us to manipulate the magnetic structure of materials without the heat-loss of conventional electronics.
Introducing curvature to these heterostructures is a candidate for the generation of long range triplet correlations, and comes with the advantages that it is in principle dynamically tuneable and not directly dependent on intrinsic properties of the material.
In this thesis, we investigate the properties of curved superconductor-ferromagnet heterostructures in the diffusive regime. We reformulate the Usadel equation with a non-zero spin orbit field for 1D planar curves, as well as the quantum kinetic equations for investigating the non-equilibrium properties of the system. Furthermore, we introduce an arc length parametrization for a class of curves of non-uniform curvature to investigate the effects of non-uniform curvature on the system.
Analysis of the equilibrium supercurrent predict a curvature-induced amplification of the total charge current, that depending on the symmetry of the curved region the addition of curvature could induce a 0-π transition. The 0-π transition is also indicated to appear at different amplitudes of curvature depending on the symmetry of the curved region. A curvature induced 0-π transition is in principle dynamically tuneable, and thus promising for spintronic applications.
Analysis of the spin accumulation of a curved wire revealed curvature dependent spin accumulation profiles that could be further manipulated by an applied voltage bias; this may open new degrees of freedom in manipulating spintronic devices. The framework may also facilitate further investigation into non-equilibrium effects in superconductor heterostructures
A study of proximity-induced and magnon-mediated superconductivity on the surface of topological insulators
No full textSummary:
This thesis presents a study of superconducting phases in different effectively two-dimensional (2D) systems with spin-orbit coupling, with particular emphasis on systems consisting topological insulators (TIs) in proximity to superconductors (S) and magnetic insulators. The research has led to five papers.
The first paper examines the possible superconducting phases in a 2D repulsive Hubbard model with Zeeman splitting and Rashba spin-orbit coupling, showing that the Kohn-Luttinger mechanism is responsible for the effective attractive pairing. The spin-orbit coupling, however, indirectly affects the symmetry of the order parameter, leading to a chiral p ± ip or p state depending on the orientation of the Zeeman field.
Two papers consider the proximity effect between a superconductor and topological insulator, and the interplay with exchange fields. When a spin valve is placed on top of a TI Josephson junction, we find that vortices can be induced on the surface of the TI depending on the spin valve configuration. We also study the possibility of a strong inverse proximity effect — a significant reduction in the superconducting gap — in an S-TI bilayer, finding that this is unlikely for a conventional s-wave superconductor, but might occur in unconventional superconductors with low Fermi energies.
The final two papers examine superconductivity mediated by magnons on the surface of a TI coupled to a magnetic insulator. When neglecting the frequency dependence of the magnons we find that, depending on the coupling between the magnons, both BCS type and Amperean p-wave pairing is possible. Including the magnon frequency dependence, we also find the possibility of odd-frequency s-wave Amperean pairing
Possible odd-frequency Amperean magnon-mediated superconductivity in topological insulator–ferromagnetic insulator bilayer
Full text linkWe study the magnon-mediated pairing between fermions on the surface of a topological insulator (TI) coupled to a ferromagnetic insulator with a tilted mean field magnetization. Tilting the magnetization toward the interfacial plane reduces the magnetic band gap and leads to a shift in the effective TI dispersions. We derive and solve the self-consistency equation for the superconducting gap in two different situations, where we neglect or include the frequency dependence of the magnon propagator. Neglecting the frequency dependence results in p-wave Amperean solutions. We also find that tilting the magnetization into the interface plane favors Cooper pairs with center-of-mass momenta parallel to the magnetization vector, increasing Tc compared to the out-of-plane case. Including the frequency dependence of the magnon propagator, and solving for a low number of Matsubara frequencies, we find that the eigenvectors of the Amperean solutions at the critical temperature are dominantly odd in frequency and even in momentum, thus opening the possibility for odd-frequency Amperean pairing
Quasiclassical theory for the superconducting proximity effect in Dirac materials
No full textWe derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking p· σ¯, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field
Vortex spin valve on a topological insulator
No full textSpin-valve structures are usually associated with the ability to modify the resistance of electrical currents. We here demonstrate a profoundly different effect of a spin-valve. In combination with a topological insulator and superconducting materials, we show that a spin-valve can be used to toggle quantum vortices in and out of existence. In the antiparallel configuration, the spin valve causes superconducting vortex nucleation. In the parallel configuration, however, no vortices appear. This switching effect suggests a new way to control quantum vortices
Vortex spin valve on a topological insulator
Full text linkSpin-valve structures are usually associated with the ability to modify the resistance of electrical currents. We here demonstrate a profoundly different effect of a spin-valve. In combination with a topological insulator and superconducting materials, we show that a spin-valve can be used to toggle quantum vortices in and out of existence. In the antiparallel configuration, the spin valve causes superconducting vortex nucleation. In the parallel configuration, however, no vortices appear. This switching effect suggests a new way to control quantum vortices.publishedVersion©2018 American Physical Societ
Dichroic cavity mode splitting and lifetimes from interactions with a ferromagnetic metal
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Inverse proximity effect in s-wave and d-wave superconductors coupled to topological insulators
Full text linkWe study the inverse proximity effect in a bilayer consisting of a thin s- or d-wave superconductor (S) and a topological insulator (TI). Integrating out the topological fermions of the TI, we find that spin-orbit coupling is induced in the S, which leads to spin-triplet p-wave ( f -wave) correlations in the anomalous Green’s function for an s-wave (d-wave) superconductor. Solving the self-consistency equation for the superconducting order parameter, we find that the inverse proximity effect can be strong for parameters for which the Fermi momenta of the S and TI coincide. The suppression of the gap is approximately proportional to e−1/λ, where λ is the dimensionless superconducting coupling constant. This is consistent with the fact that a higher λ gives a more robust superconducting state. For an s-wave S, the interval of TI chemical potentials for which the suppression of the gap is strong is centered at μTI = ± √ 2mv2 Fμ, and increases quadratically with the hopping parameter t . Since the S chemical potential μ typically is high for conventional superconductors, the inverse proximity effect is negligible except for t above a critical value. For sufficiently low t , however, the inverse proximity effect is negligible, in agreement with what has thus far been assumed in most works studying the proximity effect in S-TI structures. In superconductors with low Fermi energies, such as high-Tc cuprates with d-wave symmetry, we again find a suppression of the order parameter. However, since μ is much smaller in this case, a strong inverse proximity effect can occur at μTI = 0 for much lower values of t . Moreover, the onset of a strong inverse proximity effect is preceded by an increase in the order parameter, allowing the gap to be tuned by several orders of magnitude by small variations in μTI. DOI: 10.1103
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