This thesis presents the work done on electronic transport in various interacting and non-interacting systems in one and two dimensions. The systems under study are: an interacting quantum dot [1], a non-interacting quantum wire and a ring in which time-dependent potentials are applied [2], an interacting quantum wire and networks of multiple quantum wires with resistive regions [3, 4], one-dimensional edge stages of a two-dimensional topological insulator [5], and a hybrid system of two-dimensional surface states of a three-dimensional topological insulator and a superconductor [6]. In the first chapter, we introduce a number of concepts which are used in the rest of the thesis, such as scattering theory, Landauer conductance formula, quantum wires, bosonization, topological insulators and superconductor. In the second chapter, we study transport through a quantum dot with interacting electrons which is connected to two reservoirs. The quantum dot is modeled by two sites within a tight-binding model with spinless electrons. Using the Lippman-Schwinger method, we write down an exact two-particle wave function for the dot-reservoir system with the interaction localized in the region of the dot. We discuss the phenomena of two-particle resonance and rectification. In the third chapter, we study pumping in two kinds of one-dimensional systems: (i) an infinite line connected to reservoirs at the two ends, and (ii) an isolated ring. The infinite line is modeled by the Dirac equation with two time-independent point-like backscatterers that create a resonant barrier. We demonstrate that even if the reservoirs are at the same chemical potential, a net current can be driven through the channel by the application of one or more time-dependent point-like potentials. When the left-right symmetry is broken, a net current can be pumped from one reservoir to the other by applying a time-varying potential at only one site. For a finite ring, we model the system by a tight-binding model. The ring is isolated in the sense that it is not connected to any reservoir or environment. The system is driven by one or more time-varying on-site potentials. We develop an exact method to calculate the current averaged over an infinite amount of time by converting it to the calculation of the current carried by certain states averaged over just one time period. Using this method, we demonstrate that an oscillating potential at only one site cannot pump charge, and oscillating potentials at two or more sites are necessary to pump charge. Further we study the dependence of the pumped current on the phases and the amplitudes of the oscillating potentials at two sites. In the fourth chapter, we study the effect of resistances present in an extended region in a one-dimensional quantum wire described by a Tomonaga-Luttinger liquid model. We combine the concept of a Rayleigh dissipation function with the technique of bosonization to model the dissipative region. In the DC limit, we find that the resistance of the dissipative patch adds in series to the contact resistance. Using a current splitting matrix M to describe junctions, we study in detail the conductances of: a three-wire junction with resistances and a parallel combination of resistances. The conductance and power dissipated in these networks depend in general on the resistances and the current splitting matrices that make up the network. We also show that the idea of a Rayleigh dissipation function can be extended to couple two wires; this gives rise to a finite transconductance analogous to the Coulomb drag. In the fifth chapter, we study the effect of a Zeeman field coupled to the edge states of a two-dimensional topological insulator. These edge states form two one-dimensional channels with spin-momentum locking which are protected by time-reversal symmetry. We study what happens when time-reversal symmetry is broken by a magnetic field which is Zeeman-coupled to the edge states. We show that a magnetic field over a finite region leads to Fabry-P´erot type resonances and the conductance can be controlled by changing the direction of the magnetic field. We also study the effect of a static impurity in the patch that can backscatter electrons in the presence of a magnetic field. In the sixth chapter, we use the Blonder-Tinkham-Klapwijk formalism to study trans-port across a line junction lying between two orthogonal topological insulator surfaces and a superconductor (which can have either s-wave or p-wave pairing). The charge and spin conductances across such a junction and their behaviors as a function of the bias voltage applied across the junction and various junction parameters are studied. Our study reveals that in addition to the zero conductance bias peak, there is a non-zero spin conductance for some particular spin states of the triplet Cooper pairs. We also find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for a p-wave symmetry of the superconductor order parameter.

The physics of iron pnictides has been the subject of intense research for half a decade since the discovery of superconductivity in doped LaFeAsO in 2008. By now there exists a large number of different materials that are summarized under the term "pnictides'' with significant differences in their crystal structure, electronic properties, and their phase diagrams. This thesis is concerned with the investigation of the various phase transitions that are observed in the underdoped compounds of the pnictide subgroups RFeAsO, where R is a rare-earth element, and AFe_2As_2, where A is an alkaline-earth element. These compounds display two closely bound transitions from a tetragonal to an orthorhombic phase and from a paramagnetic to an antiferromagnetic metal. Both symmetry-broken phases are suppressed by doping or pressure and close to their disappearance superconductivity sets in. The superconducting state is stabilized until some optimal doping or pressure is reached and gets suppressed thereafter. The central goal of this thesis is to improve our understanding of the interplay between these three phases and to describe the various phase transitions. We start from an itinerant picture that explains the magnetism as a result of an excitonic instability and show how the other phases can be included into this picture. This approach is based on the the observation that the compounds we are interested in have a Fermi surface with multiple nested electron and hole pockets and that they have small to intermediate interaction strengths. The thesis starts with a study of the doping dependence of the antiferromagnetic phase transition in four different five-orbital models. We use the random-phase approximation to determine the transition temperature, the dominant ordering vector, and the contribution of the different orbitals to the ordering. This allows us to identify the more realistic models, which give results that are in good agreement with experimental observations. In addition to the frequently made assumption of orbital-independent interaction potentials we study the effect of a reduction of the interaction strengths that involve the d_{xy} orbital. We find that this tunes the system between two different nesting instabilities. A reduction of the interactions that involve the d_{xy} orbital also enhances the tendency towards incommensurate (IC) order. For a weak reduction this tendency is compensated by the presence of the orthorhombic phase. However, for a reduction of 30%, as it is suggested by constrained random-phase-approximation calculations, we always find large doping ranges, where a state with IC order has the highest transition temperature. We continue the investigation of the magnetic phase transition by studying the competition of different possible types of antiferromagnetic order that arises from the presence of two degenerate nesting instabilities with the ordering vectors (pi,0) and (0,pi). We derive a Ginzburg-Landau free energy from a microscopic two-band model and find that the presence of the experimentally observed stripe phase strongly depends on the number and size of the hole pockets in the system and on the doping. We show that within the picture of a purely magnetically driven nematic phase transition, which breaks the C_4 symmetry and induces the orthorhombic distortion, the nematic phase displays exactly the same dependence on the model parameters as the magnetic stripe phase. We propose that in addition to the purely magnetically driven nematic instability there is a ferro-orbital instability in the system that stabilizes the nematic transition and, thus, explains the experimentally observed robustness of the orthorhombic transition. We argue that including a ferro-orbital instability into the picture may also be necessary to reproduce the transition from simultaneous first-order transitions into an orthorhombic antiferromagnetic state to two separate second-order transitions, which is observed as a function of doping. Finally, a study of the superconducting phase transition inside the antiferromagnetic phase that is observed in some pnictide compounds is presented. We present an approach to calculate the fluctuation-mediated pairing interaction in the spin-density-wave phase of a multiband system, which is based on the random-phase approximation. This approach is applied to a minimal two-band model for the pnictides to study the effect of the various symmetry-allowed bare on-site interactions on the gap symmetry and structure. We find a competition between various even- and odd-parity states and over a limited parameter range a p_x-wave state is the dominant instability. The largest part of the parameter space is dominated by even parity states but the gap structure sensitively depends on the bare interactions. We propose that the experimentally observed transition from a nodeless to a nodal gap can be due to changes in the on-site interaction potentials.

In der vorliegenden Arbeit wurden vor allem das Auftreten und der Mechanismus von feldinduzierten Übergängen und der damit verbundenen kritischen Felder untersucht. Die verwendete Magnetisierungsmessmethode ist auf die bestehende Impulsfeldanlage des IFW Dresden abgestimmt. Die Magnetisierung in Feldern bis zu 48 T wurde gemessen. Erstmals wurde für Sm2Fe17N3 der Anisotropiekoeffizient aus der Kombination der Messung des Austauschfeldes mittels inelastischer Neutronenstreuung und der Messung der Anisotropiekonstanten K1 am gleichen Material bestimmt. Für den führenden Anisotropiekoeffizienten konnte mit K1 von rund 13 MJ/m³ der Wert A20<r²> = -28 meV bestimmt werden. Der in SmCo2,5Cu2,5 und SmCo2Cu3 beobachtete Hochfeldübergang konnte mit der Mikrostruktur verknüpft werden. Die laminare Mikrostruktur bestehend aus Phasen mit unterschiedlichem Sm-Anteil ist eine notwendige Bedingung für das Auftreten des Übergangs. Das Koerzitivfeld steigt mit dem Kupfergehalt und erreicht bei tiefen Temperaturen sehr hohe Werte. Das Koerzitivfeld und das Übergangsfeld zeigen eine große magnetische Viskosität. In DyFe6Al6 wird das Verschwinden der spontanen Magnetisierung bei tiefen Temperaturen durch starke antiferromagnetische Kopplungen verursacht. Durch ein feldinduziertes magnetisches Moment an einem ungeordneten Kristallgitterplatz könnte der magnetische Übergang bei tiefen Temperaturen erklärt werden. An hexagonalem DyMn6Ge6 wurde erstmals der Temperaturverlauf des Übergangsfeldes zur gekanteten antiferromagnetischen Struktur gemessen. Oberhalb von 100 K ruft das angelegte Feld den Übergang von der helimagnetischen zu einer Fächerstruktur hervor. Bei tiefen Temperaturen tritt ein Spinflop-Übergang auf, der durch die magnetische Anisotropie des Dysprosiumions unterstützt wird. Bei magnetokalorischen Materialien zeigt sich eine Abhängigkeit der gemessenen Magnetisierung von der Feldänderungsrate. Dies lässt sich qualitativ auf die Messbedingungen zurückführen: So herrschen bei Impulsfeldmessungen adiabatische Bedingungen, während bei statischen Messungen isotherme Verhältnisse vorliegen. Neben herkömmlichen magnetischen Verbindungen wurden auch stark korrelierte Elektronensysteme untersucht. Der gefundene Magnetisierungsübergang bei 43 T in CeNi2Ge2 lässt sich auf das Unterdrücken des Kondoeffekts und das Aufbrechen der antiferromagnetischen Struktur zurückführen. Darüber hinaus wurden Magnetisierungsmessungen an Hochtemperatursupraleitern durchgeführt. Die Messungen im Impulsfeld sind ein Beitrag zur Bestimmung des Phasendiagramms von schmelztexturiertem YBa2Cu3O7-d. Das Irreversibilitätsfeld Hirr konnte an massiven Proben bis zu tiefen Temperaturen bestimmt werden. Hirr(T) zeigt einen unerwarteten linearen Anstieg bis zu tiefen Temperaturen. Aufgrund der hohen Feldänderungsraten und großen Unterschiede von Ummagnetisierungsprozessen in magnetischen Materialien gibt es derzeit keine einheitliche Beschreibung der magnetischen Viskosität für Feldänderungsraten im Bereich von 0,001 bis zu 1000 T/s. Durch die Messung im Impulsfeld konnte die Größenordnung der magnetischen Viskosität in nanokristallinem Bariumferrit bestimmt werden. Magnetisierungsmessungen im Impulsfeld stellen sowohl durch das hohe Magnetfeld als auch aufgrund der hohen bzw. variierenden Feldänderungsrate ein sehr nützliches Instrument zur Untersuchung feld- und zeitabhängiger Eigenschaften von Festkörpern dar. / In this work, the occurrence and the mechanism of field induced transitions and the related critical fields were investigated. The way of measuring the magnetisation was designed for the existing pulsed field device of the IFW Dresden. The magnetisation was measured in fields up to 48 T. For the first time, the anisotropy coefficient of Sm2Fe17N3 was obtained in the combined measurement of the exchange field via inelastic neutron scattering and the measurement of the anisotropy constant K1 for the same material. For the leading anisotropy coefficient, a value of A20<r²> = -28 meV was found using K1 of about 13 MJ/m³. It was shown that the observed high field transition in SmCo2.5Cu2.5 and SmCo2Cu3 is connected with the microstructure. The laminar microstructure consisting of phases with different Sm-content is a necessary precondition for the occurrence of the transition. The coercivity increases with the Cu-content and reaches high values at low temperature. The coercivity and the transition field show big magnetic viscosity. In DyFe6Al6, the disappearance of the spontaneous magnetisation at low temperature is caused by a strong antiferromagnetic coupling. The magnetic transition at low temperature could be explained by a field induced magnetic moment on a disordered crystal site. For the hexagonal DyMn6Ge6, the temperature dependence of the transition field towards the canted antiferromagnetic structure was measured for the first time. Above 100 K, the applied field causes the transition from the helimagnetic to the fan structure. At low temperature, a spin flop transition occurs, which is supported by the magnetic anisotropy of the Dy-ion. The magnetisation of magnetocaloric materials exhibits a dependence of the field changing rate. This can be explained qualitatively by the measurement condition: The pulsed field measurement is adiabatic, whereas during static measurements, the condition is isothermal. Besides common magnetic compounds, highly correlated electron systems were also investigated. The magnetic transition at 43 T in CeNi2Ge2 can be explained by the suppression of the Kondo effect and the breaking up of the antiferromagnetic structure. Furthermore, magnetisation of high temperature superconductors was measured. The measurements in the pulsed field are a contribution to the determination of the phase diagram of melt textured YBa2Cu3O7-d. The irreversibility field Hirr was measured for bulk samples down to low temperature. Hirr(T) shows an unexpected linear increase down to low temperature. Because of the high field-changing rates and the big differences of magnetisation processes in magnetic materials, there is no uniform description of the magnetic viscosity for field changing rates in the magnitude from 0,001 up to 1000 T/s. By the measurement in the pulsed field, the magnitude of the magnetic viscosity of nanocrystalline barium ferrite was determined. Magnetisation measurement in pulsed fields is a very useful instrument to investigate field and time dependent properties of solids due to their high magnetic field and their high and varying field changing rate.

Nuclear Magnetic Resonance (NMR) has been a fundamental player in the studies of superconducting materials for many decades. This local probe technique allows for the study of the static electronic properties as well as the low energy excitations of the electrons in the normal and the superconducting state. On that account it has also been widely applied to Fe-based superconductors from the very beginning of their discovery in February 2008. This dissertation comprises some of these very first NMR results, reflecting the unconventional nature of superconductivity and its strong link to magnetism in the investigated compounds LaO(1-x)F(x)FeAs and LiFeAs.:1. Introduction 2. Basic Principles of NMR 3. NMR in the Superconducting State 4. Iron-based Superconductors 5. Experimental Setup 6. NMR on LaO(1-x)F(x)FeAs in the Normal State 7. MR and NQR on LaO(1-x)F(x)FeAs in the Superconducting State 8. NMR and NQR on LiFeAs 9. Conclusions

In dieser Arbeit werden niederfrequente optische Messungen an vier neuartigen Supraleitern vorgestellt. Im Bereich von 100 GHz bis 3 THz zeigen die vier untersuchten Systeme – LuNi2B2C, Ba(Fe0,9Co0,1)2As2, T’-Pr2CuO4 und Si:Ga – ein sehr unterschiedliches Verhalten. Die beiden erst genannten Supraleiter sind Mehrbandsupraleiter, bei denen die Cooper-Paarkopplung unterschiedlich für verschiedene Fermiflächen ist. T’-Pr2CuO4 ist ein undotierter Kupratsupraleiter, der nach bisheriger Lehrmeinung nicht existieren dürfte. Mit THz-Spektroskopie konnte erstmals die Bildung einer Meißner-Phase in T’-Pr2CuO4 mit optischen Methoden beobachtet werden. Eine gewisse Sonderstellung nimmt Si:Ga als amorpher Supraleiter ein. Si:Ga wird durch Ionenimplantation von Gallium in einen Siliziumwafer hergestellt. Es besteht die Hoffnung, mit Si:Ga halb- und supraleitende Logikblöcke in großem Maßstab auf einem Chip vereinen zu können, da die Ionenimplantation mit den Produktionsprozessen der Halbleiterindustrie kompatibel ist.

Die vorliegende Arbeit beschäftigt sich mit der Entwicklung neuer Schichtsysteme für die Realisierung biaxial texturierter hochtemperatursupraleitender Bandleiter. Bisher sind eine Vielzahl von Bandleiterarchitekturen bekannt, die sowohl durch physikalische Depositionsmethoden als auch mittels Abscheidung aus der chemischen Lösung hergestellt werden können. Während die Funktion von YBCO-Bandleitern mit Hilfe physikalischer Depositionsmethoden in den letzten Jahren demonstriert werden konnte, zeigen auf chemischem Wege deponierte Bandleiter schlechtere Eigenschaften. Seitens der Industrie besteht ein starkes Interesse, die hohen Produktionskosten, die im Hinblick auf physikalische Depositionsmethoden mit einem hohen Anlagenaufwand verbunden sind, anhand der kostengünstigen chemischen Synthese von Einzelschichten oder der gesamten Bandleiterarchitektur zu senken. Gelöst wurde diese Aufgabe innerhalb der vorliegenden Arbeit durch die Entwicklung metallorganischer Vorstufenlösungen zur Deposition von CaTiO3-, SrTiO3-Pufferschichten und supraleitender YBa2Cu3O7-Schichten.

Robust states exist at the interfaces between topologically trivial and nontrivial phases of matter. These boundary states are expression of the nontrivial bulk properties through a connection dubbed the bulk-boundary correspondence. Whether the bulk is topological or not is determined by the value of a topological invariant. This quantity is defined with respect to symmetries and dimensionality of the system, such that it takes only quantized values. For static topological phases that are realized in ground-states of isolated, time-independent systems, the topological invariant is related to the properties of the Hamiltonian operator. In contrast, Floquet topological phases that are realized in open systems with periodical pumping of energy are topologically characterized with a unitary Floquet operator i.e., the time-evolution operator over the entire period. Topological phases of matter can be distinguished by the dimensionality of robust boundary states with respect to the protecting bulk. This dissertation concerns recently discovered higher-order topological phases where the difference between dimensionalities of bulk and boundary states is larger than one. Using analytical and numerical single-particle techniques, we focus on instances where static higher-order topology can be understood with insights from the mature field of Floquet topology. Namely, even though static systems do not admit a Floquet description, we find examples of higher-order systems to which certain unitary operators can be attributed. The understanding of topological characteristics of these systems is therefore conditioned by the knowledge on topological properties of unitary operators, among which the Floquet operator is well-known. The first half of this thesis concerns toy models of static higher-order topological phases that are topologically characterized in terms of unitary operators. We find that a class of these systems called quadrupole topological insulators exhibit a wider range of topological phases than known previously. In the second half of this dissertation, we study reflection matrices of higher-order topological phases and show that they can exhibit the same topological features as Floquet systems. Our findings suggest a new route to experimental realizations of Floquet systems, the one that avoids noise-induced decoherence inevitable in many other experimental setups.

In dieser Arbeit werden Messungen elektrischer, thermischer und insbesondere thermoelektrischer Transportkoeffizienten in topologischen Weyl-Halbmetall-Kandidaten sowie in eisenbasierten Hochtemperatur-Supraleitern vorgestellt, analysiert und diskutiert. In TaAs und TaP, zwei Weyl-Halbmetall-Kandidaten mit gebrochener Inversionssymmetrie, liefert das anomale Verhalten des Nernst-Signals in Abhängigkeit des Magnetfeldes Hinweise auf die Existenz von Weyl-Punkten in der Nähe der Fermi-Fläche, wobei sich die Verschiebung des chemischen Potenzials sowie ein Lifshitz-Übergang detektieren lassen. Die Temperaturabhängigkeit des Nernst-Signales erlaubt außerdem Rückschlüsse auf den Abstand der Weyl-Punkte zur Fermi-Fläche. In Mn3Ge, einem Weyl-Halbmetall-Kandidaten mit gebrochener Zeitumkehrsymmetrie, zeigt sich für alle gemessenen Temperaturen ein komplett anomales Verhalten des Nernst-Signals in Abhängigkeit des Magnetfeldes mit einer rechteckigen Hysterese bei kleinen Feldern, welches im Vergleich mit Daten der Magnetisierung einen eindeutigen Hinweis auf die Präsenz von Weyl-Punkten in diesem Material liefert. Mithilfe eines minimalen theoretischen Modells zweier Weyl-Punkte in der Nähe der Fermi-Fläche lässt sich eine Anpassungsformel für die Temperaturabhängigkeit des Nernst-Signals gewinnen, aus welcher sowohl geometrische Parameter der Bandstruktur als auch die Stärke der Berry-Krümmung an der Fermi-Energie extrahiert werden können. Für eisenbasierte Supraleiter besteht seit Langem der Verdacht, dass nematische Fluktuationen einen Einfluss auf die Supraleitung haben. Hier vorgestellte theoretische Betrachtungen zeigen im Rahmen eines Zweibandmodells eindeutig, dass eine endliche nematische Kopplung zu einer starken Erhöhung und einer nicht-monotonen Abhängigkeit des Nernst-Koeffizienten von der Dotierung führt, welcher ein Maximum über dem supraleitenden Dom aufweist. Dies wird anhand von Nernst-Messungen in Co-dotiertem LaFeAsO bestätigt. Ein Vergleich der Ergebnisse des Nernst-Effekts mit Elasto-Widerstandsmessungen enthüllt eine erstaunliche Ähnlichkeit der Dotierabhängigkeiten. Die Daten werden außerdem mit Messungen des Nernst-Effekts an Rh-dotiertem BaFe2As2 verglichen, wobei ebenfalls eine Erhöhung im Bereich optimaler Dotierung nachgewiesen werden kann. In Rh-dotietem BaFe2As2 zeigt sich jedoch ein Unterschied zwischen Elasto-Widerstands- und Nernst-Messungen, woraus abgeleitet wird, dass Elasto-Widerstandsmessungen kein vollständiges Bild der nematischen Fluktuation liefern. Der Nernst-Effekt ist hingegen aufgrund der Sensitivität auf nematische Fluktuationen universell in zwei Vertretern verschiedener Familien eisenbasierter Supraleiter maximal im Bereich des supraleitenden Doms. Dies liefert, zusammen mit den theoretischen Betrachtungen, einen starken Hinweis auf den Einfluss nematischer Fluktuationen auf die Supraleitung. / In this work the electric, thermal, and thermoelectric transport properties of several topological Weyl semimetal candidates and iron-based superconductors are investigated. In TaAs and TaP, two Weyl semimetal candidates with broken inversion symmetry, the Nernst signal exhibits anomalous behaviour as a function of magnetic field, consistent with Weyl points close to the Fermi surface. Furthermore, a shift of the chemical potential and a Lifshitz transition are detected. The temperature dependence of the Nernst signal allows for an estimation of the energy of the Weyl points with respect to the Fermi level. In Mn3Ge, a Weyl semimetal candidate with broken time reversal symmetry, the Nernst signal shows completely anomalous behaviour as a function of magnetic field that can be obtained at all measured temperatures. At low fields the signal exhibits a rectangular hysteresis cycle. A comparison with magnetization measurements evidently shows that these effects are caused by Weyl points lying close to the Fermi surface. With the help of a minimal model of two Weyl points in the vicinity of the Fermi level, a fitting formula of the temperature dependence of the Nernst signal can be obtained. The fit provides geometrical properties of the band structure, such as the $\boldsymbol{k}$-space separation of the Weyl points, their energy with respect to the Fermi level as well as the strength of the Berry curvature close to the Fermi energy. For a long time nematic fluctuations have been suspected to influence superconductivity in iron-based superconductors. A theoretical analysis, with the help of a two-band model, shows clearly that a finite nematic coupling causes a strong enhancement and non-monotonic behaviour of the Nernst coefficient, which develops a maximum above the superconducting dome. These findings are confirmed by Nernst measurements in Co-doped LaFeAsO. A comparison with elasto-resistivity measurements shows a stunning similarity of the doping dependencies of both quantities. Furthermore the data are compared with measurements on Rh-doped BaFe2As2, which also exhibits an enhancement of the Nernst coefficient in the region of optimal doping. However, in Rh-doped BaFe2As2 a difference between elastoresistivity and Nernst measurements is obtained, indicating that the elasto-resistivity measurements are not universally sensitive to nematic fluctuations. The Nernst effect, on the other hand, is enhanced in the vicinity of the superconducting dome in two members of different families of iron-based superconductors. Together with theoretical insights, these results provide strong evidence for the influence of nematic fluctuations on superconductivity in the iron-based superconductors.