CeCu_2Si_2 was the first heavy-fermion compound showing signatures of bulk superconductivity (T_c = 0.5 K). Further observations have put in evidence the correlations between superconductivity, magnetic order, Kondo physics, and quantum critical phenomena. In spite of the interest generated, a systematic study of such correlations was hampered by strong sample dependences. Fortunately, the inherent complexity associated to the stoichiometric composition has been recently understood. The availability of single-crystals with well-defined properties has thus reignited the interest in CeCu_2Si_2 as a window to novel phenomena, such as unconventional superconductivity. The present work summarizes the results of my doctoral research. It exemplifies the importance not only of high-quality materials, but also of suitable experimental techniques. A first step in this project involved the design of angle-dependent techniques in the milli-kelvin range, namely: electrical resistivity and thermal conductivity. It comprised the development of a rotational stage, the construction of sample holders, and the implementation of controlling and measuring components. In the second part of the project, electrical- and thermal-transport measurements on CeCu_2Si_2 were performed. Power-law behavior below T_c in the thermal conductivity suggests the presence of lines of nodes in the gap function. Also, the non-vanishing extrapolated residual terms (k_00/T ) support the presence of a residual density of states. The nodes are broadened by potential scattering, which appears to be significant in CeCu_2Si_2. The scattering hinders the determination of the symmetry of the order parameter and might be responsible for the observed isotropic angle dependence of the thermal conductivity. In contrast, angle-dependent measurements of the upper critical field exhibit a four-folded behavior, which also points towards the presence of nodes. By comparing with a weak-coupling model including the effects of Pauli limiting and anisotropic Fermi velocity, the results point towards a d_xy-wave symmetry of the order parameter. Such results represent the first angle-dependent measurements supporting a d-wave symmetry in CeCu_2Si_2.

In this thesis, an extended periodic Anderson model with an additional local Coulomb repulsion U f c between localized f electrons and conduction electrons is investigated by use of the projector-based renormalization method (PRM). First, it is shown that the model in one dimension shows a valence transition, which becomes sharper, when the energy of the f level approaches the Fermi level. The transition becomes also enhanced, when the hybridization V between the localized and conduction electrons decreases, for the case that the total number of electrons is fixed. In the two-dimensional case, one finds a similar valence transition behavior. However, in the valence transition regime also a superconducting phase may occur. To investigate this phase, we start from an Hamiltonian which includes small gauge symmetry breaking fields. We derive renormalization equations, from which the superconducting pairing functions are self-consistently determined. Our analytical and numerical results show that d- wave superconductivity becomes dominant in the valence transition regime. This confirms the suggestion by Miyake that valence fluctuations may lead to superconductivity in the Ce based heavy-fermion systems under high pressure. / In dieser Arbeit wird mit Hilfe der projektiven Renormierungsmethode (PRM) ein erweitertes periodische Anderson Modell untersucht, das zusätzlich eine Coulomb-Abstoßung zwischen den lokalisierten f-Elektronen und den Leitungselektronen enthält. In einer Dimension zeigt das Modell einen Valenzübergang, wenn sich die Energie des f-Niveaus der Fermienergie nähert. Der Übergang wird ebenfalls schärfer, wenn bei festgehaltener Gesamtelektronenzahl die Hybridisierung V zwischen den lokalisierten und den Leitungselekronen abnimmt. In zwei Dimensionen findet man ein ähnliches Valenzübergangsverhalten. Allerdings kann zusätzlich eine supraleitende Phase im Valenzübergangsgebiet auftreten. Um die supraleitende Phase zu untersuchen, betrachten wir einen Hamiltonoperator mit kleinen zusätzlichen Feldern, die die Eichsymmetrie brechen. Wir leiten Renormierungsgleichungen her, aus denen sich die supraleitenden Paarfunktionen selbstkonsistent bestimmen lassen. Unsere analytischen und numerischen Resultate zeigen, dass im Valenzübergangsgebiet d-Wellen-Supraleitung dominiert. Dies bestätigt eine Vermutung von Miyake, dass Valenzfluktuationen in Ce-basierten Schwerfermionensystemen bei hohen Drücken zur Supraleitung führen können.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

CeCu_2Si_2 was the first heavy-fermion compound showing signatures of bulk superconductivity (T_c = 0.5 K). Further observations have put in evidence the correlations between superconductivity, magnetic order, Kondo physics, and quantum critical phenomena. In spite of the interest generated, a systematic study of such correlations was hampered by strong sample dependences. Fortunately, the inherent complexity associated to the stoichiometric composition has been recently understood. The availability of single-crystals with well-defined properties has thus reignited the interest in CeCu_2Si_2 as a window to novel phenomena, such as unconventional superconductivity. The present work summarizes the results of my doctoral research. It exemplifies the importance not only of high-quality materials, but also of suitable experimental techniques. A first step in this project involved the design of angle-dependent techniques in the milli-kelvin range, namely: electrical resistivity and thermal conductivity. It comprised the development of a rotational stage, the construction of sample holders, and the implementation of controlling and measuring components. In the second part of the project, electrical- and thermal-transport measurements on CeCu_2Si_2 were performed. Power-law behavior below T_c in the thermal conductivity suggests the presence of lines of nodes in the gap function. Also, the non-vanishing extrapolated residual terms (k_00/T ) support the presence of a residual density of states. The nodes are broadened by potential scattering, which appears to be significant in CeCu_2Si_2. The scattering hinders the determination of the symmetry of the order parameter and might be responsible for the observed isotropic angle dependence of the thermal conductivity. In contrast, angle-dependent measurements of the upper critical field exhibit a four-folded behavior, which also points towards the presence of nodes. By comparing with a weak-coupling model including the effects of Pauli limiting and anisotropic Fermi velocity, the results point towards a d_xy-wave symmetry of the order parameter. Such results represent the first angle-dependent measurements supporting a d-wave symmetry in CeCu_2Si_2.

In this thesis, an extended periodic Anderson model with an additional local Coulomb repulsion U f c between localized f electrons and conduction electrons is investigated by use of the projector-based renormalization method (PRM). First, it is shown that the model in one dimension shows a valence transition, which becomes sharper, when the energy of the f level approaches the Fermi level. The transition becomes also enhanced, when the hybridization V between the localized and conduction electrons decreases, for the case that the total number of electrons is fixed. In the two-dimensional case, one finds a similar valence transition behavior. However, in the valence transition regime also a superconducting phase may occur. To investigate this phase, we start from an Hamiltonian which includes small gauge symmetry breaking fields. We derive renormalization equations, from which the superconducting pairing functions are self-consistently determined. Our analytical and numerical results show that d- wave superconductivity becomes dominant in the valence transition regime. This confirms the suggestion by Miyake that valence fluctuations may lead to superconductivity in the Ce based heavy-fermion systems under high pressure. / In dieser Arbeit wird mit Hilfe der projektiven Renormierungsmethode (PRM) ein erweitertes periodische Anderson Modell untersucht, das zusätzlich eine Coulomb-Abstoßung zwischen den lokalisierten f-Elektronen und den Leitungselektronen enthält. In einer Dimension zeigt das Modell einen Valenzübergang, wenn sich die Energie des f-Niveaus der Fermienergie nähert. Der Übergang wird ebenfalls schärfer, wenn bei festgehaltener Gesamtelektronenzahl die Hybridisierung V zwischen den lokalisierten und den Leitungselekronen abnimmt. In zwei Dimensionen findet man ein ähnliches Valenzübergangsverhalten. Allerdings kann zusätzlich eine supraleitende Phase im Valenzübergangsgebiet auftreten. Um die supraleitende Phase zu untersuchen, betrachten wir einen Hamiltonoperator mit kleinen zusätzlichen Feldern, die die Eichsymmetrie brechen. Wir leiten Renormierungsgleichungen her, aus denen sich die supraleitenden Paarfunktionen selbstkonsistent bestimmen lassen. Unsere analytischen und numerischen Resultate zeigen, dass im Valenzübergangsgebiet d-Wellen-Supraleitung dominiert. Dies bestätigt eine Vermutung von Miyake, dass Valenzfluktuationen in Ce-basierten Schwerfermionensystemen bei hohen Drücken zur Supraleitung führen können.