Refine
Has Fulltext
- yes (4)
Is part of the Bibliography
- yes (4)
Document Type
- Doctoral Thesis (4)
Keywords
- Hochtemperatursupraleitung (4) (remove)
Institute
In this thesis, a phenomenological phase-fluctuation model for the pseudogap regime of the underdoped cuprates was discussed. The key idea of the phase-fluctuation scenario in the high-T_c superconductors is the notion that the pseudogap observed in a wide variety of experiments arises from phase fluctuations of the superconducting gap. In this scenario, below a mean-field temperature scale T_c^{MF}, a d_{x^2-y^2}-wave gap amplitude is assumed to develop. However, the superconducting transition is suppressed to a considerably lower transition temperature T_c by phase fluctuations. In the intermediate temperature regime between T_c^{MF} and T_c, phase fluctuations of the superconducting order parameter give rise to the pseudogap phenomena. The phenomenological phase-fluctuation model discussed in this thesis consists of a two-dimensional BCS-like Hamiltonian where the phase of the pairing-amplitude is free to fluctuate. The fluctuations of the phase were treated by a Monte Carlo simulation of a classical XY model. First, the density of states was calculated. The quasiparticle tunneling conductance (dI/dV) obtained from our phenomenological phase fluctuation model was able to reproduce characteristic and salient features of recent scanning-tunneling studies of Bi2212 and Bi2201 suggesting that the pseudogap behavior observed in these experiments arises from phase fluctuations of the d_{x^2-y^2}-wave pairing gap. In calculating the single-particle spectral weight, we were further able to show how phase fluctuations influence the experimentally observed quasiparticle spectra in detail. In particular the disappearance of the BCS-Bogoliubov quasiparticle band at T_c and the change from a more V-like superconducting gap to a rather U-like pseudogap above T_c can be explained in a consistent way by assuming that the low-energy pseudogap in the underdoped cuprates is due to phase fluctuations of a local d_{x^2-y^2}-wave pairing gap with fixed magnitude. Furthermore, phase fluctuations can explain why the pseudogap starts closing from the nodal points, whereas it rather fills in along the anti-nodal directions and they can also account for the characteristic temperature dependence of the superconducting (pi,0)-photoemission-peak. Next, we have shown that the "violation" of the low-frequency optical sum rule recently observed in the SC state of underdoped Bi2212, which is associated with a reduction of kinetic energy, can be related to the role of phase fluctuations. The decrease in kinetic energy is due to the sharpening of the quasiparticle peaks close to the superconducting transition at T_c == T_{KT}, where the phase correlation length xi diverges. A detailed analysis of the temperature and frequency dependence of the optical conductivity sigma(omega)=sigma_1(omega)+i sigma_2(omega) revealed a superconducting scaling of sigma_2(omega), which starts already above T_c, exactly as observed in high-frequency microwave conductivity experiments on Bi2212. On the other hand, our model was only able to account for the characteristic peak, which is observed in sigma_1(omega) close to the superconducting transition, after the inclusion of an additional marginal-Fermi-liquid scattering-rate in the optical conductivity formula. Finally, we calculated the static uniform diamagnetic susceptibility. It turned out that the precursor effects of the fluctuating diamagnetism above T_c are very small and limited to temperatures close to T_c in a phase-fluctuation scenario of the pseudogap. Instead, the temperature dependence of the uniform static magnetic susceptibility is dominated by the Pauli spin susceptibility, which displayed a very characteristic temperature dependence, independent of the details of the gap function used in our model. This temperature dependence is qualitatively very similar to the experimentally observed change of the Knight-shift as a function of temperature in underdoped Bi2212.
This thesis contains two major parts: The first part introduces the reader into three independent concepts of treating strongly correlated many body physics. These are, on the analytical side the SO(5)-theory (Chap.3), which poses the general frame. On the numerical side these are the Stochastic Series Expansion (SSE) (Chap.1) and the Contractor Renormalization Group (CORE) approach (Chap. 2}). The central idea of this thesis was to combine these above concepts, in order to achieve a better understanding of the high-T_c superconductors (HTSC). The results obtained by this combination can be found in the second major part of this thesis (chapters 4 and 5). The main idea of this thesis, i.e., to combine the SO(5)-theory with the capabilities of bosonic Quantum-Monte Carlo simulations and those of the CORE approach, has been proven to be a very successful Ansatz. Two different approaches, one based on symmetry and one on renormalization-group arguments, motivate an effective bosonic Hamiltonian. In a subsequent step the effective Hamiltonian has been simulated efficiently using the SSE. The results reproduce salient experiments on high-T_c superconductors. In addition, it has been shown that the model can be extended to capture also charge ordering. These results also form a profound basis for further studies, for example one could address the open question of SO(5)-symmetry restoration at a multicritical point in the extended pSO(5) model, where longer ranged interactions are included.
Die Untersuchung stark korrelierter Elektronensysteme anhand des zweidimensionalen Hubbard-Modells bildet das zentrale Thema dieser Arbeit. Wir analysieren das Schicksal des Mott-Isolators bei Dotierung als auch bei Reduzierung der Wechselwirkungsstärke. Die numerische Auswertung erfolgt mit Hilfe von Quanten-Cluster-Approximationen, die eine thermodynamisch konsistente Beschreibung der Grundzustandseigenschaften garantieren. Der hier verwendete Rahmen der Selbstenergiefunktional-Theorie bietet eine große Flexibilität bei der Konstruktion von Cluster-Näherungen. Eine detaillierte Analyse gibt Aufschluss über die Qualität und das Konvergenzverhalten unterschiedlicher Cluster-Näherungen innerhalb der Selbstenergiefunktional-Theorie. Wir verwenden für diese Untersuchungen das eindimensionale Hubbard-Modell und vergleichen unsere Resultate mit der exakten Lösung. In zwei Dimensionen finden wir als Grundzustand des Teilchen-Loch-symmetrischen Modells bei Halbfüllung einen antiferromagnetischen Isolator unabhängig von der Wechselwirkungsstärke. Die Berücksichtigung kurzreichweitiger räumlicher Korrelationen durch unsere Cluster-Näherung führt, im Vergleich mit der dynamischen Mean-Field-Theorie, zu einer deutlichen Verbesserung des antiferromagnetischen Ordnungsparameters. Darüberhinaus beobachten wir in der paramagnetischen Phase einen Metall-Isolator-Übergang als Funktion der Wechselwirkungsstärke, der sich qualitativ vom reinen Mean-Field-Szenario unterscheidet. Ausgehend vom antiferromagnetischen Mott-Isolator zeigt sich ein füllungsgetriebener Metall-Isolator-Übergang in eine paramagnetische metallische Phase. Abhängig von der verwendeten Cluster-Approximation tritt dabei zunächst eine antiferromagnetische metallische Phase auf. Neben langreichweitiger antiferromagnetischer Ordnung haben wir in unseren Rechnungen auch Supraleitung berücksichtigt. Das Verhalten des supraleitenden Ordnungsparameters als Funktion der Dotierung ist dabei in guter Übereinstimmung sowohl mit anderen numerischen Verfahren als auch mit experimentellen Ergebnissen.
The superconducting properties of complex materials like the recently discovered iron-pnictides or strontium-ruthenate are often governed by multi-orbital effects. In order to unravel the superconductivity of those materials, we develop a multi-orbital implementation of the functional renormalization group and study the pairing states of several characteristic material systems. Starting with the iron-pnictides, we find competing spin-fluctuation channels that become attractive if the superconducting gap changes sign between the nested portions of the Fermi surface. Depending on material details like doping or pnictogen height, these spin fluctuations then give rise to $s_{\pm}$-wave pairing with or without gap nodes and, in some cases, also change the symmetry to $d$-wave. Near the transition from nodal $s_{\pm}$-wave to $d$-wave pairing, we predict the occurrence of a time-reversal symmetry-broken $(s+id)$-pairing state which avoids gap nodes and is therefore energetically favored. We further study the electronic instabilities of doped graphene, another fascinating material which has recently become accessible and which can effectively be regarded as multi-orbital system. Here, the hexagonal lattice structure assures the degeneracy of two $d$-wave pairing channels, and the system then realizes a chiral $(d+id)$-pairing state in a wide doping range around van-Hove filling. In addition, we also find spin-triplet pairing as well as an exotic spin-density wave phase which both become leading if the long-ranged hopping or interaction parameters are slightly modified, for example, by choosing different substrate materials. Finally, we consider the superconducting state of strontium-ruthenate, a possible candidate for chiral spin-triplet pairing with fascinating properties like the existence of half-quantum vortices obeying non-Abelian statistics. Using a microscopic three orbital description including spin-orbit coupling, we demonstrate that ferromagnetic fluctuations are still sufficient to induce this $\bs{\hat{z}}(p_x\pm ip_y)$-pairing state. The resulting superconducting gap reveals strong anisotropies on the $d_{xy}$-dominated Fermi-surface pocket and nearly vanishes on the other remaining two pockets.