71.27.+a Strongly correlated electron systems; heavy fermions
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Emergent phenomena in condensed matter physics like, e.g., magnetism, superconductivity, or non-trivial topology often come along with a surprise and exert great fascination to researchers up to this day. Within this thesis, we are concerned with the analysis of associated types of order that arise due to strong electronic interactions and focus on the high-\(T_c\) cuprates and Kondo systems as two prime candidates. The underlying many-body problem cannot be solved analytically and has given rise to the development of various approximation techniques to tackle the problem.
In concrete terms, we apply the auxiliary particle approach to investigate tight-binding Hamiltonians subject to a Hubbard interaction term to account for the screened Coulomb repulsion. Thereby, we adopt the so-called Kotliar-Ruckenstein slave-boson representation that reduces the problem to non-interacting quasiparticles within a mean-field approximation. Part I provides a pedagogical review of the theory and generalizes the established formalism to encompass Gaussian fluctuations around magnetic ground states as a crucial step to obtaining novel results.
Part II addresses the two-dimensional one-band Hubbard model, which is known to approximately describe the physics of the high-\(T_c\) cuprates that feature high-temperature superconductivity and various other exotic quantum phases that are not yet fully understood. First, we provide a comprehensive slave-boson analysis of the model, including the discussion of incommensurate magnetic phases, collective modes, and a comparison to other theoretical methods that shows that our results can be massively improved through the newly implemented fluctuation corrections. Afterward, we focus on the underdoped regime and find an intertwining of spin and charge order signaled by divergences of the static charge susceptibility within the antiferromagnetic domain. There is experimental evidence for such inhomogeneous phases in various cuprate materials, which has recently aroused interest because such correlations are believed to impact the formation of Cooper pairs. Our analysis identifies two distinct charge-ordering vectors, one of which can be attributed to a Fermi-surface nesting effect and quantitatively fits experimental data in \(\mathrm{Nd}_{2-\mathrm{x}}\mathrm{Ce}_\mathrm{x}\mathrm{CuO}_4\) (NCCO), an electron-doped cuprate compound. The other resembles the so-called Yamada relation implying the formation of periodic, double-occupied domain walls with a crossover to phase separation for small dopings.
Part III investigates Kondo systems by analyzing the periodic Anderson model and its generalizations. First, we consider Kondo metals and detect weakly magnetized ferromagnetic order in qualitative agreement with experimental observations, which hinders the formation of heavy fermions. Nevertheless, we suggest two different parameter regimes that could host a possible Kondo regime in the context of one or two conduction bands. The part is concluded with the study of topological order in Kondo insulators based on a three-dimensional model with centrosymmetric spin-orbit coupling. Thereby, we classify topologically distinct phases through appropriate \(\mathbb{Z}_2\) invariants and consider paramagnetic and antiferromagnetic mean-field ground states. Our model parameters are chosen to specifically describe samarium hexaboride (\(\mbox{SmB}_6\)), which is widely believed to be a topological Kondo insulator, and we identify topologically protected surface states in agreement with experimental evidence in that material. Moreover, our theory predicts the emergence of an antiferromagnetic topological insulator featuring one-dimensional hinge-states as the signature of higher-order topology in the strong coupling regime. While the nature of the true ground state is still under debate, corresponding long-range magnetic order has been observed in pressurized or alloyed \(\mbox{SmB}_6\), and recent experimental findings point towards non-trivial topology under these circumstances. The ability to understand and control topological systems brings forth promising applications in the context of spintronics and quantum computing.
The present thesis is concerned with the impact of alkali metal-doping on the electronic structure of semiconducting organic thin films. The organic molecular systems which have been studied are the polycyclic aromatic hydrocarbons picene, pentacene, and coronene. Motivated by reports about exceptional behavior like superconductivity and electronic correlations of their alkali metal-doped compounds, high quality films fabricated from the above named molecules have been studied. The electronic structure of the pristine materials and their doped compounds has been investigated using photoelectron spectroscopy. Core level and valence band studies of undoped films yield excellent photoemission spectra agreeing with or even outperforming previously reported data from the literature. Alkali metal-doping manifests itself in a uniform manner in the electronic structure for all probed samples: Opposed to reports from the literature about metallicity and even superconductivity in alkali metal-doped picene, pentacene, and coronene, all films exhibit insulating nature with an energy gap of the order of one electron-volt. Remarkably, this is independent of the doping concentration and the type of dopant, i.e., potassium, cesium, or sodium. Based on the interplay between narrow bandwidths in organic semiconductors and sufficiently high on-molecule Coulomb repulsion, the non-metallicity is attributed to the strong influence of electronic correlations leading to the formation of a Mott insulator. In the case of picene, this is consolidated by calculations using a combination of density functional theory and dynamical mean-field theory. Beyond the extensive considerations regarding electronic correlations, further intriguing aspects have been observed. The deposition of thin picene films leads to the formation of a non-equilibrium situation between substrate and film surface. Here, the establishment of a homogeneous chemical potential is hampered due to the only weak van der Waals-interactions between the molecular layers in the films. Consequently, spectral weight is measurable above the reference chemical potential in photoemission. Furthermore, it has been found that the acceptance of additional electrons in pentacene is limited. While picene and coronene are able to host up to three extra electrons, in pentacene the limit is already reached for one electron. Finally, further extrinsic effects, coming along with alkali metal-doping, have been scrutinized. The oxidation of potassium atoms induced by the reaction with molecular oxygen in the residual gas of the ultra-high vacuum system turned out to significantly influence the electronic structure of alkali metal-doped picene and coronene. Moreover, also the applied X-ray and UV irradiation caused a certain impact on the photoemission spectra. Surprisingly, both effects did not play a role in the studies of potassium-doped pentacene.
In this thesis the electronic and magnetic structure of the transition metal oxyhalides TiOCl, TiOBr and VOCl is investigated. The main experimental methods are photoemission (PES) and x-ray absorption (XAS) spectroscopy as well as resonant inelastic x-ray scattering (RIXS). The results are compared to density-functional theory, and spectral functions from dynamical mean-field theory and different kinds of model calculations. Questions addressed here are those of the dimensionality of the magnetic and electronic interactions, the suitability of the oxyhalides as prototypical strongly correlated model systems, and the possibility to induce a filling-controlled insulator-metal transition. It turns out that TiOCl is a quasi-one-dimensional system with non-negligible two-dimensional coupling, while the one-dimensional character is already quite suppressed in TiOBr. In VOCl no signatures of such one-dimensional behavior remain, and it is two-dimensional. In all cases, frustrations induced by the crystal lattice govern the magnetic and electronic properties. As it turns out, although the applied theoretical approaches display improvements compared to previous studies, the differences to the experimental data still are at least partially of qualitative instead of quantitative nature. Notably, using RIXS, it is possible for the first time in TiOCl to unambiguously identify a two-spinon excitation, and the previously assumed energy scale of magnetic excitations can be confirmed. By intercalation of alkali metal atoms (Na, K) the oxyhalides can be doped with electrons, which can be evidenced and even quantified using x-ray PES. In these experiments, also a particular vertical arrangement of dopants is observed, which can be explained, at least within experimental accuracy, using the model of a so-called "polar catastrophe". However, no transition into a metallic phase can be observed upon doping, but this can be understood qualitatively and quantitatively within an alloy Hubbard model due to the impurity potential of the dopants. Furthermore, in a canonical way a transfer of spectral weight can be observed, which is a characteristic feature of strongly correlated electron systems. Overall, it can be stated that the transition metal oxyhalides actually can be regarded as prototypical Mott insulators, yet with a rich phase diagram which is far from being fully understood.