Topological quantum phase transitions in high-temperature superconductors

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One of the most fundamental aspects of condensed matter physics is the classification of different phases of matter. A systematic approach is given by Landau's theory of phase transitions according to which different phases are characterized by distinct symmetry properties. This allows describing many thermal transitions (such as the liquid-solid transition) as well as quantum phase transitions, i.e., phase transitions at zero temperature. Instead of exhibiting different symmetries, phases can also be distinguished by their topology, i.e., global properties such as the degeneracy of the ground state, which is, e.g., important for the quantum Hall effects.Many experimental observations indicate that topological quantum phase transitions are also central to the phase diagram of the copper-based high-temperature superconductors. These materials are of high interest, not only because of the defining high transition temperature and the associated technological potential but also due to the complex phase diagram that, in many regards, still lacks theoretical understanding.In this project, we will use the recent progress in developing realistic theoretical models which exhibit the topological phases that are relevant for the copper-based high-temperature superconductors in order to improve our microscopic understanding of these materials. In particular, the predictions of different models for transport properties in the normal state, the sensitivity of the different phases to disorder, the different superconducting instabilities as well as for resonance modes in neutron scattering and Raman response will be analyzed with controlled theoretical approaches and compared in detail with experimental observations. The long-term objective is to establish a minimal and realistic low-energy model that agrees with a large number of different experiments. Important consequences for other classes of high-temperature superconductors and further strongly correlated materials with similar phenomenological properties are expected.