Spectral Properties and Heat Transport in Mesoscopic Superconducting Circuits

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It has been observed both theoretically and experimentally that superconducting correlations from a superconductor brought to the proximity of a normal metal can penetrate the latter, drastically modifying its electronic properties. This effect became known as the proximity effect. At the same time, such observations led to the emergence of the field of mesoscopic superconductivity. Besides its theoretical importance, mesoscopic superconductivity has numerous technological applications, e.g., in metrology, quantum calorimetry, and quantum computation, to mention just a few. In this Thesis, we address several problems concerning heat and charge transport in superconductor-normal-metal (SN) proximity systems. Some of those are closely related to the practical applications mentioned earlier. Most of the results are obtained within the framework of quasiclassical Green’s functions in and out of equilibrium. In Chapter 1, we provide a general overview of the theory of conventional superconductivity and phenomena occurring in the vicinity of a superconductor-normal-metal interface such as Andreev reflection, Andreev bound states, and the proximity effect. Chapter 2 provides an introduction to quantum field-theoretical methods in condensed matter physics. In Chapter 3, we extend the previously described formalism to superconducting situations with a special focus on the quasiclassical theory of superconductivity. The latter is especially advantageous in treatments of mesoscopic (inhomogeneous) systems, and therefore extensively used throughout this Thesis. The next three chapters discuss the results and represent, thus, the central part of this Thesis. Motivated by recent experiments performed in superconductor-graphene-superconductor proximity systems, we provide in Chapter 4 a systematic theoretical analysis of the local density of states (LDOS) in a clean normal-metal sheet sandwiched between two superconducting leads. We show how the spectrum of Andreev bound states (appearing inside the gap) shapes the phase-dependent LDOS in short and long junctions. We discuss the circumstances under which a gap appears in the LDOS and when the continuum displays a significant phase-dependence. The presence of a magnetic flux leads to a complex interference behavior, which is also reflected in the supercurrent-phase relation. Our findings qualitatively agree with the experimental observation. In addition, we analyze the Josephson effect. Finally, we establish a relation between the global density of states and the supercurrent in a system of arbitrary length. In Chapter 5, we examine the inelastic Cooper pair tunneling in diffusive superconductor-normal-metal-insulator-superconductor heterostructures coupled to an infinite RC transmission line. Under certain circumstances, the zero-bias anomaly, that appears in the current-voltage response of the system, scales monotonically with the temperature making, hence, this system a good candidate for an ultra-sensitive quantum thermometer. Our findings are in excellent agreement with the experiments performed recently. Finally, we provide a simplified analytic formula that qualitatively matches the experimental data in a wide range of temperatures and may be used as a calibration tool for the thermometer. In Chapter 6, we investigate electron cooling mediated by phonons in disordered systems with a special focus on mesoscopic superconducting proximity structures. We obtain a rather general expression for the cooling power perturbative in the electron-phonon coupling, but valid for arbitrary electronic systems out of equilibrium. To illustrate our theory, we apply it to two experimentally relevant geometries of a superconductor-normal-metal proximity contact. We find a significantly suppressed cooling power at low temperatures related to the existence of a minigap in the quasiparticle spectrum, which makes those structures highly promising candidates for quantum calorimetry. Moreover, due to its generality, our theory can serve as a benchmark for future experiments and as a tool for finding an optimal configuration for designing a quantum thermal detector. Finally, in Chapter 7 we enclose our discussion giving concluding remarks and perspectives.

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530 Physik
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Mesoscopic superconductivity, Quasiclassical transport, Proximity systems, Andreev physics, Josephson effect, Quantum thermodynamics
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ISO 690NIKOLIĆ, Danilo, 2021. Spectral Properties and Heat Transport in Mesoscopic Superconducting Circuits [Dissertation]. Konstanz: University of Konstanz. Konstanz
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@phdthesis{Nikolic2021Spect-55920,
  year={2021},
  title={Spectral Properties and Heat Transport in Mesoscopic Superconducting Circuits},
  author={Nikolić, Danilo},
  address={Konstanz},
  school={Universität Konstanz}
}
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June 16, 2021
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Konstanz, Univ., Diss., 2021
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