| Summary: | This thesis introduces and studies several unusual phenomena that arise in low-dimensional systems in the presence of a magnetic field. The first example that we discuss is nonreciprocal superconductivity, which occurs upon simultaneous breaking of inversion and time-reversal symmetries. Nonreciprocal superconductors describe certain classes of unconventional superconductors that include certain kinds of mixed-pairing and finite-momentum ones. They also occur in engineered systems exhibiting s-wave pairing-based superconductivity, for which we put forward several simple proposals. We demonstrate several striking observable consequences of nonreciprocal superconductivity. These include current rectification in normal metal-nonreciprocal superconductor junctions and the Josephson diode effect, for which we propose a simple and universally applicable mechanism. With the advent of novel low-dimensional symmetry-breaking materials, such as multilayer graphenes and twisted cuprates, as well as modern experimental possibilities involving engineered systems, nonreciprocal phenomena could eventually become an indispensable tool for revealing the nature of superconducting orders.
The second part of this thesis concerns doped Mott insulators in a magnetic field, described by a triangular-lattice Fermi-Hubbard model in the limit of strong interaction. This is relevant for many novel materials, such as moiré transition metal dichalcogenides bilayers. We predict a new bound state, spin polaron, formed by binding a doped hole with a magnon (spin flip). Spin polarons have large effective mass and are spin 3/2 quasiparticles. The mechanism for their formation is kinetic frustration, and therefore their binding energy is proportional to the hopping t, which is the largest energy scale within a single Hubbard band. We then propose a new phase diagram for the triangular lattice Hubbard model in a magnetic field as well as multiple experimental signatures. We hope that the prediction of the spin polaron, which has since been experimentally confirmed, will give rise to novel mechanisms for superconductivity and correlated orders in doped Hubbard models.
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