The close interplay between superconductivity and antiferromagnetism in several quantum materials can lead to the appearance of an unusual thermodynamic state in which both orders coexist microscopically, despite their competing nature. A hallmark of this coexistence state is the emergence of a spin-triplet superconducting gap component, called π-triplet, which is spatially modulated by the antiferromagnetic wave-vector, reminiscent of a pair-density wave. In this paper, we investigate the impact of these π-triplet degrees of freedom on the phase diagram of a system with competing antiferromagnetic and superconducting orders. Although we focus on a microscopic two-band model that has been widely employed in studies of iron pnictides, most of our results follow from a Ginzburg-Landau analysis, and as such should be applicable to other systems of interest, such as cuprates and heavy fermions. The Ginzburg-Landau functional reveals not only that the π-triplet gap amplitude couples tri-linearly with the singlet gap amplitude and the staggered magnetization magnitude, but also that the π-triplet d-vector couples linearly with the magnetization direction. While in the mean field level this coupling forces the d-vector to align parallel or anti-parallel to the magnetization, in the fluctuation regime it promotes two additional collective modes -a Goldstone mode related to the precession of the d-vector around the magnetization and a massive mode, related to the relative angle between the two vectors, which is nearly degenerate with a Leggett-like mode associated with the phase difference between the singlet and triplet gaps. We also investigate the impact of magnetic fluctuations on the superconducting-antiferromagnetic phase diagram, showing that due to their coupling with the π-triplet order parameter, the coexistence region is enhanced. This effect stems from the fact that the π-triplet degrees of freedom promote an effective attraction between the antiferromagnetic and singlet superconducting degrees of freedom, highlighting the complex interplay between these two orders, which goes beyond mere competition for the same electronic states.

antiferromagnetic (AFM) order [1][2][3]. One of the grand challenges in understanding the behavior of these systems is determining the physical mechanism responsible for superconductivity. Essential information on the nature of superconductivity in strongly correlated electron systems can be deduced by investigating their phase diagrams as well as the superconducting (SC) gap structure.In the parent compound of many Fe-HTS, a spin density wave forms with spins ordered antiparallel to each arXiv:1802.04458v1 [cond-mat.supr-con]

The entanglement of different parts of a quantum system is expected to be proportional to the common interface area. Therefore alterations across the interface will lead to changes on the behavior of entanglement entropy. In this work, the effects of bond defects at the boundaries of Kitaev ladders are considered. We find a logarithmic scaling for the ground state entanglement entropy between the two pieces. The prefactor of the logarithm (effective central charge (ECC)) varies continuously with the defect strength. The energy dispersion is also obtained and sharp features in the von Neumann entanglement entropy are observed when bands cross. Phase diagrams for homogeneous Kitaev Hamiltonians with nonzero superconducting paring potential are presented. They show that for chains/legs that are connected to one another through inter-leg hopping, when certain parameters are fine-tuned, the phase transition lines correspond to either single or double gapless modes dispersion. Moreover, even when the defect is turned on, the ECC for ladders with two gapless modes is exactly twice the one for ladders with a single gapless mode. On the other hand, in the absence of superconductivity, we can tune the parameters to obtain homogeneous systems whose number of gapless modes is up to the number of legs of the ladder. Additionally, in this situation, the presence of the bond defect makes the ECC becomes smaller than the number of gapless modes times the ECC of Hamiltonians with one gapless mode. Furthermore, the relationship between the cases with and without superconductivity is presented.

In this thesis, we study the interplay between antiferromagnetism and superconductivity in iron pnictides. This study will be done analyzing a free energy of coupled order parameters which will be derived from a microscopic model. In particular, we are interested if the phase transition between the ordered states is first order or if the two orders can coexist. For the case of conventional superconductivity, the two phases cannot coexist. However, when superconductivity is unconventional and the perfect nesting condition is not satisfied, there can exist an intermediary state of microscopic coexistence of the two orders. In this new thermodynamic phase, spin rotation, time reversal and U (1) symmetries are simultaneously and locally broken. Therefore, the singlet and triplet superconductivity channels are quantum mechanically mixed. In other words, a secondary triplet component is generated. The phase diagrams of the system are presented and we also analyze the effect of magnetic fluctuations above the pure Néel temperature on the triplet temperature transition. We also investigate the effects of the staggered magnetization on the Josephson effect, i.e., on the supercurrent that flows through a junction of two superconductors in the coexistence phase. Last, but not least, we study the proximity effect at an interface between a superconductor and an antiferromagnet. We will see that the Cooper pairs can penetrate the magnetic region and consequently a triplet component is induced near the interface.