The P21P_2^1 Margolis homology of connective topological modular forms

The element $P_2^1$ of the mod 2 Steenrod algebra has the property $(P_2^1)^2=0$. This property allows one to view $P_2^1$ as a differential on $H_*(X, \mathbb{F}_2)$ for any spectrum $X$. Homology with respect to this differential, $\mathcal{M}(X, P_2^1)$, is called the $P_2^1$ Margolis homology of $X$. In this paper we give a complete calculation of the $P_2^1$ Margolis homology of the 2-local spectrum of topological modular forms $tmf$ and identify its $\mathbb{F}_2$ basis via an iterated algorithm. We apply the same techniques to calculate $P_2^1$ Margolis homology for any smash power of $tmf$

The topological modular forms of RP2\mathbb{R}P^2 and RP2∧CP2\mathbb{R}P^2 \wedge \mathbb{C}P^2

In this paper, we study the elliptic spectral sequence computing $tmf_*(\mathbb{R} P^2)$ and $tmf_* (\mathbb{R} P^2 \wedge \mathbb{C} P^2)$. Specifically, we compute all differentials and resolve exotic extensions by 2, $\eta$, and $\nu$. For $tmf_* (\mathbb{R} P^2 \wedge \mathbb{C} P^2)$, we also compute the effect of the $v_1$-self maps of $\mathbb{R} P^2 \wedge \mathbb{C} P^2$ on $tmf$-homology

Generation of spin-triplet Cooper pairs via a canted antiferromagnet

Spinful triplet Cooper pairs can be generated from their singlet counterparts available in a conventional superconductor (S) using two or more noncollinear magnetic moments, typically contributed by different magnets in a multilayered heterostructure. Here, we theoretically demonstrate that an S interfaced with a canted antiferromagnet (AF) harbors spinful triplet Cooper pairs capitalizing on the intrinsic noncollinearity between the two AF sublattice magnetizations. As the AF canting can be controlled by an applied field, our work proposes a simple bilayer structure that admits controllable generation of spin-triplet Cooper pairs. Employing the Bogoliubov-de Gennes framework, we delineate the spatial dependence of the spin-triplet correlations. We further evaluate the superconducting critical temperature as a function of the AF canting, which provides one experimental observable associated with the emergence of these triplet correlations.Comment: 24 pages, 7 figure