Magnetoresistance studies of La2/3Sr1/3MnO3La_{2/3} Sr_{1/3} MnO_3 - YBa2Cu3O7YBa_2 Cu_3 O_7 - La2/3Sr1/3MnO3La_{2/3} Sr_{1/3} Mn O_3 trilayers with ferromagnetic coupling along the nodal direction of YBa2Cu3O7YBa_2 Cu_3 O_7

I have successfully prepared (110) trilayers of \LSMO-\YBCO-\LSMO. Magnetization measurements on these samples reveal a stronger coupling between the ferromagnetic layers. The coupling is an order of magnitude higher than that seen in the case of (001) trilayers. Magnetoresistance measurements show a first order transition in the data coinciding with the antiferromagnetic regime deduced from the magnetization measurements. I have also measured the anisotropic magnetoresistance (AMR) of these samples revealing an unusually high AMR ($\sim 72000$). I attribute such a high AMR to the pair breaking effects in these films.Comment: 12 pages, 7 figure

Counting Majorana bound states using complex momenta

Recently, the connection between Majorana fermions bound to defects in arbitrary dimensions, and complex momentum roots of the vanishing determinant of the corresponding bulk Bogoliubov-de Gennes (BdG) Hamiltonian, has been established (EPL, 2015, $\textbf{110}$, 67005). Based on this understanding, a formula has been proposed to count the number ($n$) of the zero energy Majorana bound states, which is related to the topological phase of the system. In this paper, we provide a proof of the counting formula and we apply this formula to a variety of 1d and 2d models belonging to the classes BDI, DIII and D. We show that we can successfully chart out the topological phase diagrams. Studying these examples also enables us to explicitly observe the correspondence between these complex momentum solutions in the Fourier space, and the localized Majorana fermion wavefunctions in the position space. Finally, we corroborate the fact that for systems with a chiral symmetry, these solutions are the so-called "exceptional points", where two or more eigenvalues of the complexified Hamiltonian coalesce.Comment: 21 pages, 10 figure

Exceptional points for chiral Majorana fermions in arbitrary dimensions

Certain real parameters of a Hamiltonian, when continued to complex values, can give rise to singular points called exceptional points ($EP$'s), where two or more eigenvalues coincide and the complexified Hamiltonian becomes non-diagonalizable. We show that for a generic $d$-dimensional topological superconductor/superfluid with a chiral symmetry, one can find $EP$'s associated with the chiral zero energy Majorana fermions bound to a topological defect/edge. Exploiting the chiral symmetry, we propose a formula for counting the number ($n$) of such chiral zero modes. We also establish the connection of these solutions to the Majorana fermion wavefunctions in the position space. The imaginary parts of these momenta are related to the exponential decay of the wavefunctions localized at the defect/edge, and hence their change of sign at a topological phase transition point signals the appearance or disappearance of a chiral Majorana zero mode. Our analysis thus explains why topological invariants like the winding number, defined for the corresponding Hamiltonian in the momentum space for a defectless system with periodic boundary conditions, captures the number of admissible Majorana fermion solutions for the position space Hamiltonian with defect(s). Finally, we conclude that $EP$'s cannot be associated with the Majorana fermion wavefunctions for systems with no chiral symmetry, though one can use our formula for counting $n$, using complex $k$ solutions where the determinant of the corresponding BdG Hamiltonian vanishes.Comment: 5 pages; published versio

Electric Field Response In Breathing Pyrochlores

We study the effects of a uniform electric field on the the ground state and excitations of the three-dimensional U(1) spin liquid phase of a breathing pyrochlore lattice, arising due to the coupling between the conventional (Maxwell) electric field and the emergent electrodynamics of the quantum spin ice material. This is an extension of the studies for isotropic pyrochlores in Phys. Rev. B 96, 125145 (2017) to the anisotropic case, as the lattice inversion symmetry is broken in breathing pyrochlores. The emergent photons are found to exhibit birefringence, analogous to the isotropic case. However, the system possesses a nonzero polarization even in the absence of an external electric field, unlike the isotropic pyrochlore. We also find that a sufficiently strong electric field triggers a quantum phase transition into new U(1) quantum spin liquid phases which trap $\pi$-fluxes of the emergent electric field. Such transitions are seen to occur even when the applied electric field is along a direction that does not show a phase transition in the isotropic limit.Comment: minor updates; journal versio