Time-reversal symmetry breaking in topological and unconventional superconducting heterostructures

Abstract:

Time-reversal symmetry breaking (TRSB) effects can be detrimental to superconductivity. For example, TRSB caused by magnetic fields can destroy superconducting states. However, the coexistence of TRSB and superconductivity can give rise to intriguing phenomena, such as non-trivial topological phases of matter. We explore TRSB in two-dimensional unconventional and topological superconducting heterostructures without external magnetic fields across three different platforms.

First, we examine a superconductor-ferromagnet heterostructure in which TRSB effects are engineered through a magnetic vortex. Here, a magnetic vortex couples with a superconducting vortex, creating a stable hybrid vortex structure that can host robust zero-energy Majorana modes at its core and a partner mode at the boundary of a topologically non-trivial region. We propose a novel mechanism for this topological phase formation that relies on the orbital effects of the magnetization field rather than the conventional Zeeman effect.

Second, we investigate TRSB in a twisted bilayer of the high-Tc cuprate Bi2212 with a twist angle near 45 degrees, which is theoretically predicted to exhibit chiral topological d+id' order parameter. Using a fully self-consistent microscopic model, we estimate the size of spontaneous chiral edge currents in this phase, finding small but non-vanishing currents that vary based on edge type. Importantly, we predict that the current magnitude exceeds the detection threshold of advanced magnetic scanning probe microscopy techniques.

Finally, we examine a d/s superconducting bilayer that exhibits a non-topological, time-reversal symmetry breaking d_{xy}+is order parameter. Such a system hosts non-chiral edge currents. Our findings indicate that supercurrents do not flow uniformly along the edges; instead, it appears that the currents along the horizontal and vertical edges converge into or diverge from the corners. This frustration of supercurrents at the corners, and their eventual resolution through bulk flow, gives rise to spontaneous flux patterns resembling large supercurrent vortices. We thoroughly characterize these currents using both fully self-consistent microscopic lattice models and an iterative multi-component Ginzburg-Landau formalism, exploring various shapes and edge configurations of the system. It can be possible to realize these effects in a high-Tc cuprate paired with an s-wave iron-based superconductor.

These findings deepen our understanding of engineered and spontaneous TRSB in superconducting heterostructures, offering insights into topological phases, unconventional superconductivity, and potential applications.