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## Hybrid helical state and superconducting diode effect in superconductor/ferromagnet/topological insulator heterostructures

It is well-known that the ground state of homogeneous superconducting systems with spin-orbit

coupling (SOC) in the presence of the Zeeman field is the so-called helical state, which is characterized

by the phase modulation of the order parameter, but zero supercurrent density. In this work

we investigate the realization of the helical state in a hybrid system with spatially separated superconductivity

and exchange field by considering superconductor/ferromagnet (S/F) bilayer on top

of a 3D topological insulator. This system is characterized by strong spin-momentum locking and,

consequently, provides the most favorable conditions for the helical state generation. The analysis

is based on the microscopic theory in terms of the quasiclassical Green’s functions. We demonstrate

that in the bilayer the helical state survives if the exchange field has non-zero component perpendicular

to the S/F interface even in spite of the fact that the superconducting order parameter and

the exchange field are spatially separated. At the same time, in this spatially inhomogeneous situation

the helical state is accompanied by the spontaneous currents distributed over the bilayer in

such a way that the net current vanishes. Further, we show that this hybrid helical state gives rise

to nonreciprocity in the system. We demonstrate the realization of the nonreciprocity in the form

of the superconducting diode effect and investigate its dependence on the parameters of bilayer.