Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Giant spin splitting and $0 - \pi$ Josephson transitions from the
  Edelstein effect in quantum spin-Hall insulators   Hybrid structures of quantum spin-Hall insulators (QSHIs) and superconductors
(Ss) present a unique opportunity to access dissipationless topological states
of matter, which, however, is frequently hindered by the lack of control over
the spin polarization in QSHIs. We propose a very efficient spin-polarization
mechanism based on the magnetoelectric (Edelstein) effect in superconducting
QSHI structures. It acts akin to the Zeeman splitting in an external magnetic
field, but with an effective $g$-factor of order of 1000, resulting in an
unprecedented spin-splitting effect. It allows a magnetic control of the QSHI/S
hybrids without destroying superconductivity. As an example, we demonstrate a
recurrent crossover from $\Phi_0$ - to $\Phi_0/2$ - periodic oscillations of
the Josephson current in an rf superconducting quantum interference device
($\Phi_0=h/2e$ is the magnetic flux quantum). The predicted period halving is a
striking manifestation of $0-\pi$ Josephson transitions with a superharmonic
$\pi$-periodic current-phase relationship at the transition. Such controllable
$0-\pi$ transitions may offer new perspectives for dissipationless spintronics
and engineering flux qubits.

18
The categories of this paper are: econ
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess