Abstract
A Rashba nanowire is subjected to a magnetic field that assumes opposite signs in two sections of the nanowire, and, thus, creates a magnetic domain wall. The direction of magnetic field is chosen to be perpendicular to the Rashba spin-orbit vector such that there is only a partial gap in the spectrum. Nevertheless, we prove analytically and numerically that such a domain wall hosts a bound state whose energy is at bottom of the spectrum below the energy of all bulk states. Thus, this magnetically-confined bound state is well-isolated and can be accessed experimentally. We further show that the same type of magnetic confinement can be implemented in two-dimensional systems with strong spin-orbit interaction. A quantum channel along the magnetic domain wall emerges with a non-degenerate dispersive band that lies energetically below the bulk states. We show that this magnetic confinement is robust against disorder and various parameter variations.
Highlights
The possibility of confining electrons to manipulate their quantum state plays an extremely important role in condensed matter physics and paves the way for various quantum computing schemes [1,2,3,4]
If the direction of the magnetic field is perpendicular to the Rashba spin-orbit interaction (SOI) vector [34,35,36,37], we find a bound state that lies in energy below all extended states
In order to demonstrate the existence of a bound state at the interface x = 0 for a sharp domain wall analytically, one has to solve the Schrodinger equation H(x)ψ (x) = E ψ (x), where we focus on solutions below the bottom of the band E < E1, see Fig. 2
Summary
The possibility of confining electrons to manipulate their quantum state plays an extremely important role in condensed matter physics and paves the way for various quantum computing schemes [1,2,3,4]. It is natural to ask if there are further ways to confine electrons and thereby open up new platforms for bound states Motivated by this question, we consider systems with uniform Rashba SOI in the presence of a nonuniform magnetic field with a domain wall. We note that the configuration described above can be mapped to an equivalent system without Rashba SOI by applying the spin-dependent gauge transformation σ (x) → eiσksox σ (x) [40] This transformation eliminates the term HR in the Hamiltonian and changes the Zeeman energy to Z (x) → Z (x)[cos(2ksox)z + sin(2ksox)x]. At the domain wall, where the sign of the magnetic field flips, this averaging does not occur, giving rise to a non-zero local Zeeman term, shifting the bottom of the band down and thereby creating a local potential minimum that traps a bound state [52]
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