Torus Quantization for Spinning Particles

Keppeler, Stefan

doi:10.1103/physrevlett.89.210405

Cited by 11 publications

(17 citation statements)

References 16 publications

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“…In this section, we demonstrate the general expression (16) of the main text for the spectrum of the Andreev bound states when the junction has some barriers. We first consider the scattering of particles and holes with E < ∆ at a single interface between a normal metal (left half space) and a superconductor (right half space).…”

Section: Appendix D: Junction With Barriersmentioning

confidence: 96%

“…(8). This precession preserves, as in the non-superconducting case [16,17], the latitude with respect to the local spin quantization axis n, which obeys a classical equation [Eq. (7)].…”

mentioning

confidence: 99%

“…It is now possible to give a semiclassical interpretation of the AW-loops (see Fig.1) inspired by the picture of quantization for spinning particles proposed in Refs. [16,17]. When transported along the loop the "classical spins" s e,h (x) of electrons and holes precess around local axes, n e (x) for the electrons and n h (x) for the holes, in such a way that latitude with respect to those axes is always preserved.…”

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confidence: 99%

“…The spin-splitted ABS energy E/∆ in a S/N/S junction with a finite interface transparency versus the phasedifference ϕ, in the limit Φ 2EL/vF from Eq. (16). Left column: the strength of the interface δ-barrier Z = 0, right column: Z = 0.5. such generic spin-dependent field.…”

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confidence: 99%

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Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions

2016

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A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semi-classic limit. The spectrum of Andreev bound states is obtained from the single-valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position/particle-hole/spin space is constructed, and shown to depend on only two parameters, namely a magnetic phase shift and a local precession axis for the spin. In the last years the spin-orbit and spin-splitting effects in superconducting heterostructures [1,2] are receiving a great deal of attention in the context of an emerging superconducting spintronics [3,4] and in connection with possible realizations of Majorana bound states in nanowires [5]. A Josephson junction with a magnetoactive normal bridge exemplify a prototype structure hosting such kind of spin interactions. The physics of superconductor/normal metal/superconductor (S/N/S) ballistic Josephson junctions is mainly determined by the so called Andreev bound states (ABS) localized in the Nregion. These states, which carry a significant fraction of the Josephson supercurrent [6,7], have been extensively studied in ballistic superconducting point contacts [8][9][10].Theoretically the quantization of states trapped in some classically allowed region can be understood from the Bohr-Sommerfeld quantization rule [11,12] which requires the phase accumulated along a closed classical trajectory to be a multiple of 2π. In a ballistic S/N/S junction the trapping in the N-region occurs due to Andreev reflections with conversion of the incident electron to the reflected hole and vice versa at the S/N interfaces [13]. Each Andreev reflection brings a phase shift θ (E) = arccos (E/∆), where E < ∆ is the energy measured with respect to the Fermi level [14]. The classical loop trajectory is now defined in the space composed of the position and particle-hole subspaces. In the position subspace the electron and the reflected hole accumulate the phase equal to 2EL/v, where L is the distance between the S electrodes and v is the component of the velocity perpendicular to the junction plane. From the two Andreev reflections (shifts in the particle-hole subspace) the phase acquires the contribution 2θ (E) ± ϕ, depending on the propagating direction, where ϕ is the phase difference between the two S-electrodes (see Fig.1), [15]. Hence the quantization condition for ABS reads: 2E n L/|v| − 2θ (E n ) + sgn(v)ϕ = 2nπ. The spin-orbit coupling (SOC) and spin-splitting (exchange or Zeeman), possibly textured fields in a magnetic material, generate precession of the electron and hole spins, which should modify the properties of ABS. How the semiclassical condition is modified in th...

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Section: Appendix D: Junction With Barriersmentioning

confidence: 96%

“…(8). This precession preserves, as in the non-superconducting case [16,17], the latitude with respect to the local spin quantization axis n, which obeys a classical equation [Eq. (7)].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions

2016

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“…Next, it is suggested that the Fermi-Dirac (for electrons) and the Bose-Einstein (for photons) statistics used in the quantum mechanical description of the EPR-Bohm problem [16] seem to be a reminiscence of two consecutive steps. In the case of fermions that are ruled by the Dirac equation, the first step consists of the appearance of the generalized Einstein-Brillouin-Keller quantization conditions [17]. In the case of the free electromagnetic field that fulfills the Maxwell equations, the first step consists of the existence of the conserved generalized helicity [18].…”

Section: Introductionmentioning

confidence: 99%

Frieden wave-function representations via an Einstein-Podolsky-Rosen-Bohm experiment

Syska

2013

Phys. Rev. E

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The appearance of the spin-1 2 and spin-1 representations in the Frieden-Soffer extreme physical information (EPI) statistical approach to the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment is shown. In order to obtain the EPR-Bohm result, in addition to the observed structural and variational information principles of the EPI method, the condition of the regularity of the probability distribution is used. The observed structural information principle is obtained from the analyticity of the logarithm of the likelihood function. It is suggested that, due to the self-consistent analysis of both information principles, quantum mechanics is covered by the statistical information theory. The estimation of the angle between the analyzers in the EPR-Bohm experiment is discussed.

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