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Register a new userTunable Aharonov-Anandan phase in transport through mesoscopic hole rings
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M. Pletyukhov
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We present a theoretical study of spin-3/2 hole transport through mesoscopic rings, based on the spherical Luttinger model. The quasi-one-dimensional ring is created in a symmetric two-dimensional quantum well by a singular-oscillator potential for the radial in-plane coordinate. The quantum-interference contribution to the two-terminal ring conductance exhibits an energy-dependent Aharonov-Anandan phase, even though Rashba and Dresselhaus spin splittings are absent. Instead, confinement-induced heavy-hole - light-hole mixing is found to be the origin of this phase, which has ramifications for magneto-transport measurements in gated hole rings.
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We have obtained numerically exact results for the spin-related geometric quantum phases that arise in p-type semiconductor ring structures. The interplay between gate-controllable (Rashba) spin splitting and quantum-confinement-induced mixing between hole-spin states causes a much higher sensitivity of magnetoconductance oscillations to external parameters than previously expected. Our results imply a much-enhanced functionality of hole-ring spin-interference devices and shed new light on recent experimental findings.
Two important features of mesoscopic Aharonov-Bohm (A-B) electronic interferometers are analyzed: decoherence due to coupling with other degrees of freedom and the coupled transport of charge and heat. We first review the principles of decoherence of electronic interference. We then analyze the thermoelectric transport in a ring threaded by such a flux, with a molecular bridge on one of its arms. The charge carriers may also interact inelastically with the molecular vibrations. This nano-system is connected to three termi- nals; two of them are electric and thermal, held at slightly different chemical potentials and temperatures, and the third is purely thermal. For example, a phonon bath thermalizing the molecular vibrations. When this third terminal is held at a temperature different from those of the electronic reservoirs, both an electrical and a heat current are, in general, gen- erated between the latter. Likewise, a voltage and/or temperature difference between the electronic terminals leads to thermal current between the thermal and electronic terminals. The transport coefficients governing these
Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding persistent 1e-periodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Plancks constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes, could also be observed, suggesting additional non-Majorana mechanisms for 1e transport through these moderately short wires.
The Josephson current through an Aharonov-Bohm (AB) interferometer, in which a quantum dot (QD) is situated on one arm and a magnetic flux $Phi$ threads through the ring, has been investigated. With the existence of the magnetic flux, the relation of the Josephson current and the superconductor phase is complex, and the system can be adjusted to $pi$ junction by either modulating the magnetic flux or the QDs energy level $varepsilon_d$. Due to the electron-hole symmetry, the Josephson current $I$ has the property $I(varepsilon_d,Phi)=I(-varepsilon_d,Phi+pi)$. The Josephson current exhibits a jump when a pair of Andreev bound states aligns with the Fermi energy. The condition for the current jump is given. In particularly, we find that the position of the current jump and the position of the maximum value of the critical current $I_c$ are identical. Due to the interference between the two paths, the critical current $I_c$ versus the QDs level $varepsilon_d$ shows a typical Fano shape, which is similar to the Fano effect in the corresponding normal device. But they also show some differences. For example, the critical current never reaches zero for any parameters, while the current in the normal device can reach zero at the destruction point.
There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems typically involves wave propagation through a nanoscale geometry such as a quantum wire. In this paper we present a general theoretical technique to describe wave propagation through a curved wire of uniform cross-section and lying in a plane, but of otherwise arbitrary shape. The method consists of (i) introducing a local orthogonal coordinate system, the arclength and two locally perpendicular coordinate axes, dictated by the shape of the wire; (ii) rewriting the wave equation of interest in this system; (iii) identifying an effective scattering potential caused by the local curvature; and (iv), solving the associated Lippmann-Schwinger equation for the scattering matrix. We carry out this procedure in detail for the scalar Helmholtz equation with both hard-wall and stress-free boundary conditions, appropriate for the mesoscopic transport of electrons and (scalar) phonons. A novel aspect of the phonon case is that the reflection probability always vanishes in the long-wavelength limit, allowing a simple perturbative (Born approximation) treatment at low energies. Our results show that, in contrast to charge transport, curvature only barely suppresses thermal transport, even for sharply bent wires, at least within the two-dimensional scalar phonon model considered. Applications to experiments are also discussed.
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