Polarized excitons in nanorings and the optical Aharonov-Bohm effect

Abstract

The quantum nature of matter lies in the wave function phases that accumulate while particles move along their trajectories. A prominent example is the Aharonov-Bohm phase, which has been studied in connection with the conductance of nanostructures. However, optical response in solids is determined by neutral excitations, for which no sensitivity to magnetic flux would be expected. We propose a new mechanism for the topological phase of a neutral particle, a polarized exciton confined to a semiconductor quantum ring. We predict that this magnetic-field induced phase may strongly affect excitons in a system with cylindrical symmetry, resulting in switching between 'bright' exciton ground states and novel 'dark' states with nearly infinite lifetimes. Since excitons determine the optical response of semiconductors, the predicted phase can be used to tailor photon emission from quantum nanostructures.It is known that the quantum mechanical phase of a state wave function is not a physical observable. This understanding, true in its absolute form, does not preclude the important possibility of observing relative phases in a suitably prepared system. In fact, much of the physics in meso-and nanoscopic systems is intrinsically connected to interference or phase-shift phenomena that manifest themselves in a number of experimentally measurable quantities. Prominent examples include the superconducting quantum interference devices (SQUIDs) [1] the quantum-phase factors induced by adiabatic changes (known as geometric Berry phases) [2], their generalization to non-adiabatic changes due to Aharonov and Anandan [3], and the well known Aharonov-Bohm (AB) effect [4]. Such a case appears naturally in systems with ring geometry in the presence of a magnetic field. In fact, recently available semiconductor rings ≃ 10-100nm in diameter allow one to explore this interesting physics in readily attainable magnetic fields. We report here on a new mechanism of phase difference acquired in a magnetic field by a composite and polarizable object with overall zero charge. Such neutral particles, excitons, are bound states of an electron and a hole in semiconductors, and are responsible for optical emission of crystals at low temperatures. The predicted interference effect has important observable consequences, as it affects the exciton emission and lifetime in nanoscopic semiconducting rings, and provides a novel phase interference phenomenon, the 'optical' AB effect. In particular, we predict a striking effect: the exciton emission can be strongly suppressed in certain magnetic-field windows.The AB phase is most simply described as the phase acquired by a charge as it traverses a region where a magnetic flux exists, while no effects of the classical Lorentz force are present. The AB effect has been verified in a number of beautiful experiments using superconducting rings [5], where electrons move in the regions with zero magnetic field. In semiconductors, the AB effect has been used in fascinating experiments to measure the relative phases ...

Optical transitions in quantum ring complexes

“…In this connection, we would like to point out that our concentric double-rings are a good candidate to realize in-plane polarization for carriers, producing a robust Aharonov-Bohm feature in neutral excitonic transition 20 . Magnet-optical experiments using these quantum rings are now in progress.…”

“…Finally, the eigen states were obtained with diagonalizing matrix. For the present calculation, we have taken into account 35 Bessels and 35 sine functions as the base functions for each value of L, and R c (Z c ) = 120 (20) nm. Material parameters used in calculation are summarized in Table I. A series of single carrier levels of QR is shown in Fig.…”

“…On the other hand, a negative prediction has also been reported in which the AB effect can hardly take place in more-realistic rings with finite width 19 . A large difference in trajectories for an electron and a hole is necessary to exhibit the AB effect on neutral excitation 20 .…”

Magneto-optics of layers of semiconductor quantum dots and nano-rings

“…A further consequence of the unusual topology is that the center hole enables trapping of a single magnetic flux and offers the exciting possibility to observe electronic wave-function phases [5] in magneto-optical experiments. This leads to a new so-called "optical" AharonovBohm (AB) effect, which can occur only in semiconductor nano-rings [6][7][8][9].…”

Theory of electron energy spectrum and Aharonov-Bohm effect in self-assembledInxGa1−xAsquantum rings in GaAs

“…[2][3][4][5] The first experimental evidence of Aharonov-Bohm oscillations was found in metallic 6,7 and semiconductor 8 rings in the mesoscopic regime. In recent years, the fabrication and the investigation of In x Ga 1−x As self-assembled quantum rings ͑SAQRs͒ have been rapidly progressing and led to a large number of experimental [9][10][11][12][13][14] and theoretical [15][16][17][18] studies.…”