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Register a new userShape transitions in two-body systems: two-electron quantum dots in a magnetic field
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We present a thorough analysis of the electron density distribution (shape) of two electrons, confined in the three-dimensional harmonic oscillator potential, as a function of the perpendicular magnetic field.Explicit algebraic expressions are derived in terms of the systems parameters and the magnetic field strength to trace the shape transformations in the ground and low-lying excited states. We found that the interplay of the classical and quantum properties lead to a quantum shape transition from a lateral to a vertical localization of electrons in low-lying excited states at relatively strong Coulomb interaction with alteration of the magnetic field. In contrast, in that regime in the ground states the electrons form always a ring type distribution in the lateral plane. The analytical results demonstrate a good agreement with quantum numerical results near the transition point and at high magnetic field.
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We use the entanglement measure to study the evolution of quantum correlations in two-electron axially-symmetric parabolic quantum dots under a perpendicular magnetic field. We found that the entanglement indicates on the shape transition in the density distribution of two electrons in the lowest state with zero angular momentum projection at the specific value of the applied magnetic field.
Using the exactly solvable excitation spectrum of two-electron quantum dots with parabolic potential, we show that the inclusion of the vertical extension of the quantum dot provides a consistent description of the experimental findings of Nishi et al. [Phys.Rev.B75, 121301(R) (2007)]. We found that the second singlet-triplet transition in the ground state is a vanishing function of the lateral confinement in the three-dimensional case, while it always persists in the two-dimensional case. We show that a slight decrease of the lateral confinement leads to a formation of the Wigner molecule at low magnetic fields.
We report density dependent instabilities in the localised regime of mesoscopic two-dimensional electron systems (2DES) with intermediate strength of background disorder. They are manifested by strong resistance oscillations induced by high perpendicular magnetic fields B_{perp}. While the amplitude of the oscillations is strongly enhanced with increasing B_{perp}, their position in density remains unaffected. The observation is accompanied by an unusual behaviour of the temperature dependence of resistance and activation energies. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation.
Using a classical and quantum mechanical analysis, we show that the magnetic field gives rise to dynamical symmetries of a three-dimensional axially symmetric two-electron quantum dot with a parabolic confinement. These symmetries manifest themselves as near-degeneracies in the quantum spectrum at specific values of the magnetic field and are robust at any strength of the electron-electron interaction.
We report on finite bias spectroscopy measurements of the two-electron spectrum in a gate defined bilayer graphene (BLG) quantum dot for varying magnetic fields. The spin and valley degree of freedom in BLG give rise to multiplets of 6 orbital symmetric and 10 orbital anti-symmetric states. We find that orbital symmetric states are lower in energy and separated by $approx 0.4 - 0.8$ meV from orbital anti-symmetric states. The symmetric multiplet exhibits an additional energy splitting of its 6 states of $approx 0.15 - 0.5$ meV due to lattice scale interactions. The experimental observations are supported by theoretical calculations, which allow to determine that inter-valley scattering and current-current interaction constants are of the same magnitude in BLG.
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