Guang-Yu Yi

BINDING ENERGIES OF HYDROGENIC IMPURITIES ON-CENTER AND OFF-CENTER IN CYLINDRICAL QUANTUM DOTS UNDER ELECTRIC AND MAGNETIC FIELDS

The ground-state binding energies of a hydrogenic impurity in cylindrical quantum dots (QDs) subjected to external electric and magnetic fields are investigated using the finite-difference method within the quasi-one-dimensional effective potential model. The QD is modeled by superposing a square-well potential and a strong lateral confinement potential by the combination of a parabolic potential and a changeable magnetic field. We define an effective radius of a cylindrical QD which can describe the strength of the lateral confinement. The effects of the electric fields are less important when the effective radius is very tiny, and the effects are manifested as the effective radius increases. Meanwhile, one finds that the binding energies highly depend on the impurity positions under the applied transverse fields. When the impurity is located at the right half of the cylinder,the electric field pushes the electron to the left side, then the binding energy decreases;when the impurity is located at the left, the binding energy first increases and reaches a peak value, then deceases with the electric field.

Stark effect of electrons in semiconducting rectangular quantum boxes

The Stark shift of the electronic energy levels in semiconducting rectangular quantum boxes with different sizes is investigated by the use of variational solutions to the effective-mass approximation for electric fields of various orientations with respect to the center axis of the box. The asymptotic expansions of the Stark shift are given in the limits of low and high fields, respectively; they clearly indicate that the Stark shift is a quadratic function of the electric field for low electric fields and is an approximate linear function of the electric field for high electric fields. Likewise, our results also show that the largest Stark shift is obtained for the field directed along the diagonal in a cubic box, and is found for the low field directed along a side of the box and for the high field along the diagonal in a rectangular one. The large Stark shift of the electron and hole trapped in a quantum box leads to an obvious reduction of the interband recombination.

Influence of an embedded quantum dot on the Josephson effect in the topological superconducting junction with Majorana doublets.

One Majorana doublet can be realized at each end of the time-reversal-invariant Majorana nanowires. We investigate the Josephson effect in the Majorana-doublet-presented junction modified by different inter-doublet coupling manners. It is found that when the Majorana doublets couple indirectly via a non-magnetic quantum dot, only the normal Josephson effect occurs, and the fermion parity in the system just affects the current direction and amplitude. However, one magnetic field applied on the dot can induce the fractional Josephson effect in the odd-parity case. Next if the direct and indirect couplings between the Majorana doublets coexist, no fractional Josephson effect takes place, regardless of the presence of magnetic field. Instead, there almost appears the π-period-like current in some special cases. All the results are clarified by analyzing the influence of the fermion occupation in the quantum dot on the parity conservation in the whole system. We ascertain that this work will be helpful for describing the dot-assisted Josephson effect between the Majorana doublets.

Majorana modes in a triple-terminal Josephson junction with embedded parallel-coupled double quantum dots

Abstract We investigate the Josephson effect in one triple-terminal junction with embedded parallel-coupled double quantum dots. It is found that the inter-superconductor supercurrent has opportunities to oscillate in period 4 π , with the adjustment of the phase differences among the superconductors. What is notable is that such a result is robust and independent of fermion parities, intradot Coulomb strength, and the dot-superconductor coupling manner. By introducing the concept of spinful many-particle Majorana modes, we present the analytical definition of the Majorana operator via superposing electron and hole operators. It can be believed that this work provide a simple but feasible proposal for the realization of Majorana modes in a nonmagnetic system.

Realization of a Nonlocal Persistent Current Qubit with the Help of Majorana Bound States

We investigate the persistent currents in one coupled quantum-ring structure in which each ring is formed by the couplings between one of the Majorana bound states and the end dots of a quantum dot chain. It is found that even in the case of Majorana zero mode, the persistent current in one ring can be efficiently manipulated by tuning the magnetic flux in the other ring if the two rings both possess the odd quantum dots. This means that the Majorana bound states can assist to realize the coherent nonlocal manipulation of the persistent currents. Accordingly, a nonlocal persistent current qubit can be achieved with the help of Majorana bound states. However, if even quantum dots exist in one ring, the nonlocal control of the persistent currents will vanish and the qubit cannot be realized. By performing the representation transformation, we present a detailed explanation about the odd–even effect of the persistent current.

Odd–Even Effect of the Persistent Current in a Quantum Dot Ring with Embedded Majorana Bound States

We investigate the persistent current in one mesoscopic ring formed by the couplings between the end dots of a quantum dot chain and one Majorana bound states (MBS). It is found that the persistent-current properties are dependent on the dot-number parity of the chain. When the dot number is odd, the persistent current emerges with its oscillation by tuning the magnetic flux in the ring. However, if the dot number is even, the persistent current will always be zero regardless of the presence of Majorana zero mode. By transforming the system Hamiltonian into the Majorana representation, all the results are analyzed in detail. We believe that these results provide new information for understanding the MBS-assisted electron motion property in the mesoscopic system.

Josephson current through a quantum-dot ring: π-junction transition and persistent current magnification

By means of the exact diagonalization approach, the Josephson and persistent currents in a superconductor/quantum-dot ring/superconductor (S/QDR/S) structure are theoretically investigated. The ground state is obtained within zero bandwidth approximation in which the superconductors are replaced by effective local pairing potentials. It is found that Josephson current can flow through this structure in the presence of various electron correlations. Furthermore, in the half-filled case, a novel 0-π transition behavior is observed, which arises from the interplay of interdot antiferromagnetic coupling and electron correlations. When the symmetry of the two arms in the QDR is broken down, the quantum interference efficiently causes the persistent current magnification, even in the case of equilibrium and zero magnetic flux.