Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots

Abstract

We introduce the concept of spinful many-particle Majorana modes with local odd operator products, thereby preserving their local statistics. We consider a superconductor -double quantum dot system where these modes can arise with negligible Zeeman splitting when Coulomb interactions are present. We find a reverse Mottinsulator transition, where the even and odd parity bands become degenerate. Above this transition, Majorana operators move the system between the odd parity ground state, associated with elastic co-tunneling, and the even parity ground state, associated with crossed Andreev reflection. These Majorana modes are described in terms of one, three and five operator products. Parity conservation results in a 4π periodic supercurrent in the even state and no supercurrent in the odd state.The prediction for the existence of Majorana modes [1] has attracted enormous attention in condensed matter physics [2][3][4][5][6][7]. Allured by the possibility of constructing topological qubits for quantum computation [2,4], a plethora of schemes promising the positive identification of Majorana modes has emerged [8][9][10][11][12]. Although superconductors are a natural habitat of chargeless quasiparticles, spin degeneracy in standard s-wave superconductors prevents the appearance of localized Majorana modes. Effective spinless p-wave superconductors can be realized using strong spin-orbit coupling, for example at the interface of a superconductor and a topological insulator [5], or in semiconducting nanowires in the presence of Zeeman and Rashba fields [6,7]. Experimentally, supercurrents [13], Fraunhofer patterns and Shapiro steps [14], SQUIDs [15], and zero bias conductance peaks [16] have been observed in topological insulator systems, which, together with the zero bias conductance peaks in nanowire systems [17], provide prospects for the observation of the Majorana mode, but to date, no conclusive evidence has been observed.Superconductor -quantum dot systems are also proposed to realize Majorana modes [11,18,19], by including spin-orbit coupling [11], or in the presence of anisotropic magnetic fields [19]. Although quantum dots have several advantages, the strong spin-orbit or anisotropic magnetic fields required forms a major hurdle and limits material flexibility. For example, anisotropic magnetic fields only result in spinless localized Majorana modes in fields E Z ≫ ∆ ∼ t, with ∆ the induced superconducting gap and t the inter-site hopping. Here, generalizing the proposal of Ref.[19] to strongly correlated quantum dots, we show that in the presence of small anisotropic magnetic fields, E Z ∼ k B T , a new arena emerges: the concept of spinful many-particle Majorana modes. These Majorana modes are localized in their odd operator products, and thereby preserve the local statistics of spinless proposals [20]. Furthermore, this demonstrates that interactions can greatly relax the constraints of large Zeeman splitting and large spin FIG. 1: (a) Schematic representation of the device. Two superconductors (with p...

Reprint of : Floquet Majorana fermions in superconducting quantum dots

“…In the case of a triple QD, assuming 23 . In the case where μ 2 or μ 3 are zero the MFs are spatially separated [25].…”

“…In a system where neighboring QDs are coupled through superconducting reservoirs as in Fig. 1, in the limit of large superconducting gap the superconductors can be traced out and an effective Hamiltonian for the dots is obtained [23,24] as…”

Many-particle Majorana bound states: Derivation and signatures in superconducting double quantum dots

“…This can be treated as a uniform spin rotation on the respective site, sending . The effective Hamiltonian is then (): …”

“…Fortunately, these requirements can be strongly relaxed as shown recently by Wright and Veldhorst (), who considered the effect of strong correlations for the engineering of Majorana bound states. They demonstrated that only vanishingly small anisotropic Zeeman splitting, , is required.…”

A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario

“…Moreover, the effects of time-reversal symmetry breaking can be easily measured by applying a magnetic field [3]. Nowadays, a variety of theoretical and experimental research about small conducting devices, such as QDs, has been the focus of many scientists and engineers attention [4][5][6][7].…”