Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gappe
d phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.
When a local and attractive potential is quenched in a nanowire, the spectrum changes its topology from a purely continuum to a continuum and discrete portion. We show that, under appropriate conditions, this quench leads to stable coherent oscillati
ons in the observables time evolution. In particular, we demonstrate that ballistic nanowires with spin-orbit coupling (SOC) exposed to a uniform magnetic field are especially suitable to observe this effect. Indeed, while in ordinary nanowires the effect occurs only if the strength $U_0$ of the attractive potential is sufficiently strong, even a weak value of $U_0$ is sufficient in SOC nanowires. Furthermore, in these systems coherent oscillations in the spin sector can be generated and controlled electrically by quenching the gate voltage acting on the charge sector. We interpret the origin of this phenomenon, analyze the effect of variation of the chemical potential and the switching time of the quenched attractive potential, and address possible implementation schemes.
Recently, it has been proposed that a mechanism for the appearance of non-equilibrium superconductivity in a resonantly driven semiconductor with repulsive interband interactions exists.~cite{Goldstein_PRB15} The underlying microscopic model relies o
n the appearance of a specific fermionic dissipation mechanism and the careful simultaneous tailoring of the electronic dispersion relation and electron-electron interactions. We, instead, show that the phenomenon is rather general and does not need a special fine tuning of parameters. By considering a pair of bands with locally the same sign of concavity, we demonstrate that interband pairing arises under the natural assumption of the presence of phononic baths and radiative recombination. In light of these findings, we demonstrate how the emergence of superconductivity can be understood in terms of standard equilibrium interband BCS theory.
Topological superconductors give rise to unconventional superconductivity, which is mainly characterized by the symmetry of the superconducting pairing amplitude. However, since the symmetry of the superconducting pairing amplitude is not directly ob
servable, its experimental identification is rather difficult. In our work, we propose a system, composed of a quantum point contact and proximity induced s-wave superconductivity at the helical edge of a two dimensional topological insulator, for which we demonstrate the presence of odd-frequency pairing and its intimate connection to unambiguous transport signatures. Notably, our proposal requires no time-reversal symmetry breaking terms. We discover the domination of crossed Andreev reflection over electron cotunneling in a wide range of parameter space, which is a quite unusual transport regime.
We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating th
e fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier.
Motivated by recent experiments, we investigate the excitation energy of a proximitized Rashba wire in the presence of a position dependent pairing. In particular, we focus on the spectroscopic pattern produced by the overlap between two Majorana bou
nd states that appear for values of the Zeeman field smaller than the value necessary for reaching the bulk topological superconducting phase. The two Majorana bound states can arise because locally the wire is in the topological regime. We find three parameter ranges with different spectral properties: crossings, anticrossings and asymptotic reduction of the energy as a function of the applied Zeeman field. Interestingly, all these cases have already been observed experimentally. Moreover, since an increment of the magnetic field implies the increase of the distance between the Majorana bound states, the amplitude of the energy oscillations, when present, gets reduced. The existence of the different Majorana scenarios crucially relies on the fact that the two Majorana bound states have distinct $k$-space structures. We develop analytical models that clearly explain the microscopic origin of the predicted behavior.
Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is a fundamental goal of nanoscale spintronics and an important prerequisite for the formation of Majorana bound states. Such a helical state is predicted in one-di
mensional (1D) nanowires subject to strong Rashba SOC and spin-mixing, its hallmark being a characteristic reentrant behaviour in the conductance. Here, we report the first direct experimental observations of the reentrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingly, the feature is very prominent also in the absence of magnetic fields. This behaviour suggests that exchange interaction exhibits substantial impact on transport in our device. We attribute the opening of the pseudogap to spin-flipping two-particle backscattering. The all-electric origin of the ideal helical transport bears momentous implications for topological quantum computing.
We show that correlated two-particle backscattering can induce fractional charge oscillations in a quantum dot built at the edge of a two-dimensional topological insulator by means of magnetic barriers. The result nicely complements recent works wher
e the fractional oscillations were obtained employing of semiclassical treatments. Moreover, since by rotating the magnetization of the barriers a fractional charge can be trapped in the dot via the Jackiw-Rebbi mechanism, the system we analyze offers the opportunity to study the interplay between this noninteracting charge fractionalization and the fractionalization due to two-particle backscattering. In this context, we demonstrate that the number of fractional oscillations of the charge density depends on the magnetization angle. Finally, we address the renormalization induced by two-particle backscattering on the spin density, which is characterized by a dominant oscillation, sensitive to the Jackiw-Rebbi charge, with a wavelength twice as large as the charge density oscillations.
The transport properties of a suspended carbon nanotube probed by means of a STM tip are investigated. A microscopic theory of the coupling between electrons and mechanical vibrations is developed. It predicts a position-dependent coupling constant,
sizeable only in the region where the vibron is located. This fact has profound consequences on the transport properties, which allow to extract information on the location and size of the vibrating portions of the nanotube.
