One of the main features of the Majorana state, which attracts a considerable current interest to these excitations in solid-state systems, is related to its nonlocal character. It is demonstrated that the direct consequence of such nonlocality is the collapse of the Fano resonance manifesting itself in the conductance of an asymmetric interference device, the arms of which are connected by a one-dimensional topological superconductor. In the framework of the spinless model, it is shown that the predicted effect is associated with an increase in the multiplicity of the degeneracy of the zero-energy state of the structure arising at a specific case of the Kitaev model. Such an increase leads to the formation of a bound state in the continuum.
Majorana bound states (MBS) differ from the regular zero energy Andreev bound states in their nonlocal properties, since two MBS form a single fermion. We design strategies for detection of this nonlocality by using the phenomenon of Coulomb-mediated Majorana coupling in a simplest setting which still retains falsifiability. Focusing on the implementation of MBS based on the quantum spin Hall effect, we also design a way to probe Majoranas without the need to open a magnetic gap in the helical edge states. In the setup that we analyse, long range MBS coupling manifests in the $h/e$ magnetic fl…
We investigate the Josephson current in a Fano-Josephson junction formed by the direct coupling between two topological superconducting wires and their indirect coupling via a quantum dot. It is found that when two Majorana zero modes respectively appear in the wires, the Fano interference causes abundant Josephson phase transition processes. What is notable is that in the presence of appropriate direct and indirect inter-wire couplings, the fractional Josephson effect disappears and then such a structure transforms into a $0$-phase normal Josephson junction. On the other hand, if finite coupl…
Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed…
Kitaev chain (KC) is a prototypical model for the study of Majorana fermions (MFs). In the topological phase, a KC hosts two MFs at its ends. Being separated in space, these two MFs are nonlocal. The nonlocal transport in a KC biased between two normal metal leads is mediated by electron tunneling (ET) and crossed Andreev reflection (CAR). ET contributes positively while CAR contributes negatively to the nonlocal conductance. Enhanced CAR and hence a negative nonlocal conductance is a hallmark of nonlocality of MFs. But simple conductance measurements in the above setup cannot probe the nonloc…
We investigate theoretically a Fano interferometer composed by STM and AFM tips close to a Kitaev dimer of superconducting adatoms, in which the adatom placed under the AFM tip, encloses a pair of Majorana fermions (MFs). For the binding energy $Δ$ of the Cooper pair delocalized into the adatoms under the tips coincident with the tunneling amplitude $t$ between them, namely $Δ$ = $t$, we find that only one MF beneath the AFM tip hybridizes with the adatom coupled to the STM tips. As a result, a gate invariance feature emerges: the Fano profile of the transmittance rises as an invariant quantit…
As the Fano effect is an interference phenomenon where tunneling paths compete for the electronic transport, it becomes a probe to catch fingerprints of Majorana fermions lying on condensed matter systems. In this work we benefit of this mechanism by proposing as a route for that an Aharonov-Bohm-like interferometer composed by two quantum dots, being one of them coupled to a Majorana bound state, which is attached to one of the edges of a semi-infinite Kitaev wire within the topological phase. By changing the Fermi energy of the leads and the symmetric detuning of the levels for the dots, we …
We explore the tunneling transport properties of a quantum dot embedded in an optical microcavity and coupled to a semiconductor-superconductor one-dimensional nanowire (Majorana nanowire) hosting Majorana zero modes (MZMs) at their edges. Conductance profiles reveal that strong light-matter coupling can be employed to distinguish between the cases of highly nonlocal MZMs, overlapped MZMs and MZMs with less degree of nonlocal feature. Moreover, we show that it is possible to access the degree of Majorana nonlocality (topological quality factor) by changing the dot spectrum through photon-induc…
We explore theoretically the influence of Fano interference in the so-called Majorana oscillations in a T-shaped hybrid setup formed by a quantum dot (QD) placed between conducting leads and side-coupled to a topological superconducting nanowire (TSNW) hosting zero-energy Majorana bound states (MBSs) at the ends. Differential conductance as a function of the external magnetic field reveals oscillatory behavior. Both the shape and amplitude of the oscillations depend on the bias-voltage, degree of MBSs non-locality and Fano parameter of the system determining the regime of interference. When th…
We investigate the transport properties through a nanostructure composed of parallel double quantum dots coupled to two normal contacts. Additionally, each quantum dot is connected to a topological superconducting nanowire, hosting Majorana zero modes at its ends. A magnetic flux threading across the area enclosed by the interferometer is considered. First, we investigate the physical quantities of the system employing Green's function formalism. We find that the emergence of bound states appears in symmetric configurations of topological superconducting nanowires, i.e., depending on their len…
We investigate transport properties through a crossbar-shaped structure formed by a quantum dot (QD) coupled to two normal leads and embedded between two one-dimensional topological superconductors (TSCs). Each TSC hosts Majorana bound states (MBSs) at its ends, which can interact between them with an effective coupling strength. We find a signature of bound states in continuum (BIC) in the MBSs spectral function. By allowing finite inter MBSs coupling, BICs splitting is observed and shows projection in transmission for asymmetric coupling case as cuasi-BICs. As a consequence, we also show tha…
Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that no…
Hybrid system composed by a semiconducting nanowire with proximity-induced superconductivity and a quantum dot at the end working as spectrometer was recently used to quantify the so-called degree of Majorana nonlocality [Deng et al., Phys.Rev.B, 98, 085125 (2018)]. Here we demonstrate that spin-resolved density of states of the dot responsible for zero-bias conductance peak strongly depends on the separation between the Majorana bound states (MBSs) and their relative couplings with the dot and investigate how the charging energy affects the spectrum of the system in the distinct scenarios of …
We consider a quantum wire, containing two Majorana bound states (MBS) at its ends that are coupled to a current lead on one side and to a quantum dot (QD) on the other side. Using the method of full counting statistics we calculate the conductance and the zero-frequency noise. Using an effective low-energy model, we analyze in detail the Andreev reflection probability as a function of the various system parameters and show that it exhibits a Fano resonance (FR) line shape in the case of a weakly coupled QD as a function of the QD energy level when the two MBS overlap. The asymmetry parameter …
We demonstrate theoretically the Fano resonance and the conversion from fast to slow light in a hybrid quantum dot-semiconductor/superconductor ring device, where the QD is coupled to a pair of MFs appearing in the hybrid S/S ring device. The absorption spectra of the weak probe field can exhibit a series of asymmetric Fano line shapes and their related propagation properties such as fast and slow light effects are investigated based on the hybrid system for suitable parametric regimes. The positions of the Fano resonances can be determined by the parameters, such as different detuning regimes…
There are still debates on whether the observed zero energy peak in the experiment by Stevan {\it et al.} [Science 346, 602(2014)] reveals the existence of the long pursuing Majorana bound states (MBS). we propose that, by mounting two scanning tunneling microscopic tips on top of the topological superconducting chain and measure the transmission spectrum between these two metallic tips, there are two kinds of characteristics on the spectrum that are caused by MBS uniquely. One is symmetric peaks with respect to zero energy and the other is $4π$ period caused by a nearby Josephson junction. Th…
According to the Phys. Rev. B 84, 201308(R) (2011), an isolated Majorana state bound to one edge of a long enough Kitaev chain in the topological phase and connected to a quantum dot, results in a robust transmittance of $1/2$ at zero-bias. In this work, we show that the removal of such a hallmark can be achieved by using a metallic surface hosting two adatoms in a scenario where there is a lack of symmetry in the Fano effect, which is feasible by coupling the Kitaev chain to one of these adatoms. Thus in order to detect this feature experimentally, one should apply the following two-stage pro…
Majorana fermions are promising building blocks of forthcoming technology in quantum computing. However, their non-ambiguous identification has remained a difficult issue because of the concomitant competition with other topologically trivial fermionic states, which poison their detection in most spectroscopic probes. By employing numerical and analytical methods, here we show that the Fano factor tomography is a key distinctive feature of a Majorana bound state, displaying a spatially constant Poissonian value equal to one. In contrast, the Fano factor of other trivial fermionic states, like …
We consider theoretically a $1D$-semiconducting wire with strong Rashba interaction in proximity with $s$-wave superconductor, driven into topological phase by external magnetic field. Additionally, we take into account on-site Coulomb interactions inside the wire. The system is modelled by a tight binding Hamiltonian with Rashba hopping term and induced $s$-wave superconductivity. Calculations are performed utilizing recursive Green's function method, and Coulomb interactions are treated selfconsistently within Hubbard $I$ approximation. For the Hubbard levels residing within $p$-wave superco…
One-dimensional topological superconductors host Majorana zero modes (MZMs), the non-local property of which could be exploited for quantum computing applications. Spin- polarized scanning tunneling microscopy measurements show that MZMs realized in self- assembled Fe chains on the surface of Pb have a spin polarization that exceeds that due to the magnetism of these chains. This feature, captured by our model calculations, is a direct consequence of the nonlocality of the Hilbert space of MZMs emerging from a topological band structure. Our study establishes spin polarization measurements as …
In this work, we demonstrate an equivalence on the single-electron transport properties between systems of different nature, a topological quantum system and a (conventional) non-topological one. Our results predicts that the Fano resonances obtained in a T-shaped double quantum dot system coupled to two normal leads and one superconducting lead (QD-QD-S) are identical to the obtained in a ring system composed of a quantum dot coupled to two Majorana bound states confined at the ends of a one dimensional topological superconductor nanowire (QD-MBSs). We show that the non-zero value of the Fano…
We investigate theoretically the features of the Majorana hallmark in the presence of Coulomb repulsion between two quantum dots describing a spinless Aharonov-Bohm-like interferometer, where one of the dots is strongly coupled to a Kitaev wire within the topological phase. Such a system has been originally proposed without Coulomb interaction in J. of Appl. Phys. 116, 173701 (2014). Our findings reveal that for dots in resonance, the ratio between the strength of Coulomb repulsion and the dot-wire coupling changes the width of the Majorana zero-bias peak for both Fano regimes studied, indicat…
Motivated by recent experiments we consider transport across an interacting magnetic impurity coupled to the Majorana zero mode (MZM) observed at the boundary of a topological superconductor (SC). In the presence of a finite tunneling amplitude we observe hybridization of the MZM with the quantum dot, which is manifested by a half-integer zero-bias conductance $G_0=e^2/2h$ measured on the metallic contacts. The low-energy feature in the conductance drops abruptly by crossing the transition line from the topological to the non-topological superconducting regime. Differently from the in-gap Yu-S…
