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The "Poor Man's Majorana" [Phys. Rev. B 86, 134528 (2012)] devoid of topological protection has been theoretically predicted to rely on the minimal Kitaev chain. Afterward, a pair of superconducting and spinless quantum dots turned the proposal practicable and differential conductance pinpointed consistent fingerprints with such a scenario [Nature 614, 445 (2023) and Nature 630, 329 (2024)]. In this work, we propose a model wherein the "Poor Man's Majorana" presents protection when one of the dots is exchange coupled to a quantum spin. If this quantum dot is perturbed by tuning the exchange coupling, the well-known spill over-like behavior of this Majorana surprisingly remains unchanged, and solely half of the fine structure is unexpectedly viewed. As a matter of fact, the "Poor Man's Majorana" zero mode consists in squeezing of the other half at zero frequency, which imposes its pinning there and prevents the mixing of the mode with the explicit fine structure. We claim that if the supposed unavoidable split of the zero mode by the fine structure is unexpectedly absent, then the "Poor Man's Majorana" can be considered robust against the quantum spin. In this way, it becomes protected and the lack of topological protection paradigm of the "Poor Man's Majorana" has been revisited, pushing this seemingly well-established issue into a new direction.

We theoretically investigate the possibility of obtaining Majorana zero modes (MZMs) in penta-silicene nanoribbons (p-SiNRs) with induced \textit{p}-wave superconductivity. The model explicitly considers an external magnetic field perpendicularly applied to the nanoribbon plane, as well as an extrinsic Rashba spin-orbit coupling (RSOC), in addition to the first nearest neighbor hopping term and \textit{p}-wave superconducting pairing. By analyzing the dispersion relation profiles, we observe the successive closing and reopening of the induced superconducting gap with a single spin component, indicating a spin-polarized topological phase transition (TPT). Correspondingly, the plots of the energy spectrum versus the chemical potential reveal the existence of zero-energy states with a preferential spin orientation characterized by nonoverlapping wave functions localized at opposite ends of the superconducting p-SiNRs. These findings strongly suggest the emergence of topologically protected, spin-polarized MZMs at the ends of the p-SiNRs with induced \textit{p}-wave superconducting pairing, which can be realized by proximitizing the nanoribbon with an \textit{s}-wave superconductor, such as lead. The proposal paves the way for silicene-based Majorana devices hosting multiple MZMs with a well-defined spin orientation, with possible applications in fault-tolerant quantum computing platforms and Majorana spintronics., Comment: 12 pages, 9 figures

We theoretically investigate the spectral properties of a quantum impurity (QI) hosting the here proposed {Majorana-Ising-type quasiparticle (MIQ) excitation}. It arises from the coupling between a finite topological superconductor (TSC) based on a chain of magnetic adatoms-superconducting hybrid system and an integer large spin $S$ flanking the QI. Noteworthy, the spin $S$ couples to the QI via the Ising-type exchange interaction. As the Majorana zero-modes (MZMs) at the edges of the TSC chain are overlapped, we counterintuitively find a regime wherein the Ising term modulates the localization of a fractionalized and resonant MZM at the QI site. Interestingly enough, the fermionic nature of this state is revealed as purely of electron tunneling-type and most astonishingly, it has the Andreev conductance completely null in its birth. Therefore, we find that a resonant edge state appears as a zero-mode and discuss it in terms of a poor man's Majorana[Nature 614, 445 (2023)].

We study the optical properties of a hybrid device composed by a quantum dot (QD) resonantly coupled to a photonic mode of an optical microcavity and a Majorana nanowire: a topological superconducting segment hosting Majorana bound states (MBSs) at the opposite ends. In the regime of strong light-matter coupling, it is demonstrated that the leakage of the Majorana mode into the QD opens new optical transitions between polaritonic states formed due to hybridisation of material excitation with cavity photons, which leads to the reshaping of the Jaynes-Cummings ladder and can lead to the formation of a robust single-peak at cavity eigenfrequency in the emission spectrum. Moreover, weak satellite peaks in the low and high frequency regions are revealed for the distinct cases of highly isolated MBSs, overlapped MBSs and MBSs not well localized at the nanowire ends.

We theoretically analyze the Fano interference in a single impurity multi-Weyl semimetal hybrid system and show the emergence of the topological charge Fano effect in the bulk local density of states. In multi-Weyl semimetals, the number of Fermi arcs at the system boundaries is determined by the topological charge $J$, a direct consequence of the "bulk-boundary" correspondence principle. Analogously, we find that $J$ also modulates the bulk Fano profile of the system with an embedded quantum impurity. Thus, by increasing $J$, the Fano lineshape evolves from resonant, typical for $J=1$ (single Weyl), towards antiresonant, extrapolating to the so-called hyper Weyl semimetals with $J\gg1$. Specially for the maximum case protected by the rotational symmetry $C_{2J=6}$, namely the $J=3$ (triple Weyl), which acquires asymmetric Fano profile, the Fano parameter absolute value is predicted to be $\tan(C_{2J=6})$, where $C_{2J}\equiv(360^{\circ}/2J)$ defines the rotational angle. Hence, the Fano discretization in the $J$ term introduces the topological charge Fano effect in multi-Weyl semimetals. We also suggest a transport device where we expect that the proposed Fano effect could be detected.

We study the emergence of Majorana zero modes (MZMs) at the ends of a finite double zigzag honeycomb nanoribbon (zHNR). We show that a double zHNR geometry can host spin-polarized MZMs at its ends. We considered a minimal model composed by first nearest neighbor hopping, Rashba spin-orbit coupling (RSOC), p-wave superconducting pairing, and an applied external magnetic field (EMF). The energy spectrum regions with either spin up or down MZMs belong to distinct topological phase transitions characterized by their corresponding winding numbers and can be accessed by tunning the chemical potential of the nanoribbons. Hybrid systems constituted by zHNRs deposited on conventional s-wave superconductors are potential candidates for experimentally realizing the proposal. The spin's discrimination of MZMs suggests a possible route for performing topological-conventional qubit operations using Majorana spintronics., Comment: Main text (6 pages, 3 figures) + Supplemental Material (5 pages, 3 figures)

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-induced transitions tuned by an external pump applied to the microcavity.

We study the low-energy transport properties of a hybrid device composed by a native quantum dot coupled to both ends of a topological superconducting nanowire section hosting Majorana zero-modes. The account of the coupling between the dot and the farthest Majorana zero-mode allows to introduce the topological quality factor, characterizing the level of topological protection in the system. We demonstrate that Coulomb interaction between the dot and the topological superconducting section leads to the onset of the additional overlap of the wavefunctions describing the Majorana zero-modes, leading to the formation of trivial Andreev bound states even for spatially well-separated Majoranas. This leads to the spoiling of the quality factor and introduces a constraint for the braiding process required to perform topological quantum computing operations.

We theoretically analyze the effect of the inversion symmetry breaking on the structure of the impurity molecular states in Weyl metals. We show that for the case of a highly noncentrosymmetric Weyl metallic host, the standard picture of the alternating bonding and antibonding orbitals breaks down, and a qualitatively different frustrated atomic state emerges. This is a consequence of the pseudogap closing and related delicate Fano interplay between intra- and inter-impurity scattering channels.

We consider transport properties of a hybrid device composed by a quantum dot placed between normal and superconducting reservoirs, and coupled to a Majorana nanowire: a topological superconducting segment hosting Majorana zero-modes at the opposite ends. It is demonstrated that if topologically protected (nonoverlapping) Majorana zero-modes are formed in the system, zero-bias Andreev conductance through the dot exhibits isoconductance profiles with the shape depending on the spin asymmetry of the coupling between a dot and a topological superconductor. Otherwise, for the topologically trivial situation corresponding to the formation of Andreev bound states, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an experimental protocol for distinguishing between isolated Majorana zero-modes and Andreev bound states.

We introduce the concept of a Majorana molecule, a topological bound state appearing in the geometry of a double quantum dot (QD) structure flanking a topological superconducting nanowire. We demonstrate that, if the Majorana bound states (MBSs) at opposite edges are probed nonlocally in a two probe experiment, the spectral density of the system reveals the so-called half-bowtie profiles, while Andreev bound states (ABSs) become resolved into bonding and antibonding molecular configurations. We reveal that this effect is due to the Fano interference between pseudospin superconducting pairing channels and propose that it can be catched by a pseudospin resolved Scanning Tunneling Microscope (STM)-tip.

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 Majorana nonlocality (topological quality). Our findings suggest that spin-resolved spectroscopy of the local density of states of the dot can be used as a powerful tool for discriminating between different scenarios of the emergence of zero-bias conductance peak.

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 the latter is such that direct lead-lead path dominates over lead-QD-lead path and the bias is tuned in resonance with QD zero-energy, pronounced fractional Fano-like resonances are observed around zero-bias for highly non-local geometries. Further, the conductance profiles as a function of both bias-voltage and QD energy level display "bowtie" and "diamond" shapes, in qualitative agreement with both previous theoretical and experimental works. These findings ensure that our proposal can be used to estimate the degree of MBS non-locality, thus allowing to investigate their topological properties.

The ground state of the diatomic molecules in nature is inevitably bonding, and its first excited state is antibonding. We demonstrate theoretically that, for a pair of distant adatoms placed buried in three-dimensional-Dirac semimetals, this natural order of the states can be reversed and an antibonding ground state occurs at the lowest energy of the so-called bound states in the continuum. We propose an experimental protocol with the use of a scanning tunneling microscope tip to visualize the topographic map of the local density of states on the surface of the system to reveal the emerging physics.

We theoretically investigate a topological Kitaev chain connected to a double quantum-dot (QD) setup hybridized with metallic leads. In this system we observe the emergence of two striking phenomena: (i) a decrypted Majorana fermion (MF) qubit recorded over a single QD, which is detectable by means of conductance measurements due to the asymmetrical MF-qubit leaked state into the QDs; (ii) an encrypted qubit recorded in both QDs when the leakage is symmetrical. In such a regime, we have a cryptographylike manifestation, since the MF qubit becomes bound states in the continuum, which is not detectable in conductance experiments.

The zero-bias peak (ZBP) is understood as the definite signature of a Majorana bound state (MBS) when attached to a semi-infinite Kitaev nanowire (KNW) nearby zero temperature. However, such characteristics concerning the realization of the KNW constitute a profound experimental challenge. We explore theoretically a QD connected to a topological KNW of finite size at non-zero temperatures and show that overlapped MBSs of the wire edges can become effectively decoupled from each other and the characteristic ZBP can be fully recovered if one tunes the system into the leaked Majorana fermion fixed point. At very low temperatures, the MBSs become strongly coupled similarly to what happens in the Kondo effect. We derive universal features of the conductance as a function of the temperature and the relevant crossover temperatures. Our findings offer additional guides to identify signatures of MBSs in solid state setups.

We investigate theoretically thermal and electrical conductances for the system consisting of a quantum dot (QD) connected both to a pair of Majorana fermions residing the edges of a Kitaev wire and two metallic leads. We demonstrate that both quantities reveal pronounced resonances, whose positions can be controlled by tuning of an asymmetry of the couplings of the QD and a pair of MFs. Similar behavior is revealed for the thermopower, Wiedemann-Franz law and dimensionless thermoelectric figure of merit. The considered geometry can thus be used as a tuner of heat and charge transport assisted by MFs.

It is generally believed that free-standing graphene does not demonstrate any ferroic properties. In the present work we revise this statement and show that single graphene sheet with a pair of magnetic adatoms can be driven into ferroelectric (FE) and multiferroic (MF) phases by tuning the Dirac cones slope. The transition into the FE phase occurs gradually, but an anomalous MF phase appears abruptly by means of a Quantum Phase Transition. Our findings suggest that such features should exist in graphene recently investigated by Scanning Tunneling Microscopy (Science 352, 437 (2016)).

We propose a theoretical approach based on an interferometer composed by two quantum dots asymmetrically coupled to isolated Majorana quasiparticles (MQPs), lying on the edges of two topological Kitaev chains, respectively via couplings $(t+\Delta)$ and $(\Delta-t)$. This setup enables us to probe MQPs in a quite distinct way from the zero-bias peak feature. Most importantly, the system behaves as a current switch made by two distinct paths: (i) for the upper dot connected to both chains, the device perceives both MQPs as an ordinary fermion and the current crosses solely the lower dot, since current in the upper dot is prevented due to the presence of the superconducting gap; and (ii) by suppressing slightly the hybridization of the upper dot with one chain, the current is abruptly switched to flow through this dot, once a trapped electron as a bound state in the continuum (BIC) (Phys. Rev. B 93, 165116 (2016)) appears in the lower dot. Such a current switch between upper and lower dots characterizes the Quantum Phase Transition (QPT) proposed here, being the ratio $t/\Delta$ the control parameter of the transition. This QPT is associated with a change from an ordinary fermionic excitation regime to a MQP in the interferometer, which enables not only the fundamental revealing of MQPs, but also yields a current switch assisted by them.

We report on a theoretical investigation of the interplay between vacuum fluctuations, Majorana quasiparticles (MQPs) and bound states in the continuum (BICs) by proposing a new venue for qubit storage.BICs emerge due to quantum interference processes as the Fano effect and, since such a mechanism is unbalanced, these states decay as regular into the continuum. Such fingerprints identify BICs in graphene as we have discussed in detail in Phys. Rev. B 92, 245107 and 045409 (2015). Here by considering two semi-infinite Kitaev chains within the topological phase, coupled to a quantum dot (QD) hybridized with leads, we show the emergence of a novel type of BICs, in which MQPs are trapped. As the MQPs of these chains far apart build a delocalized fermion and qubit, we identify that the decay of these BICs is not connected to Fano and it occurs when finite fluctuations are observed in the vacuum composed by electron pairs for this qubit. From the experimental point of view, we also show that vacuum fluctuations can be induced just by changing the chain-dot couplings from symmetric to asymmetric. Hence, we show how to perform the qubit storage within two delocalized BICs of MQPs and to access it when the vacuum fluctuates by means of a complete controllable way in quantum transport experiments., Comment: New version

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, indicating thus that the electronic interdots correlation influences the Majorana state lifetime in the dot hybridized with the wire. Moreover, for the off-resonance case, the swap between the energy levels of the dots also modifies the width of the Majorana peak, which does not happen for the noninteracting case. The results obtained here can guide experimentalists that pursuit a way of revealing Majorana signatures.

Graphene hosting a pair of collinear adatoms in the phantom atom configuration has pseudogap with cubic scaling on energy, $\Delta\propto|\varepsilon|^{3}$ which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)]. In the case when adatoms are locally coupled to a single carbon atom the pseudogap scales linearly with energy, which prevents the formation of BICs. In this Letter, we explore the effects of non-local coupling characterized by the Fano factor of interference $q_{0},$ tunable by changing the slope of the Dirac cones in the graphene band-structure. We demonstrate that three distinct regimes can be identified: i) for $q_{0}q_{c2}$ the cubic scaling of the pseudogap with energy $\Delta\propto|\varepsilon|^{3}$ characteristic to the phantom atom configuration is restored and the phase with non-magnetic BICs is recovered. The phase with magnetic BICs can be described in terms of an effective intrinsic exchange field of ferromagnetic nature between the adatoms mediated by graphene monolayer. We thus propose a new type of quantum phase transition resulting from the competition between the states characterized by spin-degenerate and magnetic BICs.

We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states (LDOS) near the Dirac points exhibits two characteristic features: i) the cubic dependence on energy instead of the linear one for graphene as found in New J. Phys. 16, 013045 (2014) and ii) formation of BICs as aftermath of a Fano destructive interference assisted by the Coulomb correlations in the adatoms. For the geometry where adatoms are collinear to carbon atoms, we report absence of BICs.

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 $\Delta$ of the Cooper pair delocalized into the adatoms under the tips coincident with the tunneling amplitude $t$ between them, namely $\Delta$ = $t$, 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 quantity depending upon the STM tips Fermi energy, due to the symmetric swap in the gate potential of the AFM tip., Comment: Online version published in Physica E

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 show that opposing Fano regimes result in a transmittance characterized by distinct conducting and insulating regions, which are fingerprints of an isolated Majorana quasiparticle. Furthermore, we show that the maximum fluctuation of the transmittance as a function of the detuning is half for a semi-infinite wire, while it corresponds to the unity for a finite system. The setup proposed here constitutes an alternative experimental tool to detect Majorana excitations., Comment: Featured article: cover of the Journal of Applied Physics 116, 17 (2014)