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 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 propose that a multi-graphene of ABC-type stacking yields virtual bound states lying within the Coulomb insulating gap of an Anderson-like adatom. Wondrously, a virtual state constitutes the counterpart of the atomic collapse phenomenon proposed in relativistic atomic Physics, while the second emerges as its particle-hole symmetric, analogous to a positron state. Thus, we introduce the effect as the adatomic collapse, which occurs due to a flat band with a dispersionless state and a divergent density of states $\sim|\varepsilon-\varepsilon_{F}|^{2/J-1}$ near the Fermi energy $\varepsilon_{F}$ for $J\geq3,$ where $J\pi$ is the Berry phase. We conclude this scenario based on the Kramers-Kronig transformation of the quasiparticle broadening, from where we observe that the aforementioned van Hove singularity induces virtual bound states. Counterintuitively, near the singularity, we find these states above and below the Fermi energy correlated to the existence of the bottom and top edges of the Coulomb insulating region, respectively. As such a behavior rises without a twist, the system is known as Moir\'eless and the phenomenon emerges also assisted by the adatom Coulomb correlations. Similarly to Science 340, 734 (2013) we find the effective critical atomic number $\mathcal{Z}_{c}\sim0.96$ in contrast to an ultra-heavy nucleus. Thus, we point out that multi-graphene is a proper playground for testing a predicted phenomenon of the relativistic atomic Physics in the domain of the condensed matter Physics.

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 line shape evolves from resonant, typical for J = 1 (single Weyl), towards antiresonant, extrapolating to the so-called hyper Weyl semimetals with J >> 1. 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 (360 degrees/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 theoretically investigate atomic frustrated states in diatomic molecules hosted by the bilayer graphene setup twisted by the first magic angle and with broken inversion symmetry in the Dirac cones of the system mini Brillouin zones. Such states show local spectral features typically from uncoupled atoms, but counterintuitively, they also exhibit nonlocal molecular correlations, which turn them into atomically frustrated. By considering a particle-hole symmetric molecule in the Moiré superlattice length-scale, we reveal distinctly from the metallic Weyl counterparts, a molecular zero mode atomically frustrated at the spectral densities of the dimer’s atoms. To this end, a strong metallic phase with a plateau in the density of states established by the broken inversion symmetry, together with pronounced blue and red shifts in the molecular levels, due to the magic angle condition, should occur synergistically with atomic Coulomb correlations. Consequently, an entire collapse of these molecular peaks into a single one atomically frustrated, taking place exactly at the Fermi energy, becomes feasible just by tuning properly opposite gate voltages attached to the graphene monolayers. Therefore, we propose that unusual molecular bindings can be engineered via the twistronics of the bilayer graphene system, in particular, if its metallic phase is fully established.

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 bound states (MBSs) at the opposite ends. It is demonstrated that if highly nonlocal and nonoverlapping MBSs are formed in the system, the zero-bias Andreev conductance through the dot exhibits characteristic isoconductance profiles with the shape depending on the spin asymmetry of the coupling between the dot and the topological superconductor. Otherwise, for overlapping MBSs with less degree of nonlocality, the conductance is insensitive to the spin polarization and the isoconductance signatures disappear. This allows to propose an alternative experimental protocol for probing the nonlocality of the MBSs in Majorana nanowires.

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 interimpurity scattering channels.

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 one to introduce the topological quality factor, characterizing the level of topological protection in the system. We demonstrate that the Coulomb interaction between the dot and the topological superconducting section leads to the onset of the additional overlap of the wave functions 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 introduce the concept of a Majorana molecule, a topological bound state appearing in the geometry of a double quantum dot structure flanking a topological superconducting nanowire. We demonstrate that, if the Majorana bound states 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 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 we propose that it can be captured by a pseudospin resolved scanning tunneling microscope tip.