Pasquale Marra

Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle–hole symmetric, and spatially-separated end modes which are topologically protected by the particle–hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the

A one-dimensional quantum charge pump transfers a quantized charge in each pumping cycle. This quantization is topologically robust, being analogous to the quantum Hall effect. The charge transferred in a fraction of the pumping period is instead generally unquantized. We show, however, that with specific symmetries in parameter space the charge transferred at well-defined fractions of the pumping period is quantized as integer fractions of the Chern number. We illustrate this in a one-dimension

Topological superconductors differ from topologically trivial ones due to the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken

Majorana bound states have been recently observed at the boundaries of one-dimensional topological superconductors. Yet, controlling the localization of the Majorana states, which is essential to the realization of any topological quantum device, is an ongoing challenge. To this end, we introduce a mechanism which can break a topologically homogeneous state via the formation of topological domains, and which can be exploited to control the position of Majorana states. We found, in fact, that in

Andreev bound states are low-energy excitations appearing below the particle-hole gap of superconductors, and are expected to be topologically trivial. Here, we report the theoretical prediction of topologically nontrivial Andreev bound states in one-dimensional superconductors. These states correspond to another topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which we construct in analogy to the spin Chern number in quantum spin Hall systems.

Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, densit

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition-metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries, we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This esta

Abstract Realizing Majorana modes in topological superconductors, i.e., the condensed-matter counterpart of Majorana fermions in particle physics, may lead to a major advance in the field of topologically-protected quantum computation. Here, we introduce one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized nanowires via periodically-modulated fields. This system realize

In condensed matter systems, zero-dimensional or one-dimensional Majorana modes can be realized respectively as the end and edge states of one-dimensional and two-dimensional topological superconductors. In this top-down approach, $(d\ensuremath{-}1)$-dimensional Majorana modes are obtained as the boundary states of a topologically nontrivial $d$-dimensional bulk. In a bottom-up approach instead, $d$-dimensional Majorana modes in a $d$-dimensional system can be realized as the continuous limit o

The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., systems with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superco

Majorana zero modes have gained significant interest due to their potential applications in topological quantum computing and in the realization of exotic quantum phases. These zero-energy quasiparticle excitations localize at the vortex cores of two-dimensional topological superconductors or at the ends of one-dimensional topological superconductors. Here we describe an alternative platform: a two-dimensional topological superconductor with inhomogeneous superconductivity, where Majorana modes

The Hofstadter model allows to describe and understand several phenomena in condensed matter such as the quantum Hall effect, Anderson localization, charge pumping, and flat-bands in quasiperiodic structures, and is a rare example of fractality in the quantum world. An apparently unrelated system, the relativistic Toda lattice, has been extensively studied in the context of complex nonlinear dynamics, and more recently for its connection to supersymmetric Yang-Mills theories and topological stri

Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle-hole symmetric, and spatially-separated end modes which are topologically protected by the particle-hole symmetry of the superconducting state. Due to their topological nature, they are robust against local perturbations and, in an ideal environment, free from decoherence. Furthermore, unlike ordinary fermions and bosons, the