Majorana quasiparticles in condensed matter

In the space of less than one decade, the search for Majorana quasiparticles in condensed matter has become one of the hottest topics in physics. The aim of this review is to provide a brief perspective of where we are with strong focus on artificial implementations of one-dimensional topological superconductivity. After a self-contained introduction and some technical parts, an overview of the current experimental status is given and some of the most successful experiments of the last few years are discussed in detail. These include the novel generation of ballistic InSb nanowire devices, epitaxial Al-InAs nanowires and Majorana boxes, high frequency experiments with proximitized quantum spin Hall insulators realised in HgTe quantum wells and recent experiments on ferromagnetic atomic chains on top of superconducting surfaces.Comment: 75 pages, 26 figures. Minor modifications and updated reference

Mapping the Topological Phase Diagram of Multiband Semiconductors with Supercurrents

We show that Josephson junctions made of multiband semiconductors with strong spin-orbit coupling carry a critical supercurrent $I_c$ that contains information about the non-trivial topology of the system. In particular, we find that the emergence and annihilation of Majorana bound states in the junction is reflected in strong even-odd effects in $I_c$ at small junction transparency. This effect allows for a mapping between $I_c$ and the topological phase diagram of the junction, thus providing a dc measurement of its topology.Comment: 5 pages 3 figures. Published versio

Spin filtering through excited states in double quantum dot pumps

Recently it has been shown that ac-driven double quantum dots can act as spin pumps and spin filters. By calculating the current through the system for each spin polarization, by means of the time evolution of the reduced density matrix in the sequential tunneling regime (Born-Markov approximation), we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. Importantly, the pumped current as a function of the applied frequency presents a series of peaks which are uniquely associated with a definite spin polarization. We discuss how excited states participating in the current allow the system to behave as a bipolar spin filter by tuning the ac frequency and intensity. We also discuss spin relaxation and decoherence effects in the pumped current and show that measuring the width of the current vs frequency peaks allows to determine the spin decoherence time $T_{2}$.Comment: 10 pages. 5 figure

SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum

We study normal transport and the sub-gap spectrum of superconductor-normal-superconductor (SNS) junctions made of semiconducting nanowires with strong Rashba spin-orbit coupling. We focus, in particular, on the role of confinement effects in long ballistic junctions. In the normal regime, scattering at the two contacts gives rise to two distinct features in conductance, Fabry-Perot resonances and Fano dips. The latter arise in the presence of a strong Zeeman field $B$ that removes a spin sector in the leads (\emph{helical} leads), but not in the central region. Conversely, a helical central region between non-helical leads exhibits helical gaps of half-quantum conductance, with superimposed helical Fabry-Perot oscillations. These normal features translate into distinct subgap states when the leads become superconducting. In particular, Fabry-Perot resonances within the helical gap become parity-protected zero-energy states (parity crossings), well below the critical field $B_c$ at which the superconducting leads become topological. As a function of Zeeman field or Fermi energy, these zero-modes oscillate around zero energy, forming characteristic loops, which evolve continuously into Majorana bound states as $B$ exceeds $B_c$. The relation with the physics of parity crossings of Yu-Shiba-Rusinov bound states is discussed.Comment: 12 pages main article, 14 figures + 5 pages supplementary material, 5 figures. Added new appendix. Other minor changes. Published versio

Multiple Andreev reflection and critical current in topological superconducting nanowire junctions

We study transport in a voltage biased superconductor-normal-superconductor (SNS) junction made of semiconducting nanowires with strong spin-orbit coupling, as it transitions into a topological superconducting phase for increasing Zeeman field. Despite the absence of a fractional steady-state ac Josephson current in the topological phase, the dissipative multiple Andreev reflection (MAR) current I_dc at different junction transparencies is particularly revealing. It exhibits unique features related to topology, such as the gap inversion, the formation of Majorana bound states, and fermion-parity conservation. Moreover, the critical current I_c, which remarkably does not vanish at the critical point where the system becomes gapless, provides direct evidence of the topological transition.Comment: Published version, 21 pages, 7 figures, 3 appendice

Quantifying wave-function overlaps in inhomogeneous Majorana nanowires

A key property of Majorana zero modes is their protection against local perturbations. In the standard picture, this protection is guaranteed by a high degree of spatial nonlocality of the Majoranas, namely a suppressed wave-function overlap, in the topological phase. However, a careful characterization of resilience to local noise goes beyond mere spatial separation and must also take into account the projection of wave-function spin. By considering the susceptibility of a given zero mode to different local perturbations, we find the relevant forms of spin-resolved wave-function overlaps that measure its resilience. We quantify these overlaps and study their dependence with nanowire parameters in several classes of experimentally relevant configurations. These include nanowires with inhomogeneous depletion and induced pairing, barriers, and quantum dots. Smooth inhomogeneities have been shown to produce near-zero modes, so-called pseudo-Majoranas, below the critical Zeeman field in the bulk. Surprisingly, their resilience is found to be comparable or better than that of topological Majoranas in realistic systems. We further study how accurately their overlaps can be estimated using a purely local measurement on one end of the nanowire, accessible through conventional transport experiments. In uniform nanowires, this local estimator is remarkably accurate. In inhomogeneous cases, it is less accurate but can still provide reasonable estimates for potential inhomogeneities of the order of the superconducting gap. We further analyze the zero-mode wave-function structure, spin texture, and spectral features associated with each type of inhomogeneity. All our results highlight the strong connection between internal wave-function degrees of freedom, nonlocality, and protection in smoothly inhomogeneous nanowiresWe acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2015-65706-P, No. FIS2015-64654-P, and No. FIS2016-80434-P (AEI/FEDER, EU), the Ramón y Cajal programme, Grants No. RYC-2011-09345 and No. RYC-2013-14645, and the “María de Maeztu” Programme for Units of Excellence in Research and Development (MDM-2014-0377

Microscopic Model for Sequential Tunneling in Semiconductor Multiple Quantum Wells

We propose a selfconsistent microscopic model of vertical sequential tunneling through a multi-quantum well.The model includes a detailed description of the contacts,uses the Transfer Hamiltonian for expressions of the current and it treats the Coulomb interaction within a mean field approximation. We analyze the current density through a double well and a superlattice and study the formation of electric field domains and multistability coming from the Coulomb interaction. Phase diagrams of parameter regions (bias, doping in the heterostructure and in the contacts,etc) where the different solutions exist are given.Comment: 4 pages, 8 Postscript Figure

Single-electron transport in electrically tunable nanomagnets

We study a single-electron transistor (SET) based upon a II–VI semiconductor quantum dot doped with a single-Mn ion. We present evidence that this system behaves like a quantum nanomagnet whose total spin and magnetic anisotropy depend dramatically both on the number of carriers and their orbital nature. Thereby, the magnetic properties of the nanomagnet can be controlled electrically. Conversely, the electrical properties of this SET depend on the quantum state of the Mn spin, giving rise to spin-dependent charging energies and hysteresis in the Coulomb blockade oscillations of the linear conductance.This work has been financially supported by MEC-Spain (Grants No. FIS200402356, No. MAT2005-07369-C03-03, and the Ramon y Cajal Program) and by CAV (No. GV05-152)

AC-driven double quantum dots as spin pumps and spin filters

We propose and analyze a new scheme of realizing both spin filtering and spin pumping by using ac-driven double quantum dots in the Coulomb blockade regime. By calculating the current through the system we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. We also discuss spin relaxation and decoherence effects in the pumped current.Comment: 5 pages, 4 figure