We propose a new mechanism for topological superconductivity based on an antiferromagnetically ordered chain of magnetic atoms on the surface of a conventional superconductor. In a weak Zeeman field, a supercurrent in the substrate generates a staggered spin-current, which converts the preexisting topologically-unprotected Shiba states into Majorana fermions (MFs). The two experimental knobs can be finely tuned providing a platform with enhanced functionality for applications. Remarkably, the electronic spin-polarization of the arising edge MF wavefunctions depends solely on the parity of the number of magnetic moments, which can serve as a distinctive signature of the MFs. We introduce the basic concepts within a minimal model and make contact with experiments by a microscopic analysis based on the Shiba states. [8,9]. Other proposals [5,[10][11][12][13][14][15][16][17][18]20, 21] consider a conventional SC under the influence of a helical magnetic order [22], which effectively generates spin-momentum locking that can be stronger than the intrinsic one of semiconducting nanowires. The required inhomogeneous magnetic order can be realized by placing nano-magnets [11] or magnetic atoms on top of a SC [5, 12, 14-18, 20, 21]. In fact, ongoing experiments involving magnetic chains have provided the first promising MF fingerprints [23,24]. However, it has been shown that the presence of helicity is not indinspensable for obtaining MFs [1], opening perspectives for new platforms.In this article we propose a new route towards MFs without involving helical states or helical magnetic fields. Specifically, we consider an antiferromagnetically (AFM) ordered chain of classical spins on the surface of a conventional superconductor. The low-energy sector of this hybrid system is dominated by topologically-unprotected Shiba states [26], i.e. electronic states that are localized at the magnetic atoms' sites with energies lying inside the superconducting gap. We demonstrate that one can convert the Shiba states into MFs by imposing a supercurrent flow J in the superconductor and applying a weak in-plane Zeeman field B (Fig. 1). The two control fields cooperate with the AFM order to generate a staggered * Electronic address: andreas.heimes@kit.edu spin-current, which can be viewed as an engineered timereversal symmetry breaking spin-momentum locking.The functional device that we propose, offers the possibility of manipulating the topological phase diagram via the two easily controllable fields, a feature that can facilitate the detection and braiding of MFs. Furthermore, the AFM ordering of the magnetic atoms sets stringent constraints on the spin-texture [27] of the MF wavefunctions, resulting in an electronic polarization of the edge states that depends on the number-parity of the magnetic moments (Fig. 1). The resulting even-odd effect should be experimentally detectable by spin-polarized scanning tunneling microscope (STM) techiques and could help identifying the emergence of MFs.It is encouraging to note that recent STM exp...

We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin-orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration.Materials with Rashba spin-orbit coupling (SOC) have recently attracted renewed attention due to their pivotal role for realizing artificial topological superconductors (TSCs) which harbor Majorana fermions (MFs) [1][2][3][4][5]. Early proposals involved materials with SOC, such as topological insulators [6], noncentrosymmetric SCs [7], and Rashba semiconductors [8][9][10][11], which stimulated significant experimental progress. Remarkably, a number of promising but yet not fully conclusive MF-signatures have been already reported in semiconductor-based heterostructures [12][13][14][15]. The unsettled witnessing of MFs [16][17][18] constitutes a strong motivation for engineering and testing alternative hybrid devices. For instance, platforms based on magnetic adatoms which can be manipulated and probed via spin-polarized and spatially-resolved scanning tunneling microscopy (STM) techniques, appear capable of unambiguously revealing the presence of MFs.This new perspective opened the door for new MF devices based on magnetic adatoms on the surface of conventional superconductors. One finds implementations with magnetic adatoms where the ordering is random [19], spiral [20-29], antiferromagnetic (AFM) with SOC induced by the combination of Zeeman fields and supercurrents [30], and ferromagnetic (FM) on top of a superconducting surface with Rashba SOC [31,32]. According to very recent experimental findings [33], MFs seem to indeed emerge in magnetic adatom hybrid devices, where the ordering of the chain appears to be FM. This type of ordering can lead to MFs only if Rashba SOC is present, arising from the broken inversion associated with the Pb superconducting substrate. In fact, this is a plausible scenario for Pb which owes already a non-...

We investigate the dynamics of individual quasiparticle excitations on a small superconducting aluminum island connected to normal metallic leads by tunnel junctions. We find the island to be free of excitations within the measurement resolution. This allows us to show that the residual heating, which typically limits experiments on superconductors, has an ultralow value of less than 0.1 aW. By injecting electrons with a periodic gate voltage, we probe electron-phonon interaction and relaxation down to a single quasiparticle excitation pair, with a measured recombination rate of 16 kHz. Our experiment yields a strong test of BCS theory in aluminum as the results are consistent with it without free parameters.

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an Al/AlOx/Al Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating AlOx barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc-SQUID driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge. I: INTRODUCTIONWhile superconducting circuits based on Josephson junctions (JJs) rapidly mature towards favorable and applicable qubits for quantum computers [1-3], a major source of their decoherence traces back to spurious material defects that give rise to the formation of low-energy two-level systems (TLSs). On the other hand, sensitivity to tiny perturbations turns JJ qubits into ideal tools to study the properties of TLSs. For example, microwave spectroscopy of JJ phase qubits shows avoided level crossings revealing the TLSs' quantum character as well as their coherent interaction with the qubit [4]. Various microscopic models including dangling bonds, Andreev bound states [5], and Kondo fluctuators [6] have been suggested to explain the origin of TLSs. There is growing evidence [7,8], however, that they are formed by small groups of atoms that are able to tunnel between two energetically almost equivalent configurations. This is most strongly supported by recent experiments where the TLSs' energy splittings were tuned by applying external static strain [9]. TLSs are the source of lowenergy excitations, which are also responsible for the thermal, acoustic, and dielectric properties of glasses at temperatures below 1 K [10,11], which are well studied in bulk materials. Inherent to disordered solids, they are present in surface oxides and insulating layers of any microfabricated device as well as in the tunnel barriers of Josephson junctions.In contrast to traditional measurements performed on glasses that probe huge ensembles of TLSs, the sensitivity of JJ-based qubits allows one to address single TLSs and determine their individual properties. Strain-tuning experiments, e.g., measure a TLS's deformation potential [9] and allow for a detailed analysis of the coherent interaction between two TLSs brought into resonance [12]. In another experiment, the temperatu...

We investigate the properties of a hybrid single-electron transistor, involving a small superconducting island sandwiched between normal metal leads, which is driven by dc plus ac voltages. In order to describe its properties we derive from the microscopic theory a set of coupled equations. They consist of a master equation for the probability to find excess charges on the island, with rates depending on the distribution of nonequilibrium quasiparticles. Their dynamics follows from a kinetic equation which accounts for the excitation by singleelectron tunneling as well as the relaxation and eventual recombination due to the interaction with phonons. Our low-temperature results compare well with recent experimental findings obtained for ac-driven hybrid single-electron turnstiles.