Spectroscopy of Spin-Split Andreev Levels in a Quantum Dot with Superconducting Leads.

We use a hybrid superconductor-semiconductor transmon device to perform spectroscopy of a quantum dot Josephson junction tuned to be in a spin-1/2 ground state with an unpaired quasiparticle. Because of spin-orbit coupling, we resolve two flux-sensitive branches in the transmon spectrum, depending on the spin of the quasiparticle. A finite magnetic field shifts the two branches in energy, favoring one spin state and resulting in the anomalous Josephson effect. We demonstrate the excitation of the direct spin-flip transition using all-electrical control. Manipulation and control of the spin-flip transition enable the future implementation of charging energy protected Andreev spin qubits.

Long-term outcomes in Hodgkin lymphoma survivors. Temporary trends and comparison with general population.

The high cure rates of Hodgkin lymphoma (HL) make this oncological disease among those with the greatest number of long-term survivors. This single-institution study including 383 HL patients with up to 45 years of follow-up, analyses the morbidity and mortality of this population after treatments in comparison with the overall Spanish population, and investigates whether it has changed over time stratifying by periods of time, as a consequence of therapeutic optimization. The median age was 34.8 years (range 15-87) with median overall survival of 30 years, significantly higher in women (HR 0.58, 95% CI 0.42-0.79) (p = 0.0002). 185 late-stage diseases were noted (35% patients), cardiovascular disease (CVD) being the most frequent (23.2%). 30% of patients developed at least one second malignant neoplasm (SMN) to give a total of 174 SMNs. 20.9% of the patients died from HL and 67.0% died from non-HL causes (32.2% from SMN, 17% from CVD). The overall standardized mortality ratio (SMR) was 3.57 (95% CI: 3.0-4.2), with striking values of 7.73 (95% CI: 5.02-8.69) and of 14.75 (95% CI: 11.38-19.12) for women and patients <30 years at diagnosis, respectively. Excluding HL as the cause of death, the SMRs of those diagnosed before 2000 and from 2000 were proved to be similar (3.88 vs 2.73), maintaining in this last period an unacceptable excess of mortality due to secondary toxicity in patients cured of HL. Our study confirm that HL treatment substantially reduces the life expectancy of patients cured of HL. In recent periods, despite therapeutic optimization, deaths from toxicity continue to occur, mainly from CVD and SMN. Risk-factor monitoring should be intensified, prevention programs developed, and therapeutic optimization of LH investigated, especially in two vulnerable groups: those aged <30 years at diagnosis, and women.

Majorana-like Coulomb spectroscopy in the absence of zero-bias peaks.

Hybrid semiconductor-superconductor devices hold great promise for realizing topological quantum computing with Majorana zero modes1-5. However, multiple claims of Majorana detection, based on either tunnelling6-10 or Coulomb blockade (CB) spectroscopy11,12, remain disputed. Here we devise an experimental protocol that allows us to perform both types of measurement on the same hybrid island by adjusting its charging energy via tunable junctions to the normal leads. This method reduces ambiguities of Majorana detections by checking the consistency between CB spectroscopy and zero-bias peaks in non-blockaded transport. Specifically, we observe junction-dependent, even-odd modulated, single-electron CB peaks in InAs/Al hybrid nanowires without concomitant low-bias peaks in tunnelling spectroscopy. We provide a theoretical interpretation of the experimental observations in terms of low-energy, longitudinally confined island states rather than overlapping Majorana modes. Our results highlight the importance of combined measurements on the same device for the identification of topological Majorana zero modes.

Nontopological zero-bias peaks in full-shell nanowires induced by flux-tunable Andreev states.

A semiconducting nanowire fully wrapped by a superconducting shell has been proposed as a platform for obtaining Majorana modes at small magnetic fields. In this study, we demonstrate that the appearance of subgap states in such structures is actually governed by the junction region in tunneling spectroscopy measurements and not the full-shell nanowire itself. Short tunneling regions never show subgap states, whereas longer junctions always do. This can be understood in terms of quantum dots forming in the junction and hosting Andreev levels in the Yu-Shiba-Rusinov regime. The intricate magnetic field dependence of the Andreev levels, through both the Zeeman and Little-Parks effects, may result in robust zero-bias peaks-features that could be easily misinterpreted as originating from Majorana zero modes but are unrelated to topological superconductivity.

Cancer and SARS-CoV-2 Infection: A Third-Level Hospital Experience.

INTRODUCTION: Madrid has been the epicenter of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic in Spain. We analyzed our experience with SARS-CoV-2 infected and cancer patients. PATIENTS AND METHODS: We included patients from March 1 to April 30 2020 at Hospital Universitario Puerta de Hierro, Majadahonda, Madrid (Spain). The inclusion criteria were diagnosis of SARS-CoV-2 infection made by reverse transcription polymerase chain reaction (RT-PCR) of nasopharyngeal specimens in cancer patients who were admitted to the hospital due to the need for respiratory support. The exclusion criteria were suspected cases not confirmed. The primary objective was to analyze the mortality rates of patients with cancer, especially those with lung cancer and COVID-19. RESULTS: Overall in-hospital mortality of cancer patients with coronavirus disease 2019 (COVID-19) was 15.2% similar to 12.7% of the global COVID-19 hospitalized population (p=0.615) and greater than that of patients admitted without SARS-CoV-2 infection during the same period 4.3% (p<0.001). Among 653 patients receiving active cancer therapy during the study period, 24 (3.7%) developed COVID-19 and required admission, 4.2% of those receiving chemotherapy, 9.5% immunotherapy and 2.1% targeted therapies. Lung and breast cancer were the most frequent cancer types (26.1%), followed by colorectal cancer (19.6%). Mortality in patients with lung cancer was 25%. The univariate analysis comparing patients who developed a serious event to those who did not showed that the higher Brescia index, CURB-65 scale, lactate dehydrogenase (LDH) or C-reactive protein (CRP) were the risk factors of developing severe complications. CONCLUSION: Patients with cancer, especially lung cancer, and SARS-CoV-2 infection have a worse overall prognosis than the general population.

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states.

Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

Proximity-Induced Shiba States in a Molecular Junction.

Superconductors containing magnetic impurities exhibit intriguing phenomena derived from the competition between Cooper pairing and Kondo screening. At the heart of this competition are the Yu-Shiba-Rusinov (Shiba) states which arise from the pair breaking effects a magnetic impurity has on a superconducting host. Hybrid superconductor-molecular junctions offer unique access to these states but the added complexity in fabricating such devices has kept their exploration to a minimum. Here, we report on the successful integration of a model spin 1/2 impurity, in the form of a neutral and stable all organic radical molecule, in proximity-induced superconducting break junctions. Our measurements reveal excitations which are characteristic of a spin-induced Shiba state due to the radical's unpaired spin strongly coupled to a superconductor. By virtue of a variable molecule-electrode coupling, we access both the singlet and doublet ground states of the hybrid system which give rise to the doublet and singlet Shiba excited states, respectively. Our results show that Shiba states are a robust feature of the interaction between a paramagnetic impurity and a proximity-induced superconductor where the excited state is mediated by correlated electron-hole (Andreev) pairs instead of Cooper pairs.

Majorana bound states from exceptional points in non-topological superconductors.

Recent experimental efforts towards the detection of Majorana bound states have focused on creating the conditions for topological superconductivity. Here we demonstrate an alternative route, which achieves fully localised zero-energy Majorana bound states when a topologically trivial superconductor is strongly coupled to a helical normal region. Such a junction can be experimentally realised by e.g. proximitizing a finite section of a nanowire with spin-orbit coupling, and combining electrostatic depletion and a Zeeman field to drive the non-proximitized (normal) portion into a helical phase. Majorana zero modes emerge in such an open system without fine-tuning as a result of charge-conjugation symmetry, and can be ultimately linked to the existence of 'exceptional points' (EPs) in parameter space, where two quasibound Andreev levels bifurcate into two quasibound Majorana zero modes. After the EP, one of the latter becomes non-decaying as the junction approaches perfect Andreev reflection, thus resulting in a Majorana dark state (MDS) localised at the NS junction. We show that MDSs exhibit the full range of properties associated to conventional closed-system Majorana bound states (zero-energy, self-conjugation, 4π-Josephson effect and non-Abelian braiding statistics), while not requiring topological superconductivity.

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 Ic that contains information about the nontrivial 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 Ic at small junction transparency. This effect allows for a mapping between Ic and the topological phase diagram of the junction, thus providing a dc measurement of its topology.

Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures.

The physics and operating principles of hybrid superconductor-semiconductor devices rest ultimately on the magnetic properties of their elementary subgap excitations, usually called Andreev levels. Here we report a direct measurement of the Zeeman effect on the Andreev levels of a semiconductor quantum dot with large electron g-factor, strongly coupled to a conventional superconductor with a large critical magnetic field. This material combination allows spin degeneracy to be lifted without destroying superconductivity. We show that a spin-split Andreev level crossing the Fermi energy results in a quantum phase transition to a spin-polarized state, which implies a change in the fermionic parity of the system. This crossing manifests itself as a zero-bias conductance anomaly at finite magnetic field with properties that resemble those expected for Majorana modes in a topological superconductor. Although this resemblance is understood without evoking topological superconductivity, the observed parity transitions could be regarded as precursors of Majorana modes in the long-wire limit.

Odd and even Kondo effects from emergent localization in quantum point contacts.

A quantum point contact (QPC) is a basic nanometre-scale electronic device: a short and narrow transport channel between two electron reservoirs. In clean channels, electron transport is ballistic and the conductance is then quantized as a function of channel width with plateaux at integer multiples of 2e(2)/h (where e is the electron charge and h is Planck's constant). This can be understood in a picture where the electron states are propagating waves, without the need to account for electron-electron interactions. Quantized conductance could thus be the signature of ultimate control over nanoscale electron transport. However, even studies with the cleanest QPCs generically show significant anomalies in the quantized conductance traces, and there is consensus that these result from electron many-body effects. Despite extensive experimental and theoretical studies, understanding these anomalies is an open problem. Here we report that the many-body effects have their origin in one or more spontaneously localized states that emerge from Friedel oscillations in the electron charge density within the QPC channel. These localized states will have electron spins associated with them, and the Kondo effect--related to electron transport through such localized electron spins--contributes to the formation of the many-body state. We present evidence for such localization, with Kondo effects of odd or even character, directly reflecting the parity of the number of localized states; the evidence is obtained from experiments with length-tunable QPCs that show a periodic modulation of the many-body properties with Kondo signatures that alternate between odd and even Kondo effects. Our results are of importance for assessing the role of QPCs in more complex hybrid devices and for proposals for spintronic and quantum information applications. In addition, our results show that tunable QPCs offer a versatile platform for investigating many-body effects in nanoscale systems, with the ability to probe such physics at the level of a single site.

Zero-bias anomaly in a nanowire quantum dot coupled to superconductors.

We studied the low-energy states of spin-1/2 quantum dots defined in InAs/InP nanowires and coupled to aluminum superconducting leads. By varying the superconducting gap Δ with a magnetic field B we investigated the transition from strong coupling Δ << T(K) to weak-coupling Δ >> T(K), where T(K) is the Kondo temperature. Below the critical field, we observe a persisting zero-bias Kondo resonance that vanishes only for low B or higher temperatures, leaving the room to more robust subgap structures at bias voltages between Δ and 2Δ. For strong and approximately symmetric tunnel couplings, a Josephson supercurrent is observed in addition to the Kondo peak. We ascribe the coexistence of a Kondo resonance and a superconducting gap to a significant density of intragap quasiparticle states, and the finite-bias subgap structures to tunneling through Shiba states. Our results, supported by numerical calculations, own relevance also in relation to tunnel-spectroscopy experiments aiming at the observation of Majorana fermions in hybrid nanostructures.

ac Josephson effect in finite-length nanowire junctions with Majorana modes.

It has been predicted that superconducting junctions made with topological nanowires hosting Majorana bound states (MBS) exhibit an anomalous 4π-periodic Josephson effect. Finding an experimental setup with these unconventional properties poses, however, a serious challenge: for finite-length wires, the equilibrium supercurrents are always 2π periodic as anticrossings of states with the same fermionic parity are possible. We show, however, that the anomaly survives in the transient regime of the ac Josephson effect. Transients are, moreover, protected against decay by quasiparticle poisoning as a consequence of the quantum Zeno effect, which fixes the parity of Majorana qubits. The resulting long-lived ac Josephson transients may be effectively used to detect MBS.

Josephson current in carbon nanotubes with spin-orbit interaction.

We demonstrate that curvature-induced spin-orbit coupling induces a 0-π transition in the Josephson current through a carbon nanotube quantum dot coupled to superconducting leads. In the noninteracting regime, the transition can be tuned by applying a parallel magnetic field near the critical field where orbital states become degenerate. Moreover, the interplay between charging and spin-orbit effects in the Coulomb blockade and cotunneling regimes leads to a rich phase diagram with well-defined (analytical) boundaries in parameter space. Finally, the 0 phase always prevails in the Kondo regime. Our calculations are relevant in view of recent experimental advances in transport through ultraclean carbon nanotubes.

Josephson current in strongly correlated double quantum dots.

We study the Josephson current through a serial double quantum dot and the associated 0-π transitions which result from the subtle interplay between the superconductivity, the Kondo physics, and the interdot superexchange interaction. The competition between them is examined by tuning the relative strength Δ/T(K) of the superconducting gap and the Kondo temperature, for different strengths of the superexchange coupling determined by the interdot tunneling t relative to the level broadening Γ. We find strong renormalization of t, a significant role of the superexchange coupling J, and a rich phase diagram of the 0 and π-junction regimes. In particular, when both the superconductivity and the exchange interaction compete with the Kondo physics (Δ∼J∼T(K)), there appears an island of π' phase at large values of the superconducting phase difference.

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.

SU(4) Kondo effect in carbon nanotubes.

We investigate theoretically the nonequilibrium transport properties of carbon nanotube quantum dots. Owing to the two-dimensional band structure of graphene, a double orbital degeneracy plays the role of a pseudospin, which is entangled with the spin. Quantum fluctuations between these 4 degrees of freedom result in an SU(4) Kondo effect at low temperatures. This exotic Kondo effect manifests as a four-peak splitting in the nonlinear conductance when an axial magnetic field is applied.

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 in the sequential tunneling regime, 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.

Shot noise spectrum of open dissipative quantum two-level systems.

We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level systems can be extracted from noise. In the strong dissipation regime, the localization-delocalization transition becomes visible in the low-frequency noise.

Nonequilibrium transport through double quantum dots: Kondo effect versus antiferromagnetic coupling.

We theoretically study the nonequilibrium transport properties of double quantum dots, in both series and parallel configurations. Our results lead to novel experimental predictions that unambiguously signal the transition from a Kondo state to an antiferromagnetic spin-singlet state, directly reflecting the physics of the two-impurity Kondo problem. We prove that the nonlinear conductance through parallel dots directly measures the exchange constant J between the spins of the dots. In serial dots, the nonlinear conductance provides an upper bound on J.