Belzig, Wolfgang

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## Suchergebnisse Publikationen

#### Full Counting Statistics of Yu-Shiba-Rusinov Bound States

2023-09-11, Ohnmacht, David, Belzig, Wolfgang, Cuevas, Juan Carlos

With the help of scanning tunneling microscopy (STM) it has become possible to address single magnetic impurities on superconducting surfaces and to investigate the peculiar properties of the in-gap states known as Yu-Shiba-Rusinov (YSR) states. However, until very recently YSR states were only investigated with conventional tunneling spectroscopy, missing the crucial information contained in other transport properties such as shot noise. Here, we adapt the concept of full counting statistics (FCS) to provide a very deep insight into the spin-dependent transport in these hybrid systems. We illustrate the power of FCS by analyzing different situations in which YSR states show up including single-impurity junctions, as well as double-impurity systems where one can probe the tunneling between individual YSR states. The FCS concept allows us to unambiguously identify every tunneling process that plays a role in these situations. Moreover, FCS provides all the relevant transport properties, including current, shot noise and all the cumulants of the current distribution. Our approach can reproduce the experimental results recently reported on the shot noise of a single-impurity junction with a normal STM tip. We also predict the signatures of resonant (and non-resonant) multiple Andreev reflections in the shot noise of single-impurity junctions with two superconducting electrodes. In the case of double-impurity junctions we show that the direct tunneling between YSR states is characterized by a strong reduction of the Fano factor that reaches a minimum value of 7/32, a new fundamental result in quantum transport. The FCS approach presented here can be naturally extended to investigate the spin-dependent superconducting transport in a variety of situations, and it is also suitable to analyze multi-terminal superconducting junctions, irradiated contacts, and many other basic situations.

#### Demonstration of nonlocal Josephson effect in Andreev molecules

2023-06-01, Haxell, Daniel Z., Coraiola, Marco, Hinderling, Manuel, ten Kate, Sofieke C., Sabonis, Deividas, Svetogorov, A. E., Belzig, Wolfgang, Cheah, Erik, Krizek, Filip, Schott, Rüdiger, Wegscheider, Werner, Nichele, Fabrizio

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode, with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current--phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates a nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift was larger for shorter distances between the JJs and vanished for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of ABSs, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source, and could enable new coupling schemes for hybrid quantum devices.

#### Magnon squeezing in conical spin spirals

2023-04-13, Wuhrer, Dennis, Rózsa, Levente, Nowak, Ulrich, Belzig, Wolfgang

We investigate squeezing of magnons in a conical spin spiral configuration. We find that while the energy of magnons propagating along the k and the −k directions can be different due to the non-reciprocal dispersion, these two modes are connected by the squeezing, hence can be described by the same squeezing parameter. The squeezing parameter diverges at the center of the Brillouin zone due to the translational Goldstone mode of the system, but the squeezing also vanishes for certain wave vectors. We discuss possible ways of detecting the squeezing.

#### Optimized proximity thermometer for ultrasensitive detection : Role of an ohmic electromagnetic environment

2023-03-10, Nikolić, Danilo, Karimi, Bayan, Rengel, Diego Subero, Pekola, Jukka P., Belzig, Wolfgang

We propose a mesoscopic thermometer for ultrasensitive detection based on the proximity effect in superconductor (S)-normal-metal (N) heterostructures. The device is based on the zero-bias anomaly (ZBA) due to the inelastic Cooper pair tunneling in an SNIS junction (I stands for an insulator) coupled to an ohmic electromagnetic (EM) environment. The theoretical model is done in the framework of the quasiclassical Usadel Green's formalism and the dynamical Coulomb blockade. The usage of an ohmic EM environment makes the thermometer highly sensitive and not saturating down to very low temperatures, T≲5 mK. Moreover, defined in this way, the thermometer is stable against small but non-vanishing voltage amplitudes typically used for measuring the zero-bias differential conductance in experiments. Finally, we proposed a simplified view, based on an analytic treatment, which is in very good agreement with numerical results and can serve as a tool for the development, calibration, and optimization of such devices in future experiments in quantum calorimetry.

#### DC Josephson effect between two Yu-Shiba-Rusinov bound states

2023-08-03, Chakraborty, Subrata, Nikolić, Danilo, Souto, Rubén Seoane, Belzig, Wolfgang, Cuevas, Juan Carlos

Motivated by recent experiments [Nat. Phys. 16, 1227 (2020)] we present here a theoretical study of the dc Josephson effect in a system comprising two magnetic impurities coupled to their respective superconducting electrodes and that exhibit Yu-Shiba-Rusinov (YSR) states. We make use of a mean-field Anderson model with broken spin symmetry to compute the supercurrent in this system for arbitrary range of parameters (coupling between the impurities, orientation of the impurity spins, etc.). We predict a variety of physical phenomena such as: (i) the occurrence of multiple 0-π transitions in the regime of weak coupling that can be induced by changing the energy of the YSR states or the temperature, (ii) the critical current strongly depends on the relative orientation of the impurity spins and it is maximized when the spins are either parallel or antiparallel, depending on the ground state of the impurities, and (iii) upon increasing the coupling between impurities, triplet superconductivity is generated in the system and it is manifested in a highly non-sinusoidal current-phase relation. In principle, these predictions can be tested experimentally with the existing realization of this system and the main lessons of this Letter are of great relevance for the field of superconducting spintronics.

#### Andreev and normal reflections in gapped bilayer graphene-superconductor junctions

2023-06-01, Ram, Panch, Beckmann, Detlef, Danneau, Romain, Belzig, Wolfgang

We study the Andreev and normal reflection processes -- retro as well as specular -- in a bilayer graphene-superconductor junction where equal and opposite displacement fields are applied for the top and bottom layers to induce a band gap. By employing the Dirac-Bogoliubov-de Gennes equation for the gapped bilayer graphene-superconductor junction, we calculate the reflections probabilities within the scattering theory approach. The subgap conductance, calculated in the framework of Blonder-Tinkham-Klapwijk formalism, shows the contribution from the Andreev retro-reflection (specular-reflection) when the applied bias voltage is below (above) the Fermi energy. Notably, both retro and specular reflections are modified in the presence of the displacement field, and the retro-to-specular crossover gets amplified when the displacement field is relatively small. They can be further tuned to either specular or retro Andreev reflection by adjusting the Fermi energy. Furthermore, our study reveals the simultaneous existence of double Andreev reflections and double normal reflections when the displacement field becomes comparable to the interlayer coupling strength. The existence of the normal retro-reflection process in a bilayer graphene-superconductor junction is a new finding which shows a distinctive feature in the conductance that can be experimentally verified.

#### Full counting statistics of ultrafast quantum transport

2023-03-28, Hübler, Matthias, Belzig, Wolfgang

Quantum transport in the presence of time-dependent drives is dominated by quantum interference and many-body effects at low temperatures. For a periodic driving, the analysis of the full counting statistics revealed the elementary events that determine the statistical properties of the charge transport. As a result, the noise correlations display quantum oscillation as functions of the ratio of the voltage amplitude and the drive frequency reflecting the detailed shape of the drive. However, so far only continuous wave excitations were considered, but recently transport by few-cycle light pulses were investigated and the need for a statistical interpretation became eminent. We address the charge transfer generated by single- or few-cycle light pulses. The fingerprints of these time-dependent voltage pulses are imprinted in the full counting statistics of a coherent mesoscopic conductor at zero temperature. In addition, we identify the elementary processes that occur in the form of electron-hole pair creations, which can be investigated by the excess noise. We study the quantum oscillations in the differential noise induced by a wave packet consisting of an oscillating carrier modulated by a Gaussian- or a box-shaped envelope. As expected, the differential noise exhibits an oscillatory behavior with increasing amplitude. In particular, we find clear signature of the so-called carrier-envelope phase in the peak heights and positions of these quantum oscillations. More carrier cycles under the Gaussian envelope diminish the influence of the carrier-envelope phase, while this is not true for the box pulses, probably related to the abrupt onset. As the quantum oscillations are due to the energy-time uncertainty of the short pulses, our results pave the way to a description of the nonequilibrium electron transport in terms of a many-body Wigner function of the electronic system.

#### Experimental detectability of spin current shot noise

2023-07-12, Siegl, Luise, Lammel, Michaela, Kamra, Akashdeep, Huebl, Hans, Belzig, Wolfgang, Gönnenwein, Sebastian T. B.

A magnonic spin current crossing a ferromagnet-metal interface is accompanied by spin current shot noise arising from the discrete quanta of spin carried by magnons. In thin films, e.g., the spin of so-called squeezed magnons have been shown to deviate from the common value ℏ, with corresponding changes in the spin noise. In experiments, spin currents are typically converted to charge currents via the inverse spin Hall effect. We here analyze the magnitude of the spin current shot noise in the charge channel for a typical electrically detected spin pumping experiment, and find that the voltage noise originating from the spin current shot noise is much smaller than the inevitable Johnson-Nyquist noise. Furthermore, due to the local nature of the spin-charge conversion, the ratio between spin current shot noise and Johnson-Nyquist noise does not scale with sample geometry and sensitively depends on material-specific transport properties. Our analysis thus provides guidance for the experimental detection of squeezed magnons through spin pumping shot noise.

#### Generation of long-ranged spin-triplet pairs across a two-dimensional superconductor/helimagnet van der Waals interface

2023-05-03, Spuri, Alfredo, Nikolić, Danilo, Chakraborty, Subrata, Klang, Maya, Alpern, Hen, Millo, Oded, Steinberg, Hadar, Belzig, Wolfgang, Scheer, Elke, Di Bernardo, Angelo

The combination of a superconductor with a magnetically inhomogeneous material has been established as an efficient mechanism for the generation of long-ranged spin-polarized (spin-triplet) Cooper pairs. Evidence for this mechanism, however, has been established based on studies done on three-dimensional systems, where the strong bonds existing at the interface between the superconductor and the magnetic material should in principle enhance proximity effects and strengthen any electronic correlations. Here, we fabricate devices based on van der Waals stacks of flakes of the two-dimensional superconductor NbS2 combined with flakes of Cr1/3NbS2, which has a built-in magnetic inhomogeneity due to its helimagnetic spin texture at low temperatures. We find that the critical temperature of these vdW bilayers is strongly dependent on the magnetic state of Cr1/3NbS2, whose degree of magnetic inhomogeneity can be controlled via an applied magnetic field. Our results demonstrate evidence for the generation of long-ranged spin-triplet pairs across the Cr1/3NbS2/NbS2 vdW interface.

#### Microscopic theory of supercurrent suppression by gate-controlled surface depairing

2023-03-14, Chakraborty, Subrata, Nikolić, Danilo, Cuevas, Juan Carlos, Giazotto, Francesco, Di Bernardo, Angelo, Scheer, Elke, Cuoco, Mario, Belzig, Wolfgang

Recently gate-mediated supercurrent suppression in superconducting nano-bridges has been reported in many experiments. This could be either a direct or an indirect gate effect. The microscopic understanding of this observation is not clear till now. Using the quasiclassical Green's function method, we show that a small concentration of magnetic impurities at the surface of the bridges can significantly help to suppress superconductivity and hence the supercurrent inside the systems while applying a gate field. This is because the gate field can enhance the depairing through the exchange interaction between the magnetic impurities at the surface and the superconductor. We also obtain a \emph{symmetric} suppression of the supercurrent with respect to the gate field, a signature of a direct gate effect. Future experiments can verify our predictions by modifying the surface with magnetic impurities.