Belzig, Wolfgang

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## Suchergebnisse Publikationen

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

2023-11-14, 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 reflection 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 finding which shows a distinctive feature in the conductance that can be experimentally verified.

#### Dynamical renormalisation of a spin Hamiltonian via high-order nonlinear magnonics

2023-10-30, Schönfeld, Christoph, Feuerer, Lennart, Wuhrer, Dennis, Belzig, Wolfgang, Leitenstorfer, Alfred, Juraschek, Dominik, Bossini, Davide

The macroscopic magnetic order in the ground state of solids is determined by the spin-dependent Hamiltonian of the system. In the absence of external magnetic fields, this Hamiltonian contains the exchange interaction, which is of electrostatic origin, and the spin-orbit coupling, whose magnitude depends on the atomic charge. Spin-wave theory provides a representation of the entire spectrum of collective magnetic excitations, called magnons, assuming the interactions to be constant and the number of magnons in the system negligible. However, the electric field component of light is able to perturb electrostatic interactions, charge distributions and, at the same time, can create a magnon population. A fundamental open question therefore concerns the possibility to optically renormalise the spin Hamiltonian. Here, we test this hypothesis by using femtosecond laser pulses to resonantly pump electric-dipole-active pairs of high-energy magnons near the edges of the Brillouin zone. The transient spin dynamics reveals the activation and a surprising amplification of coherent low-energy zone-centre magnons, which are not directly driven. Strikingly, the spectrum of these low-energy magnons differs from the one observed in thermal equilibrium, the latter being consistent with spin-wave theory. The light-spin interaction thus results in a room-temperature renormalisation of the magnetic Hamiltonian, with an estimated modification of the magnetic interactions by 10% of their ground-state values. We rationalise the observation in terms of a novel resonant scattering mechanism, in which zone-edge magnons couple nonlinearly to the zone-centre modes. In a quantum mechanical model, we analytically derive the corrections to the spectrum due to the photo-induced magnon population, which are consistent with our experiments. Our results present a milestone for an all-optical engineering of Hamiltonians.

#### Electrical detectability of magnon-mediated spin current shot noise

2023-10-18, Siegl, Luise, Lammel, Michaela, Kamra, Akashdeep, Hueble, 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, for example, the spin of so-called squeezed magnons has 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, we find that due to the local nature of the spin-charge conversion, the ratio of spin current shot noise and Johnson-Nyquist noise cannot be systematically enhanced by tuning the sample geometry, in contrast to the linear increase in dc spin pumping voltage with sample length. Instead, the ratio depends sensitively on material-specific transport properties. Our analysis thus provides guidance for the experimental detection of squeezed magnons through spin pumping shot noise.

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

2023-07-14, 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–normal metal (SN) heterostructures. The device is based on the zero-bias anomaly 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 down to very low temperatures, T≲5 mK. Moreover, defined in this way, the thermometer is stable against small but nonvanishing voltage amplitudes typically used for measuring the zero-bias differential conductance in experiments. Finally, we propose 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.

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

2023-11-13, 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.

#### Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet—Andreev states

2023-10-26, Haxell, Daniel Z., Coraiola, Marco, Sabonis, Deividas, Hinderling, Manuel, ten Kate, Sofieke C., Cheah, Erik, Krizek, Filip, Schott, Rüdiger, Wegscheider, Werner, Belzig, Wolfgang, Cuevas, Juan Carlos, Nichele, Fabrizio

Light–matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting–semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current–phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current–phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet–Andreev states, our study rules out this scenario. The distortion of the current–phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light–matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet–Andreev states in mesoscopic devices.

#### Fractional transconductance via nonadiabatic topological Cooper pair pumping

2023-10-16, Weisbrich, Hannes, Klees, Raffael L., Zilberberg, Oded, Belzig, Wolfgang

Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate quantized Hall conductances, associated with topology both in the single particle and the strongly correlated many-body limit. Interestingly, the topology of the integer effect can be realized in superconducting multiterminal systems, but a proposal for the more complex fractional counterpart is lacking. In this work, we theoretically demonstrate how to achieve fractional quantized transconductance in an engineered chain of Josephson junctions. Crucially, similar to the stabilization of the conductance plateaus in Hall systems by disorder, we obtain stable transconductance plateaus as a result of nonadiabatic Landau-Zener transitions. We furthermore show that the fractional plateaus are robust to disorder and study the optimal operation regime to observe these effects. Our proposal paves the way for quantum simulation of exotic many-body out-of-equilibrium states in Josephson junction systems.

#### Magnon squeezing in conical spin spirals

2023-11-06, 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.

#### Phase-engineering the Andreev band structure of a three-terminal Josephson junction

2023-10-25, Coraiola, Marco, Haxell, Daniel Z., Sabonis, Deividas, Weisbrich, Hannes, Svetogorov, Aleksandr, Hinderling, Manuel, ten Kate, Sofieke C., Cheah, Erik, Krizek, Filip, Schott, Rüdiger, Wegscheider, Werner, Cuevas, Juan Carlos, Belzig, Wolfgang, Nichele, Fabrizio

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

#### 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.