Dr.jens.brede

Zero-energy modes localized at the ends of one-dimensional (1D) wires hold great potential as qubits for fault-tolerant quantum computing. However, all the candidates known to date exhibit a wave function that decays exponentially into the bulk and hybridizes with other nearby zero-modes, thus hampering their use for braiding operations. Here, we show that a quasi-1D diamond-necklace chain exhibits a completely unforeseen type of robust boundary state, namely compact localized zero-energy modes that do not decay into the bulk. We theoretically engineer a lattice geometry to access this mode, and experimentally realize it in an electronic quantum simulator setup. Our work provides a general route for the realization of robust and compact localized zero-energy modes that could potentially be braided without the drawbacks of hybridization.

Author(s): Damaz de Jong, Christian G. Prosko, Lin Han, Filip K. Malinowski, Yu Liu, Leo P. Kouwenhoven, and Wolfgang Pfaff

A superconducting island with quantum dots on either side allows for coherent splitting of a single Cooper pair and detection of an emerging unpaired electron.

[Phys. Rev. Lett. 131, 157001] Published Thu Oct 12, 2023

Topological insulator/superconductor two-dimensional heterostructures are promising candidates for realizing topological superconductivity and Majorana modes. In these systems, a vortex pinned by a pre-fabricated antidot in the superconductor can host Majorana zero-energy modes (MZMs), which are exotic quasiparticles that may enable quantum information processing. However, a major challenge is to design devices that can manipulate the information encoded in these MZMs. One of the key factors is to create small and clean antidots, so that the MZMs, localized in the vortex core, have a large gap to other excitations. If the antidot is too large or too disordered, the level spacing for the subgap vortex states may become smaller than temperature. In this paper, we numerically investigate the effects of disorder, chemical potential, and antidot size on the subgap vortex spectrum, using a two-dimensional effective model of the topological insulator surface. Our model allows us to simulate large system sizes with vortices up to 1.8 $\mu$m in diameter. We also compare our disorder model with the transport data from existing experiments. We find that the spectral gap can exhibit a non-monotonic behavior as a function of disorder strength, and that it can be tuned by applying a gate voltage.

We describe a transducer for low-temperature atomic force microscopy, based on electromechanical coupling due to a strain-dependent kinetic inductance of a superconducting nanowire. The force sensor is a bending triangular plate (cantilever) whose deflection is measured via a shift in resonant frequency of a high Q superconducting microwave resonator at 4.5 GHz. We present design simulations including mechanical finite-element modeling of surface strain and electromagnetic simulations of meandering nanowires with large kinetic inductance. We discuss a lumped-element model of the force sensor and describe the role of an additional shunt inductance for optimal coupling to the transmission line used for the measurement of the microwave resonance. A step-by-step description of our fabrication is presented, including information about the process parameters used for each layer. We also discuss the fabrication of sharp tips on the cantilever using focused electron beam-induced deposition of platinum. Finally, we present measurements that characterize the spread of mechanical resonant frequency, temperature dependence of the microwave resonance, and the sensor's operation as an electromechanical transducer of force.

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.

Identifying intrinsic noncollinear magnetic order in monolayer van der Waals (vdW) crystals is highly desirable for understanding the delicate magnetic interactions at reduced spatial constraints and miniaturized spintronic applications, but remains elusive in experiments. Here, we achieved spin-resolved imaging of helimagnetism at atomic scale in monolayer NiI2 crystals, that were grown on graphene-covered SiC(0001) substrate, using spin-polarized scanning tunneling microscopy. Our experiments identify the existence of a spin spiral state with canted plane in monolayer NiI2. The spin modulation Q vector of the spin spiral is determined as (0.2203, 0, 0), which is different from its bulk value or its in-plane projection, but agrees well with our first principles calculations. The spin spiral surprisingly indicates collective spin switching behavior under magnetic field, whose origin is ascribed to the incommensurability between the spin spiral and the crystal lattice. Our work unambiguously identifies the helimagnetic state in monolayer NiI2, paving the way for illuminating its expected type-II multiferroic order and developing spintronic devices based on vdW magnets.

We consider phase-biased Josephson junctions with spin-orbit coupling under external magnetic fields and study the emergence of the Josephson diode effect in the presence of Majorana bound states. We show that junctions having middle regions with Zeeman fields along the spin-orbit axis develop a low-energy Andreev spectrum that is asymmetric with respect to the superconducting phase difference $\phi=\pi$, which is strongly influenced by Majorana bound states in the topological phase. This asymmetric Andreev spectrum gives rise to anomalous current-phase curves and critical currents that are different for positive and negative supercurrents, thus signaling the emergence of the Josephson diode effect. While this effect exists even without Majorana states, it gets enhanced in the topological phase as Majorana bound states become truly zero modes. Our work thus establishes the utilization of topological superconductivity for enhancing the functionalities of Josephson diodes.

Nature Physics, Published online: 25 September 2023; doi:10.1038/s41567-023-02209-x

Observation of a faint Fermi surface inside the pseudogap of an electron-doped cuprate suggests that Cooper pairing is mediated by antiferromagnetic spin fluctuations.

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report the observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Neel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.

Disorder is the primary obstacle in current Majorana nanowire experiments. Reducing disorder or achieving ballistic transport is thus of paramount importance. In clean and ballistic nanowire devices, quantized conductance is expected with plateau quality serving as a benchmark for disorder assessment. Here, we introduce ballistic PbTe nanowire devices grown using the selective-area-growth (SAG) technique. Quantized conductance plateaus in units of $2e^2/h$ are observed at zero magnetic field. This observation represents an advancement in diminishing disorder within SAG nanowires, as none of the previously studied SAG nanowires (InSb or InAs) exhibit zero-field ballistic transport. Notably, the plateau values indicate that the ubiquitous valley degeneracy in PbTe is lifted in nanowire devices. This degeneracy lifting addresses an additional concern in the pursuit of Majorana realization. Moreover, these ballistic PbTe nanowires may enable the search for clean signatures of the spin-orbit helical gap in future devices.

Author(s): Vladislav D. Kurilovich and Leonid I. Glazman

A new theory of quantum Hall edge states coupled via a thin, disordered superconductor reveals an unusual state that is not, as previously suggested, a topological superconductor.

[Phys. Rev. X 13, 031027] Published Tue Sep 12, 2023

Author(s): Attila Szilva, Yaroslav Kvashnin, Evgeny A. Stepanov, Lars Nordström, Olle Eriksson, Alexander I. Lichtenstein, and Mikhail I. Katsnelson

Magnetic moments in solids become useful and interesting due to the interatomic exchange that causes them to align. Developments in calculations of the electronic structure of solids have led to the ability to predictively compute these interactions in many materials. This review describes the development of these calculations and their application in describing the behavior of materials including technologically important hard and soft magnetic materials, novel two-dimensional magnets, elemental solids, alloys, antiferromagnets, noncollinear magnets, and magnetic molecules containing hundreds of atoms.

[Rev. Mod. Phys. 95, 035004] Published Mon Sep 11, 2023

Nature Communications, Published online: 09 September 2023; doi:10.1038/s41467-023-40784-y

Magnetization reversal in magnetic topological insulators drives quantum phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Using novel analysis protocol, the authors investigate critical behaviours of these transitions and establish their electronic origin.

Author(s): Y. del Castillo and J. Fernández-Rossier

We propose a protocol to certify the presence of entanglement in artificial on-surface atomic and molecular spin arrays using electron spin resonance carried by scanning tunnel microscopy (ESR-STM). We first generalize the theorem that relates global spin susceptibility as an entanglement witness to…

[Phys. Rev. B 108, 115413] Published Thu Sep 07, 2023

The present study investigates the behavior of the Cooper pair wave function in a normal metal (NM) near superconductor-NM-junctions, specifically focusing on the ballistic regime at zero temperature. It is widely assumed that the wave function follows a power-law decay, with the decay exponents dependent on the system’s dimensionality. Our work reveals that the multiband nature of a compound significantly influences the damping degree of pair amplitudes in an NM, rendering it sensitive to the position of the Fermi level. To explore this phenomenon, we employ the numerical method of self-consistent Bogoliubov–de Gennes equations, utilizing a nanowire as a model for an electronic multiband system. By analyzing the obtained pair amplitudes, we extract relevant lengths and exponents that characterize the leakage of superconducting correlations. We further examine this phenomenon by varying the sample’s cross-sectional size and the superconducting coupling constant. Consequently, our findings demonstrate that the properties of a superconducting/NM junction’s proximity effect can be manipulated not only through temperature, total impurity and defect density, but also by controlling the position of the Fermi level. This tunability enables the transition from a long-range regime to a short-range one, providing valuable insights for designing and understanding such junctions in practical applications.

Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi$_2$Se$_3$ were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional $\boldsymbol{k} \boldsymbol{\cdot} \boldsymbol{p}$ model, it physically describes the top and bottom electronic surface states that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk bands closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the $\mathbb{Z}_{2}$ invariant in thin films of varying thickness. Moreover, we demonstrate that the topological properties of thin Bi$_2$Se$_3$ nanosheets emerge as a result of an intricate interplay between the surface and bulk states, which in fact results in nontrivial Chern numbers for the latter.

Altermagnets (AM) are a recently discovered third class of collinear magnets, distinctly different from conventional ferromagnets (FM) and antiferromagnets (AF). AM have been actively researched in the last few years, but two aspects so far remain unaddressed: (1) Are there realistic 2D single-layer altermagnets? And (2) is it possible to functionalize a conventional AF into AM by external stimuli? In this paper we address both issues by demonstrating how a well-known 2D AF, MnP(S,Se)$_3$ can be functionalized into strong AM by applying out-of-plane electric field. Of particular interest is that the induced altermagnetism is of a higher even-parity wave symmetry than expected in 3D AM with similar crystal symmetries. We confirm our finding by first-principles calculations of the electronic structure and magnetooptical response. We also propose that recent observations of the time-reversal symmetry breaking in the famous Fe-based superconducting chalchogenides, either in monolayer form or in the surface layer, may be related not to an FM, as previously assumed, but to the induced 2D AM order. Finally, we show that monolayer FeSe can simultaneously exhibit unconventional altermagnetic time-reversal symmetry breaking and quantized spin Hall conductivity indicating possibility to research an intriquing interplay of 2D altermagnetism with topological and superconducting states within a common crystal-potential environment.

A pivotal challenge in quantum technologies lies in reconciling long coherence times with efficient manipulation of the quantum states of a system. Lanthanide atoms, with their well-localized 4f electrons, emerge as a promising solution to this dilemma if provided with a rational design for manipulation and detection. Here we construct tailored spin structures to perform electron spin resonance on a single lanthanide atom using a scanning tunneling microscope. A magnetically coupled structure made of an erbium and a titanium atom enables us to both drive the erbium's 4f electron spins and indirectly probe them through the titanium's 3d electrons. In this coupled configuration, the erbium spin states exhibit a five-fold increase in the spin relaxation time and a two-fold increase in the driving efficiency compared to the 3d electron counterparts. Our work provides a new approach to accessing highly protected spin states, enabling their coherent control in an all-electric fashion.

Nature Communications, Published online: 31 August 2023; doi:10.1038/s41467-023-40931-5

The nature of the pairing symmetry in superconducting single-layer FeSe has been the subject of intense debate. Here, the authors use scanning tunneling microscopy/spectroscopy to show the absence of topological edge/corner modes, providing evidence for sign-preserving s-wave pairing.

Author(s): Eric I. Rosenthal, Christopher P. Anderson, Hannah C. Kleidermacher, Abigail J. Stein, Hope Lee, Jakob Grzesik, Giovanni Scuri, Alison E. Rugar, Daniel Riedel, Shahriar Aghaeimeibodi, Geun Ho Ahn, Kasper Van Gasse, and Jelena Vučković

Use of strain on a tin-vacancy defect in diamond allows for magnetic-field interactions that in turn enable microwave control over its spin, a key step for using such defects to encode quantum information.

[Phys. Rev. X 13, 031022] Published Wed Aug 30, 2023

Author(s): Bo Lu, Satoshi Ikegaya, Pablo Burset, Yukio Tanaka, and Naoto Nagaosa

The Josephson rectification effect, where the resistance is finite in one direction while zero in the other, has been recently realized experimentally. The resulting Josephson diode has many potential applications on superconducting devices, including quantum computers. Here, we theoretically show t…

[Phys. Rev. Lett. 131, 096001] Published Tue Aug 29, 2023

We propose a novel architecture that utilizes two 0-$\pi$ qubits based on topological Josephson junctions to implement a parity-protected superconducting qubit. The topological Josephson junctions provides protection against fabrication variations, which ensures the identical Josephson junctions required to implement the0-$\pi$ qubit. By viewing the even and odd parity ground states of a 0-$\pi$ qubit as spin-$\frac{1}{2}$ states, we construct the logic qubit states using the total parity odd subspace of two 0-$\pi$ qubits. This parity-protected qubit exhibits robustness against charge noise, similar to a singlet-triplet qubit's immunity to global magnetic field fluctuations. Meanwhile, the flux noise cannot directly couple two states with the same total parity and therefore is greatly suppressed. Benefiting from the simultaneous protection from both charge and flux noise, we demonstrate a dramatic enhancement of both $T_1$ and $T_2$ coherence times. Our work presents a new approach to engineer symmetry-protected superconducting qubits.

Author(s): Robert Drost, Shawulienu Kezilebieke, Jose L. Lado, and Peter Liljeroth

A minimal quantum magnet with triplon excitations has been engineered using molecular building blocks in the singlet ground state.

[Phys. Rev. Lett. 131, 086701] Published Tue Aug 22, 2023

To enable the practical use of skyrmion-based devices, it is essential to achieve a balance between energy efficiency and thermal stability, while also ensuring reliable electrical detection against noise. Understanding how a skyrmion interacts with material disorder and external perturbations is thus essential. Here we investigate the electronic noise of a single skyrmion under the influence of thermal fluctuations and spin currents in a magnetic thin film. We detect the thermally induced noise with a 1/f signature in the strong pinning regime but a random telegraph noise in the intermediate pinning regime. Both the thermally dominated and current-induced telegraph-like signals are detected in the weak pinning regime. Our results provide a comprehensive electronic noise picture of a single skyrmion, demonstrating the potential of noise fluctuation as a valuable tool for characterizing the pinning condition of a skyrmion. These insights could also aid in the development of low-noise and reliable skyrmion-based devices.

The study of the electromagnetic properties of 2D materials is an area of intensive research. Most of the efforts in the subject have been oriented towards the understanding and modelling of the microscopic behaviour of the charge carriers within the medium. Albeit there is a well established manner to express London's equations in the language of differential geometry, an effective geometric theory of the macroscopic phenomenon is still lacking. In this work we concentrate in obtaining the underlying geometric structure of superconductivity in two dimensional materials. To this effect, we produce an intrinsic framework which allows us to clearly identify the geometric assumptions leading to London's equations and the Meissner state. Specifically, we show that any two-dimensional medium whose response to an externally applied electromagnetic field results in a divergence free geodesically flowing induced current must be a superconductor. In this manner, we conclude that the underlying geometry of this type of media is that of a three dimensional Lorentzian contact manifold. Moreover, we show that the geometric condition macroscopically encoding the superconducting phenomena emerges from a variational principle, exhibiting that the macroscopic hallmark of superconductivity is expressed as the non-vanishing of the induced current's helicity.

Nature, Published online: 16 August 2023; doi:10.1038/s41586-023-06312-0

Proximity-induced superconductivity on a single spin-degenerate quantum level of a surface state confined in a quantum corral on a superconducting substrate built atom by atom by a scanning tunnelling microscope is investigated.

Author(s): Jabir Ali Ouassou, Arne Brataas, and Jacob Linder

The ability of magnetic materials to modify superconductors is an active research area for possible applications in thermoelectricity, quantum sensing, and spintronics. We consider the fundamental properties of the Josephson effect in a class of magnetic materials that recently have attracted much a…

[Phys. Rev. Lett. 131, 076003] Published Thu Aug 17, 2023

Strong interaction among electrons in two-dimensional systems in the presence of high magnetic fields gives rise to fractional quantum Hall (FQH) states that host quasi-particles with fractional charge and statistics. We perform high-resolution scanning tunneling microscopy and spectroscopy of FQH states in ultra-clean Bernal-stacked bilayer graphene (BLG) devices. Our experiments show that the formation of FQH states coincides with the appearance of sharp excitations in tunneling experiments that have been predicted to occur for electron fractionalizing into bound states of quasi-particles. From these measurements and their comparison to theoretical calculations, we find large local energy gaps that protect quasi-particles of FQH states predicted to host non-abelian anyons, making BLG an ideal setting for the exploration of these novel quasi-particles. STM studies not only provide a way to characterize the bulk properties of FQH states in the absence of disorder but also reveal previous undiscovered states in such ultra-clean samples.

Nature Communications, Published online: 12 August 2023; doi:10.1038/s41467-023-40551-z

By coupling two quantum dots via a superconductor-semiconductor hybrid region in a 2D electron gas, the authors achieve efficient splitting of Cooper pairs. Further, by applying a magnetic field perpendicular to the spin-orbit field, they can induce and measure large triplet correlations in the Cooper pair splitting process.

Anyonic Fabry-P\'erot and Mach-Zehnder interferometers have been proposed theoretically and implemented experimentally as tools to probe electric charges and statistics of anyons. The experimentally observed visibility of Aharonov-Bohm oscillations is maximal at a high transmission through an interferometer but simple theoretical expressions for the electric currents and noises are only available at low visibility. We consider an alternative version of a Mach-Zehnder interferometer, in which anyons tunnel between co-propagating chiral channels on the edges of quantum Hall liquids at the filling factors $n/(2n+1)$. We find simple exact solutions for any transmission. The solutions allow a straight-forward interpretation in terms of fractional charges and statistics.