Tunneling spectra simulation of interacting Majorana wires

Recent tunneling experiments on InSb hybrid superconductor-semiconductor devices have provided hope for a stabilization of Majorana edge modes in a spin-orbit quantum wire subject to a magnetic field and superconducting proximity effect. Connecting the experimental scenario with a microscopic description poses challenges of a different kind, such as accounting for the effect of interactions on the tunneling properties of the wire. We develop a density matrix renormalization group (DMRG) analysis of the tunneling spectra of interacting Majorana chains, which we explicate for the Kitaev chain model. Our DMRG approach allows us to calculate the spectral function down to zero frequency, where we analyze how the Majorana zero-bias peak is affected by interactions. For topological phase transitions between the topological and trivial superconducting phase in the Majorana wire, the bulk gap closure generically affects the proximity peaks and the Majorana peak.

Scanning Tunneling Microscopy using Superconducting Tips to Probe Absolute Spin Polarization

Matthias Alexander Eltschka

The interplay of superconductivity and magnetism is investigated for systems with dimensions ranging from the mesoscopic to the atomic scale by scanning tunneling microscopy (STM) at millikelvin temperatures and by numerical calculations. Based on geometrically confined superconductors in magnetic fields, a novel STM approach is introduced to quantitatively probe the spin polarization of tunneling electrons. In the first part of this work, the effects of magnetic fields and geometrical confinement are probed for superconducting vanadium STM tips. Due to the unique confinement ranging from the atomic to the mesoscopic scale, the superconducting properties of the STM tips vary considerably from their bulk counterparts. To analyze the experimentally determined magnetic field dependence of several V tips, the superconductivity is numerically calculated for modeled cone geometries with various opening angles. The numerical approach based on a one-dimensional Usadel equation leads to a direct correlation between the opening angle ¿ and the order of the superconducting phase transition. First order phase transitions occur when the opening angle is smaller than a critical value (¿ < ¿c), whilst larger opening angles (¿ > ¿c) result in second order phase transitions. The comparison of experimental findings and numerical results reveals the existence of first and second order quantum phase transitions in the V STM tips. In addition, the numerical calculations also explain experimentally observed broadening effects of the superconducting spectra by the specific tip geometry. In the second part, the superconducting V tips are employed in a novel approach to quantitatively probe the spin polarization of tunneling electrons on the nanoscale. For this purpose, the Meservey-Tedrow-Fulde technique is transferred to STM in order to combine their virtues, such as the quantitative probing capability of the spin polarization, the precise control at the atomic scale and the well-defined vacuum tunnel barrier. To demonstrate the capabilities of the new technique, the local spin structure is resolved for a magnetic Co nanoisland, where spin polarizations ranging from -56% up to 65% were found, depending on the local position. Furthermore, the spin polarization P strongly varies with the tip-to-sample distance z (dP/dz ¿ 10%/Å), which is described by the different decays of the spin-up and spin-down wave functions into the vacuum tunnel barrier. The final part describes the local interaction between isolated magnetic moments and the superconducting ground state. Copper phthalocyanine molecules on the superconducting V(100) surface induce bound states within the superconducting gap due to the magnetic coupling and the Coulomb potentials. Spatially resolved measurements reveal the non-isotropic structure of the spectral weights that is explained by the adsorption site on the 5x1 reconstruction of the V(100) surface. The quasi-particle excitations are not only observed on the magnetic molecule but also occur in its close vicinity. With increasing distance from the molecular structure, the intensities of the bound states decay within the distance x ¿ ±30Å and show periodic oscillations at the same time. Comparing the experimental findings to a one-dimensional model suggests the presence of a complicated scattering potential, which can be simplified by assuming two point scatterers within the molecular structure.

EPFL2015

Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba-Rusinov states

Haonan Huang, Klaus Kern, Jacob Senkpiel

Spin-dependent scattering from magnetic impurities inside a superconductor gives rise to Yu-Shiba-Rusinov (YSR) states within the superconducting gap. They can be modeled by the largely equivalent Kondo or Anderson impurity models. The role of the magnetic and nonmagnetic properties of the impurity in relation to the coupling to the substrate is still under debate. Here, we use a scanning tunneling microscope to make a quantitative connection between the energy of a YSR state and the impurity-substrate hybridization. We corroborate the impurity substrate coupling as a key energy scale for surface derived YSR states using the Anderson impurity model. By combining experimental data from YSR state spectra and additional conductance measurements, we can determine on which side of the quantum phase transition the system resides. We thus provide a crucial step towards a more quantitative understanding of the crucial role of impurity substrate coupling utilizing the Anderson model. The physics of Yu-Shiba-Rusinov states which exist in the superconducting gap are a topical area of research and linked to exotic phenomena such as Majorana fermions. Here, the authors use scanning tunnelling microscopy to investigate the influence of impurities on a superconducting surface and the role impurity-substrate hybridisation has on such states.

NATURE RESEARCH2020

Superconducting scanning tunneling microscopy tips in a magnetic field: Geometry-controlled order of the phase transition

Maximilian Assig, Matthias Alexander Eltschka, Markus Etzkorn, Klaus Kern

The properties of geometrically confined superconductors significantly differ from their bulk counterparts. Here, we demonstrate the geometrical impact for superconducting scanning tunneling microscopy (STM) tips, where the confinement ranges from the atomic to the mesoscopic scale. To this end, we compare the experimentally determined magnetic field dependence for several vanadium tips to microscopic calculations based on the Usadel equation. For our theoretical model of a superconducting cone, we find a direct correlation between the geometry and the order of the superconducting phase transition. Increasing the opening angle of the cone changes the phase transition from first to second order. Comparing our experimental findings to the theory reveals first and second order quantum phase transitions in the vanadium STM tips. In addition, the theory also explains experimentally observed broadening effects by the specific tip geometry. (C) 2015 AIP Publishing LLC.

Amer Inst Physics2015

Scanning Tunneling Microscopy using Superconducting Tips to Probe Absolute Spin Polarization

Matthias Alexander Eltschka

EPFL2015