Transport spectroscopy on trapped superconducting nano-islands of Pb: signature of unconventional pairing

Elemental bulk lead (Pb) is a conventional type I, spin-singlet (s-wave) superconductor with a critical temperature T c = 7.2 K and a critical magnetic field H c = 800 Oe. However, it is known that at mesoscopic length scales, like in point-contact geometries, Pb shows significantly higher critical field, sometimes up to several Tesla. We have used this property to trap a small superconducting nano-droplet of Pb by forming a metallic point contact on Pb and then applying a magnetic field larger than 800 Oe that drives the bulk of the material non-superconducting. From systematic magnetic field dependent behaviour of the point-contact spectra measured across such a trapped island of Pb we show that the superconducting order parameter of mesoscopic Pb mixes non-trivially with magnetic field possibly due to the emergence of a local spin-triplet component at such length scales. From comparative studies with Nb-based point contacts we surmise that the strong spin-orbit coupling in Pb leads to the emergence of the unconventional component in the order parameter of mesoscopic Pb.

Single layer lead iodide: computational exploration of structural, electronic and optical properties, strain induced band modulation and the role of spin-orbital-coupling

Graphitic like layered materials exhibit intriguing electronic structures and thus the search for new types of two-dimensional (2D) monolayer materials is of great interest for developing novel nano-devices. By using density functional theory (DFT) method, here we for the first time investigate the structure, stability, electronic and optical properties of monolayer lead iodide (PbI2). The stability of PbI2 monolayer is first confirmed by phonon dispersion calculation. Compared to the calculation using generalized gradient approximation, screened hybrid functional and spin-orbit coupling effects can not only predicts an accurate bandgap (2.63 eV), but also the correct position of valence and conduction band edges. The biaxial strain can tune its bandgap size in a wide range from 1 eV to 3 eV, which can be understood by the strain induced uniformly change of electric field between Pb and I atomic layer. The calculated imaginary part of the dielectric function of 2D graphene/PbI2 van der Waals type hetero-structure shows significant red shift of absorption edge compared to that of a pure monolayer PbI2. Our findings highlight a new interesting 2D material with potential applications in nanoelectronics and optoelectronics.

Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy

The type I superconductor lead (Pb) has been theoretically predicted to be a two-band superconductor. We use scanning tunneling spectroscopy (STS) to resolve two superconducting gaps with an energy difference of 150  μeV. Tunneling into Pb(111), Pb(110), and Pb(100) crystals reveals a strong dependence of the two coherence peak intensities on the crystal orientation. We show that this is the result of a selective tunneling into the two bands at the energy of the two coherence peaks. This is further sustained by the observation of signatures of the Fermi sheets in differential conductance maps around subsurface defects. A modification of the density of states of the two bands by adatoms on the surface confirms the different orbital character of each of the two subbands.

Imaging the electron-phonon interaction at the atomic scale

Thin Pb films epitaxially grown on 7×7 reconstructed Si(111) represent an ideal model system for studying the electron-phonon interaction at the metal-insulator interface. For this system, using a combination of scanning tunneling microscopy and inelastic electron tunneling spectroscopy, we performed direct real-space imaging of the electron-phonon coupling parameter. We found that λ increases when the electron scattering at the Pb/Si(111) interface is diffuse and decreases when the electron scattering is specular. We show that the effect is driven by transverse redistribution of the electron density inside a quantum well.

Interface effects on the quantum well states of Pb thin films

Using scanning tunneling spectroscopy, we have studied the interface effect on quantum well states of Pb thin films grown on various metal-terminated (Pb, Ag, and Au) n-type Si(111) surfaces and on two different p-type Si(111) surfaces. The dispersion relation E(k) of the electrons of the Pb film and the phase shift at the substrate interface were determined by applying the quantization rule to the measured energy positions of the quantum well states. Characteristic features in the phase shift versus energy curves were identified and were correlated to the directional conduction band of the silicon substrate and to the Schottky barrier formed between the metal film and the semiconductor. A model involving the band structure of the substrate, the Schottky barrier, and the effective thickness of the interface was introduced to qualitatively but comprehensively explain all the observed features of the phase shift at the substrate interface. Our physical understanding of the phase shift is critically important for using interface modification to control the quantum well states.

Relativity and the lead-acid battery

The energies of the solid reactants in the lead-acid battery are calculated ab initio using two different basis sets at nonrelativistic, scalar-relativistic, and fully relativistic levels, and using several exchange-correlation potentials. The average calculated standard voltage is 2.13 V, compared with the experimental value of 2.11 V. All calculations agree in that 1.7-1.8 V of this standard voltage arise from relativistic effects, mainly from PbO2 but also from PbSO4.

Band structure and oscillatory electron-phonon coupling of Pb thin films determined by atomic-layer-resolved quantum-well states

Using a low temperature growth method, we have prepared atomically flat Pb thin films over a wide range of film thickness on a Si-(111)-7 x 7 surface. The Pb film morphology and electronic structure are investigated in situ by scanning tunneling microscopy and angle-resolved photoemission spectroscopy. Well-defined and atomic-layer-resolved quantum-well states of the Pb films are used to determine the band structure and the electron-phonon coupling constant (lambda) of the films. We found an oscillatory behavior of lambda with an oscillation periodicity of two atomic layers. Almost all essential features in the Pb/Si(111) system, such as the growth mode, the oscillatory film stability, and the 9 monolayer envelope beating pattern, can be explained by our results in terms of the electron confinement in Pb films.

Anisotropic metal-insulator transition in epitaxial thin films

By comparing the properties of In and Pb quantum wells in a scanning tunneling microscopy subsurface imaging experiment, we found the existence of lateral bound states, a 2D Mott-Hubbard correlation gap, induced by transverse confinement. Its formation is attributed to spin or charge overscreening of quasi-2D excitations. The signature of the 2D confinement-deconfinement transition is also experimentally observed, with the correlation gap being pinned in the middle of the conduction band. A self-organized 2D Anderson lattice is suggested as a new ground state.

Imaging subsurface reflection phase with quantized electrons

Lead quantum wells (QW) epitaxially grown on annealed Pb/Si(111) interface form a model system for the study of interactions between quantized electrons and adiabatically modulated boundaries. Tunnel spectra of this system reveal a previously unknown adiabatic shift of QW resonances due to lateral variations of the electronic reflection phase at the buried interface. With this effect, lateral distribution of the subsurface reflection phase can be probed, using scanning tunneling microscopy.

Confinement-enhanced electron transport across a metal-semiconductor interface

We present a combined scanning tunneling microscopy and ballistic electron emission microscopy study of electron transport across an epitaxial Pb/Si(111) interface. Experiments with a self-assembled Pb nanoscale wedge reveal the phenomenon of confinement-enhanced interfacial transport: a proportional increase of the electron injection rate into the semiconductor with the frequency of electron oscillations in the Pb quantum well.

Evidence for large gap anisotropy in superconducting Pb from phonon imaging

We report the first ballistic phonon images of superconducting Pb. Unusual absorption lines are observed for phonon wave vectors in 111 planes. We show that a highly anisotropic energy gap can lead to sharply defined directions of phonon attenuation. Overhauser and Daemen [Phys. Rev. Lett. 61, 1885 (1988)] postulated a spin-density-wave ground state for Pb that leads to directions of strongly reduced gap. By applying their idea to the actual Fermi surface of Pb, we predict phonon attenuation directions consistent with the data.