Andreev Reflection in Scanning Tunneling Spectroscopy of Unconventional Superconductors
ORAL · Invited
Abstract
We developed a new theory for the differential conductance measured in a scanning tunneling microscopy (STM) setting [1]. Our theory allows for an arbitrary electron transmission between an STM tip and a two-dimensional superconductor with arbitrary gap structure. The developed scattering-theory formulation accounts for Andreev reflections, which become prominent at larger transmissions. We show that this provides complementary information about the superconducting gap structure beyond the tunneling density of states, strongly facilitating the ability to extract the gap symmetry and its relation to the underlying crystalline lattice. We use the developed theory to discuss the experimental results on superconductivity in twisted bilayer graphene.
An extension of the developed scattering approach allows us also to investigate the role of the Bloch functions and superconducting gap symmetries on the formation and properties of impurity-induced resonances in a two-dimensional superconductor, and elucidate their manifestation in scanning tunneling spectra [2]. The theory results are conveniently formulated in terms of the phase shifts of electron scattering off the impurity. We find that the discrete subgap states in a nodeless-gap superconductor are insensitive to the potential scattering phase shift (common for the two spin species) if time-reversal symmetry (TRS) is preserved. The independence of potential scattering is exact for s-wave superconductors. It remains an accurate approximation over a broad range of subgap energies when the gap function breaks the lattice point symmetry, except for a narrow region below the gap edge. Breaking of TRS makes potential scattering capable of creating spin-degenerate subgap states, which may be further split by spin-dependent scattering. In nodal-gap superconductors, impurity-induced resonances are broadened by coupling to the quasiparticle continuum. We identify the conditions allowing for the formation of narrow resonances. In addition to finding the energy spectrum, we evaluate the spin-resolved differential conductance for all the considered symmetries and gap structures
An extension of the developed scattering approach allows us also to investigate the role of the Bloch functions and superconducting gap symmetries on the formation and properties of impurity-induced resonances in a two-dimensional superconductor, and elucidate their manifestation in scanning tunneling spectra [2]. The theory results are conveniently formulated in terms of the phase shifts of electron scattering off the impurity. We find that the discrete subgap states in a nodeless-gap superconductor are insensitive to the potential scattering phase shift (common for the two spin species) if time-reversal symmetry (TRS) is preserved. The independence of potential scattering is exact for s-wave superconductors. It remains an accurate approximation over a broad range of subgap energies when the gap function breaks the lattice point symmetry, except for a narrow region below the gap edge. Breaking of TRS makes potential scattering capable of creating spin-degenerate subgap states, which may be further split by spin-dependent scattering. In nodal-gap superconductors, impurity-induced resonances are broadened by coupling to the quasiparticle continuum. We identify the conditions allowing for the formation of narrow resonances. In addition to finding the energy spectrum, we evaluate the spin-resolved differential conductance for all the considered symmetries and gap structures
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Publication: [1] P. O. Sukhachov, Felix von Oppen, and L. I. Glazman, Phys. Rev. Lett. v.130, p. 216002 (2023)<br>[2] P. O. Sukhachov, Felix von Oppen, and L. I. Glazman, Phys. Rev. B v.108, p.024505 (2023)
Presenters
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Leonid I Glazman
Yale University
Authors
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Leonid I Glazman
Yale University