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Register a new userTunneling spectroscopy of topological superconductors
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Authors
Satoshi Kashiwaya
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Tunneling conductance spectra of normal metal/insulator/superconductor (N/I/S) junctions are calculated to determine the potential of tunneling spectroscopy in investigations of topological superconductivity. Peculiar feature of topological superconductors is the formation of gapless edge states in them. Since the conductance of N/I/S junctions is sensitive to the formation of these edge states, topological superconductivity can be identified through edge-state detection. Herein, the effects of Fermi surface anisotropy and an applied magnetic field on the conductance spectra are analyzed to gather indications that can help to identify the topological nature of actual materials.
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Fine structures in the tunneling spectra of superconductors have been widely used to identify fingerprints of the interaction responsible for Cooper pairing. Here we show that for scanning tunneling microscopy (STM) of Pb, the inclusion of inelastic tunneling processes is crucial for the proper interpretation of these fine structures. For STM the usual McMillan inversion algorithm of tunneling spectra must therefore be modified to include inelastic tunneling events, an insight that is crucial for the identification of the pairing glue in conventional and unconventional superconductors alike.
Tunneling spectroscopy at surfaces of unconventional superconductors has proven an invaluable tool for obtaining information about the pairing symmetry. It is known that mid gap Andreev bound states manifest itself as a zero bias conductance peak in tunneling spectroscopy. The zero bias conductance peak is a signature for a non-trivial pair potential that exhibits different signs on different regions of the Fermi surface. Here, we review recent theoretical results on the spectrum of Andreev bound states near interfaces and surfaces in non-centrosymmetric superconductors. We introduce a theoretical scheme to calculate the energy spectrum of a non-centrosymmetric superconductor. Then, we discuss the interplay between the spin orbit vector field on the Fermi surface and the order parameter symmetry. The Andreev states carry a spin supercurrent and represent a helical edge mode along the interface. We study the topological nature of the resulting edge currents. If the triplet component of the order parameter dominates, then the helical edge mode exists. If, on the other hand, the singlet component dominates, the helical edge mode is absent. A quantum phase transition occurs for equal spin singlet and triplet order parameter components. We discuss the tunneling conductance and the Andreev point contact conductance between a normal metal and a non-centrosymmetric superconductor.
We present a combined experimental and theoretical study of the proximity effect in an atomic-scale controlled junction between two different superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb nanocrystal with an energy gap of 1.2 meV, connected to a crystalline atomic monolayer of lead with a gap of 0.23 meV. Using in situ scanning tunneling spectroscopy we probe the local density of states of this hybrid system both in space and in energy, at temperatures below and above the critical temperature of the superconducting monolayer. Direct and inverse proximity effects are revealed with high resolution. Our observations are precisely explained with the help of a self-consistent solution of the Usadel equations. In particular, our results demonstrate that in the vicinity of the Pb islands, the Pb monolayer locally develops a finite proximity-induced superconducting order parameter, well above its own bulk critical temperature. This leads to a giant proximity effect where the superconducting correlations penetrate inside the monolayer a distance much larger than in a non-superconducting metal.
Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.
The origin of Cooper pairing in high-temperature superconductors, such as the copper-oxide and iron-based system, is still under debate. High transition temperatures together with unconventional pairing states support the picture of an electronic pairing glue in the cuprates, where superconductivity is mediated by collective bosonic excitations of the electron fluid. In other materials, most importantly iron based systems with only hole or only electron pockets, the microscopic origin is hotly debated. Scanning tunneling microscopy (STM) has been shown to be a powerful experimental probe to detect electronic excitations and further allows to deduce some fingerprints of bosonic collective modes. Here, we demonstrate that the inclusion of inelastic tunnel events is crucial for the interpretation of tunneling spectra and allows to directly probe bosonic excitations via STM. We develop a model describing both the elastic tunneling current, which displays the electronic spectral function, and the inelastic current, that contains the information about the bosonic spectrum, in the superconducting state. Adopting this extended tunneling formalism we can naturally reproduce the tunneling spectra of various unconventional superconductors and trace the occurring features back to an opening of a spin gap in the superconducting state. More generally, our approach is a strong argument in favour of a collective mode mediating the pairing state in particular in iron-based systems. In particular, we conclude that the debated pairing mechanism in LiFeSe is also of electronic origin with sign-changing pairing symmetry.
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