Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Cheung, Sky C.; Shin, John Y.; Lau, Yenson; Chen, Zhengyu; Sun, Ju; Zhang, Yuqian; Müller, Marvin A.; Eremin, I.; Wright, John; Pasupathy, Abhay

doi:10.1038/s41467-020-14633-1

Cited by 19 publications

(12 citation statements)

References 56 publications

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“…well below the scattering strength sufficient to generate Bogoliubov bound states 11 . Another approach is to use sparse blind deconvolution 12 to analyze images of scattering interference at multiple atoms, yielding the phase-resolved real space structure of δN(r, E) although not the ρ − (q, E) of Eq. (3).…”

Section: Introductionmentioning

confidence: 99%

Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

et al. 2021

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Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α , for all momenta k on the Fermi surface of every band α. While there are a variety of techniques for determining $$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$ ∣ Δ k α ∣ , no general method existed to measure the signed values of $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α . Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting all k-space regions where $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α it generates to the $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α determined from single-atom scattering in FeSe where s± energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for $${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ Δ k α of opposite sign.

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Section: Introductionmentioning

confidence: 99%

Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

et al. 2021

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“…The HAEM method has mostly been tested on putative isotropic gap states in multiband systems and was recently successfully applied to various iron-based superconductors [24][25][26] ; the limitations of the method have been checked for multiple-impurity scattering 27 and more complex band structures 28 . Furthermore, inspired by the HAEM method its extension with respect to the impurity bound state has been recently proposed 29 and verified independently by experiment 30,31 .…”

Section: Introductionmentioning

confidence: 99%

Phase-sensitive determination of nodal $\mathbf{d}$-wave order parameter in single-band and multiband superconductors

Böker,

Sulangi,

Akbari

et al. 2020

Preprint

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Determining the exact pairing symmetry of the superconducting order parameter in candidate unconventional superconductors remains an important challenge. Recently a new method, based on phase sensitive quasiparticle interference measurements, was developed to identify gap sign changes in isotropic multiband systems. Here we extend this approach to the single-band and multiband nodal d-wave superconducting cases relevant, respectively, for the cuprates and likely for the infinitelayer nickelate superconductors. Combining analytical and numerical calculations, we show that the antisymmetrized correction to the tunneling density of states due to nonmagnetic impurities in the Born and intermediate-scattering limits shows characteristic features for sign-changing and sign-preserving scattering wavevectors, as well as for the momentum-integrated quantity. Furthermore, using a realistic approach accounting for the Wannier orbitals, we model scanning tunneling microscopy data of Bi2Sr2CaCu2O 8+δ , which should allow the comparison of our theory with experimental data.

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“…In this respect, a promising alternative technique was recently proposed based on phase-sensitive quasiparticle interference (QPI) or Fourier transform scanning tunneling microscopy (FT-STM). Its application in LiOH-intercalated FeSe [22] and NaFe 1−x Co x As [23] has revealed qualitative differences in the integrated antisymmetrized intensities of the local density of states (LDOS) to determine the sign-reversal order parameter [24][25][26]. In this paper, we make theoretical predictions on the QPI with both intraband and interband impurity scatterings in CeCu 2 Si 2 .…”

mentioning

confidence: 99%

“…One may thus expect that analyses of the integrated antisymmetrized LDOS in phase-sensitive QPI measurements can examine the sign structure of the pairing symmetry in CeCu 2 Si 2 . As a matter of fact, a similar technique has proved quite successful in LiOH-intercalated FeSe and NaFe 1−x Co x [22,23].…”

mentioning

confidence: 99%

Revealing sign-reversal $s^{+-}$-wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu$_2$Si$_2$

Zhao,

Liu,

Yang

et al. 2021

Preprint

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Recent observations of two nodeless gaps in superconducting CeCu2Si2 have raised intensive debates as to its exact gap structure of either sign-reversal (s +− ) or sign-preserving (s ++ ) pairing.Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between s +− and s ++ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor CeCu2Si2.

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Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Abstract: a These authors contributed equally to this work 1 arXiv:1807.10752v1 [physics.comp-ph] a These authors contributed equally to this work

Cited by 19 publications

References 56 publications

Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

Phase-sensitive determination of nodal $\mathbf{d}$-wave order parameter in single-band and multiband superconductors

Revealing sign-reversal $s^{+-}$-wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu$_2$Si$_2$

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