Wang-MacDonald $d$-Wave Vortex Cores Observed in Heavily Overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$

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Wang-MacDonald $d$ -Wave Vortex Cores Observed in Heavily Overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$

Tim Gazdić, Ivan Maggio-Aprile, Genda Gu, and Christoph Renner

Phys. Rev. X 11, 031040 – Published 20 August 2021

Abstract

Low-magnetic-field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ unveils a clear $d$ -wave electronic structure of the vortex core, with a zero-bias conductance peak at the vortex center that splits with increasing distance from the core. We show that previously reported unconventional electronic structures, including the low-energy checkerboard charge order in the vortex halo and the absence of a zero-bias conductance peak at the vortex center, are direct consequences of short intervortex distance and consequent vortex-vortex interactions prevailing in earlier experiments.

Received 16 February 2021
Revised 29 April 2021
Accepted 17 June 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031040

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Local density of states Vortices in superconductors d-wave

High-temperature superconductors

Scanning tunneling microscopy Scanning tunneling spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tim Gazdić¹, Ivan Maggio-Aprile ¹, Genda Gu ², and Christoph Renner ^1,*

¹Department of Quantum Matter Physics, Université de Genève, 24 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
²Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA

^*christoph.renner@unige.ch

Popular Summary

Magnetic vortices in superconductors are singular objects at the center of which the superconducting Cooper pairs of electrons are locally destroyed. As a consequence, the electronic excitations in their cores are expected to be fundamentally different from the ones occurring in the electronic superfluid surrounding the vortices. Scanning tunneling microscopy is the ideal tool to study these singular states, whose spectroscopic signatures are predicted to carry essential information about the intrinsic nature of the superconducting state. While vortex cores of “conventional” low-temperature superconductors are understood in great detail, past experiments revealed very unusual electronic vortex core structures in high-temperature superconductors not compatible with theory. Now, exploring vortices in a high-temperature superconductor using scanning tunneling microscopy at unprecedentedly low magnetic fields, we reveal their genuine electronic structure, which turns out to be consistent with a 25-year-old theoretical model.

Previous experiments showed that in the vicinity of a vortex, the electronic states were spatially modulated over a four-unit-cell distance, forming a checkerboard pattern. At the low magnetic field we use, this checkerboard is no longer observed. Moreover, precisely in the vortex center, we measure a single conductance peak that splits into two peaks with increasing distance from the vortex core. This behavior, which was never reported at high magnetic fields, is precisely the one predicted by Wang and MacDonald for a superconductor whose Cooper pairs’ wave functions are anisotropic in momentum space (known as $d$ -wave symmetry).

The proper identification of these vortex core states is of prime interest to elucidate the mechanism driving high-temperature superconductivity, which still remains unclear.

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Vol. 11, Iss. 3 — July - September 2021

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Figure 1
Electronic structure of a vortex core on heavily OD Bi2212 ( $T_{c} \approx 52 K$ ) at 3 Tesla. (a) Low-energy conductance map $σ (r, 5 mV)$ showing the roughly $4 a_{0} \times 4 a_{0}$ charge density modulation in the vortex halo. The region outlined in red is imaged at 0 mV in the inset to identify the vortex center (red dot). (b) Differential tunneling conductance spectra measured along the trace through the vortex center in panel (a) (the scale corresponds to bottom spectrum; other spectra are offset for clarity). The pink and orange spectra delimit the core region where the SGS develop and the superconducting coherence peaks are suppressed. (c) Fourier transform of (a), where the lattice peaks at $q_{0}$ and the periodic modulations at about $0.24 q_{0}$ and $0.75 q_{0}$ are clearly resolved. (d) Energy dependence of the Fourier amplitude along the orange trace in panel (c), showing the roughly $0.24 q_{0}$ checkerboard dispersion. Dashed lines are guides to the eye.
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Figure 2
Electronic structure of a vortex core on heavily OD Bi2212 ( $T_{c} \approx 52 K$ ) at 0.16 Tesla. (a) Low-energy conductance map $σ (r, 5 mV)$ showing the core of vortex 1 in Fig. 3. The region outlined in red is imaged at 0 mV in the inset to identify the vortex center (red dot). (b) Differential tunneling conductance spectra measured along the trace through the vortex center in panel (a) (the scale corresponds to the bottom spectrum; other spectra are offset for clarity). The pink and orange spectra delimit the core region where the superconducting coherence peaks are suppressed. (c) Fourier transform of panel (a), where only the lattice peaks at $q_{0}$ and features related to the superstructure are resolved. (d) Energy dependence of the Fourier amplitude along the orange trace in panel (c). Note the absence of any characteristic structure. Dashed lines are guides to the eye, where a dispersive feature is seen at a high field.
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Figure 3
$500 \times 500 {nm}^{2}$ STS conductance map of OD Bi2212 ( $T_{c} \approx 52 K$ ) revealing a disordered lattice with a vortex density corresponding to an applied magnetic field of about 0.16 Tesla. Vortex 1 and vortex 2 are further investigated in Figs. 2 and 4, respectively.
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Figure 4
Angular dependence of the low-field vortex-core structure at 0.16 Tesla. (a) Four-quadrant averaged STS conductance map $σ (r, 0 mV)$ of vortex 2 in Fig. 3. (b) Differential tunneling conductance spectra along the (110) crystallographic direction in panel (a). (c) Differential tunneling conductance spectra along the (100) crystallographic direction in panel (a). (d) Differential tunneling conductance spectra along the arc from (100) to (110) depicted in panel (a). All the spectra are four-quadrant averaged. Conductance scales correspond to bottom spectra in panels (b)–(d); other spectra are offset for clarity.
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Physical Review X

Wang-MacDonald d-Wave Vortex Cores Observed in Heavily Overdoped Bi2Sr2CaCu2O8+δ

Tim Gazdić, Ivan Maggio-Aprile, Genda Gu, and Christoph Renner

Phys. Rev. X 11, 031040 – Published 20 August 2021

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Wang-MacDonald $d$ -Wave Vortex Cores Observed in Heavily Overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$