PHYSICAL REVIEW X 11, 031040 (2021) - WANG-MACDONALD D-WAVE VORTEX CORES OBSERVED IN HEAVILY OVERDOPED BI2SR2CACU2O8 +
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PHYSICAL REVIEW X 11, 031040 (2021)
Wang-MacDonald d-Wave Vortex Cores Observed in Heavily Overdoped Bi2 Sr2 CaCu2 O8 + δ
Tim Gazdić,1 Ivan Maggio-Aprile ,1 Genda Gu ,2 and Christoph Renner 1,*
1
Department of Quantum Matter Physics, Université de Genève,
24 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
2
Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, New York 11973, USA
(Received 16 February 2021; revised 29 April 2021; accepted 17 June 2021; published 20 August 2021)
Low-magnetic-field scanning tunneling spectroscopy of individual Abrikosov vortices in heavily
overdoped Bi2 Sr2 CaCu2 O8þδ 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.
DOI: 10.1103/PhysRevX.11.031040 Subject Areas: Condensed Matter Physics,
Strongly Correlated Materials,
Superconductivity
I. INTRODUCTION states (SGS) in YBa2 Cu3 O7−δ (Y123) [6] and a pseudogap-
like spectrum in the vortex core of Bi2212 [7]. Subsequent
High-temperature superconductivity (HTS) in copper
STS mapping with improved resolution confirmed the
oxides is a challenging topic to understand. A number
presence of SGS in Bi2212 [8,9] and found a modulation
of unconventional properties, starting with their high
of about 4a0 × 4a0 of the local density of states (the
superconducting transition temperature (T c ), have sparked
checkerboard) spanning the vortex-core region [10,11].
sustained theoretical and experimental efforts to explain the
Meanwhile, there has been emerging evidence suggesting
underlying electron pairing mechanism [1,2]. Among the
that the SGS and checkerboard were not specific to the
numerous outstanding puzzles—in particular, in the exten-
vortex core. A nondispersing charge density modulation of
sively studied Bi2 Sr2 CaCu2 O8þδ (Bi2212)—is the elec-
about 4a0 × 4a0 was observed above T c in the pseudogap
tronic structure of the Abrikosov vortex cores. The
(PG) phase of slightly underdoped Bi2212 [12]. Moreover,
fundamental excitations bound to magnetic vortices in
Hanaguri et al. [13] found a striking field dependence of the
type-II superconductors carry information about essential
checkerboard in Ca2−x Nax CuO2 Cl2 , suggesting it is a field-
properties of the superconducting state. Their proper
enhanced quasiparticle interference (QPI) rather than a
identification is therefore of primary interest to elucidate genuine charge order. Out-of-phase spatial modulations of
the mechanism driving HTS. the electronlike and holelike SGS associated with the
Early scanning tunneling spectroscopy (STS) maps of checkerboard suggest they are indeed QPI features
vortex cores in Bi2212 were neither compatible with the [14,15]. The wavelength of the periodic charge modula-
discrete Caroli-de Gennes-Matricon bound states for an tions observed by STS was found to depend on energy
s-wave superconductor [3] nor with the continuum first below ΔSC and to be nondispersing at energies above it
calculated by Wang and MacDonald for a d-wave super- [16,17]. The dispersion of the low-energy features is well
conductor [4,5]. Instead of the expected zero-bias conduct- described by QPI, while the nondispersing high-energy
ance peak (ZBCP) that splits with increasing distance from features have been associated with PG and symmetry-
the core in the d-wave case, they revealed low-energy breaking charge ordered phases [12,16,18].
(E < ΔSC , where ΔSC is the superconducting gap) subgap The objective of the present study is to uncover the
true electronic structure of a d-wave vortex core. A first
*
christoph.renner@unige.ch indication of a Wang-MacDonald vortex core [4] in a
cuprate high-temperature superconductor was obtained by
Published by the American Physical Society under the terms of STS on Y123 [19]. However, in this case, the bare vortex-
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to core tunneling spectra were obscured by an unknown
the author(s) and the published article’s title, journal citation, spectral signature dominating the superconducting signal.
and DOI. Here, we choose to investigate highly overdoped (OD)
2160-3308=21=11(3)=031040(6) 031040-1 Published by the American Physical Society
GAZDIĆ, MAGGIO-APRILE, GU, and RENNER PHYS. REV. X 11, 031040 (2021)
Bi2212 at low magnetic fields: overdoped, to take advan-
tage of a simpler electronic structure, devoid of any
pseudogap and associated electronic phases [20]; low field,
to increase the vortex spacing and reduce the influence of
neighboring vortices, whose screening currents can affect
vortex cores over distances set by λ, the London penetration
depth [19,21].
II. MATERIALS AND METHODS
The as-grown Bi2212 single crystals were annealed
for 7 days at 500°C in a high pressure of oxygen
(1400 bar) in a hot-isostatic press furnace. Here, T c ≈
52 K is defined as the onset of the magnetic susceptibility
transition, with a typical transition width of 7 K.
Overdoping is achieved by oxygen doping only, and the
crystals contain no Pb. In our experience, the overdoped
crystals prepared in the above manner are stable at room
temperature for years. The crystals were cleaved at T ∼
100 K in ultrahigh vacuum shortly before their transfer into
the STM head at low temperature. All scanning tunneling
microscopy and spectroscopy (STM/STS) experiments
were carried out at or below 4.8 K using a commercial
SPECS JT Tyto STM [22], except the temperature-
FIG. 1. Electronic structure of a vortex core on heavily OD
dependent STS in the Supplemental Material [23]. We Bi2212 (T c ≈ 52 K) at 3 Tesla. (a) Low-energy conductance
used chemically etched Ir tips, carefully conditioned and map σðr; 5 mVÞ showing the roughly 4a0 × 4a0 charge density
characterized on a reconstructed Au(111) single crystal modulation in the vortex halo. The region outlined in red is
surface. The energy scales in the data refer to the sample imaged at 0 mV in the inset to identify the vortex center (red dot).
bias. A magnetic field in the range of 0–3 Tesla was applied (b) Differential tunneling conductance spectra measured along
perpendicular to the Bi2212 CuO2 planes. The lowest field the trace through the vortex center in panel (a) (the scale
of 0.16 Tesla was applied by mounting the sample on a corresponds to bottom spectrum; other spectra are offset for
small permanent magnet. The field intensity was inferred clarity). The pink and orange spectra delimit the core region
from the number of vortices per unit area observed by STS where the SGS develop and the superconducting coherence peaks
are suppressed. (c) Fourier transform of (a), where the lattice
on Bi2212 and on NbSe2 for calibration. Images of the
peaks at q0 and the periodic modulations at about 0.24q0 and
Abrikosov vortex lattice were obtained by mapping the 0.75q0 are clearly resolved. (d) Energy dependence of the Fourier
local tunneling conductance at selected biases in a low- amplitude along the orange trace in panel (c), showing the
energy range below the superconducting gap. roughly 0.24q0 checkerboard dispersion. Dashed lines are guides
to the eye.
III. HIGH-FIELD MEASUREMENTS
A single Abrikosov vortex core imaged by STS at 5 mV we find that the checkerboard pattern disperses from a
in a magnetic field of 3 Tesla on heavily OD Bi2212 characteristic wave vector q ≈ 0.375q0 at low energy
(T c ≈ 52 K) is displayed in Fig. 1(a). Its core region around 3 mV to q ≈ 0.24q0 at 10 mV [Fig. 1(d)]. Such
imaged at 0 mV shown in the inset of Fig. 1(a) allows a dispersion is not consistent with a charge-density wave
us to pinpoint the vortex center highlighted by a red dot. origin of the checkerboard.
The spatial structure of the 5-mV conductance map looks Turning to the tunneling spectra, we find that the
strikingly similar to earlier STS vortex images obtained on superconducting coherence peaks at ΔSC ≈ 20 mV are
optimally and slightly underdoped Bi2212 [24]. In par- greatly suppressed within about 6 nm of the vortex center
ticular, it shows two periodic patterns extending over the along the 17-nm-long (100) trace shown in Fig. 1(b). They
roughly 6-nm-diameter vortex halo. One is reminiscent of further show enhanced low-energy SGS developing within
the checkerboard reconstruction with q ≈ 0.24q0 [10,13], the vortex-core region, delimited by the colored points and
where q0 corresponds to the atomic lattice. The other, best spectra in Figs. 1(a) and 1(b), respectively. These SGS are
resolved in the Fourier transform (FT) shown in Fig. 1(c), not compatible with the d-wave predictions: Their weak
corresponds to a structure similar to the high-energy ladder amplitude and constant energy position with distance from
structure at q ≈ 0.75q0 [25]. Analyzing the FT of con- the core are in sharp contrast to the intense ZBCP and
ductance images of the same region at different energies, subgap peaks, which shift to higher energy with increasing
031040-2
WANG-MACDONALD d-WAVE VORTEX CORES OBSERVED IN … PHYS. REV. X 11, 031040 (2021)
distance from the center predicted for a d-wave super- consistent with an applied magnetic field of 0.16 Tesla.
conductor [4,5]. Most remarkably, we observe the systematic presence of a
ZBCP at 0.16 Tesla and the disappearance of the vortex
checkerboard in vortices sitting in a clean background.
IV. LOW-FIELD MEASUREMENTS
This case is very different from the vortex cores observed
Compared to the 3-Tesla vortex-core structure discussed at 3 Tesla, which systematically display the low-energy
in Fig. 1, a very different picture emerges when reducing checkerboard and never show a ZBCP [24].
the applied magnetic field by over an order of magnitude A single Abrikosov vortex core imaged by STS at 5 mV
compared to any previous STS study of a HTS cuprate. in a magnetic field of 0.16 Tesla on heavily OD Bi2212
The very small coherence length of Bi2212 makes it (T c ≈ 52 K) is shown in Fig. 2(a). As for the specific vortex
challenging to ensure that a given feature in a STS map shown here, almost all vortices measured at low magnetic
is actually a vortex core and not an impurity or a charge field show no sign of the q ≈ 0.24q0 or q ≈ 0.75q0
inhomogeneity [23]. The individual vortex core shown modulations, neither in real space maps [Fig. 2(a)] nor
in Fig. 2 was identified from the large-field-of-view in their Fourier transforms [Fig. 2(c)]. The strong suppres-
conductance map in Fig. 3, labeled as vortex 1. This sion of these modulations at 0.16 Tesla is consistent
STS map reveals about 20 vortices on a disordered lattice, with a field-induced QPI origin [13]. In very few cases,
we detected faint and broad signals corresponding to q ≈
0.24q0 or q ≈ 0.75q0 modulations. However, they were
too broad to draw conclusions about their dispersive or
nondispersive character. Most interestingly for the present
study, the low-field vortices have a significantly different
spectroscopic signature compared to 3 Tesla. Besides the
suppression of the superconducting coherence peaks
observed at all fields, they reveal the characteristic elec-
tronic signatures predicted by Wang and MacDonald [4]
for a d-wave vortex core [Fig. 2(b)]: (i) a marked con-
ductance peak at or very close to zero bias at the center of
the vortex; (ii) a splitting of this ZBCP into two subgap
FIG. 2. Electronic structure of a vortex core on heavily OD
Bi2212 (T c ≈ 52 K) at 0.16 Tesla. (a) Low-energy conductance
map σðr; 5 mVÞ 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 q0 and features related to the superstructure are FIG. 3. 500 × 500 nm2 STS conductance map of OD Bi2212
resolved. (d) Energy dependence of the Fourier amplitude along (T c ≈ 52 K) revealing a disordered lattice with a vortex density
the orange trace in panel (c). Note the absence of any character- corresponding to an applied magnetic field of about 0.16 Tesla.
istic structure. Dashed lines are guides to the eye, where a Vortex 1 and vortex 2 are further investigated in Figs. 2 and 4,
dispersive feature is seen at a high field. respectively.
031040-3
GAZDIĆ, MAGGIO-APRILE, GU, and RENNER PHYS. REV. X 11, 031040 (2021)
conductance peaks (SGCP) that shift away from zero bias The LDOS of an isolated vortex core in an ideal d-wave
with increasing distance from the vortex core [26]. superconductor is fourfold symmetric [19,21]. We exploit
this symmetry to enhance the signal-to-noise ratio through
four-quadrant averaging. Such angular averaging enables
V. d-WAVE CORE SIGNATURES
the resolution of finer electronic features of the cores.
A first conclusion at this stage is that the electronic Figure 4(a) shows a four-quadrant symmetrized conduct-
vortex-core structure depends, remarkably, on the applied ance map of the core of vortex 2 measured at 0.16 Tesla in
magnetic field. Previous STS studies of vortex cores Fig. 3. Line cuts along the nodal (110) and antinodal (100)
in HTS copper oxides were performed at fields above directions of this averaged data set are shown in Figs. 4(b)
2 Tesla. Berthod et al. [19,21] showed how the screening and 4(c), respectively. Overall, the spatial dependence of
currents of neighboring vortices at large fields modify the the tunneling conductance is similar along both directions,
electronic core structure and, in particular, the ZBCP and except for a more rapid suppression of the zero-bias
SGCP. These studies further showed that the cores of an conductance (ZBC) along the nodal direction. The sup-
irregular vortex lattice can each have a slightly different pression of the ZBC evolves smoothly along an arc of
electronic signature due to their distinct environment. They constant radius between the nodal and antinodal directions,
suggest that, in order to access the intrinsic electronic core as seen in Fig. 4(d). These characteristics correspond very
structure, it is necessary to increase the vortex spacing by closely to the expectations for a d-wave vortex core [19].
reducing the magnetic field. At 0.16 Tesla, we do indeed The splitting of the ZBCP observed along the antinodal
measure the elusive Wang-MacDonald vortex-core struc- direction in Bi2212 is absent in YBCO [19,26] because of
ture expected for a d-wave superconductor [4]. We check the different band structures in these two compounds. Note
that these low-energy spectroscopic features are absent at that the continuous shift in energy of the SGCP with
the exact same location in zero field [23], to make sure they increasing distance from the core along each direction in
are genuine vortex core features rather than impurity states, Fig. 4 confirms the accurate identification of the vortex
for example. center. Indeed, four-quadrant averaging around another
central point would smear out the above angular depend-
ence. The proper identification of the vortex center is
further confirmed by the coherence length extracted from
the unsymmetrized vortex core, which is consistent with
the known values for this material [23].
Resolving vortex cores at an unprecedentedly low
applied magnetic field in heavily OD Bi2212 is not only
instrumental in revealing the d-wave electronic vortex-core
structure; it also allows us to delineate extrinsic from
genuine vortex features. The present study implies that
the checkerboard pattern, the nonshifting SGS, and the
missing ZBCP are extrinsic features. They do not signify
unconventional Bi2212 vortex cores but rather result from
the interactions of neighboring vortices [19,21]. The dis-
appearance of the roughly 4a0 × 4a0 pattern in the vortex
halo at low fields and the finite dispersion of its corre-
sponding wave vector indicate that the low-energy checker-
board is a field-enhanced QPI feature [13], in agreement
with recent measurements close to optimal doping [16,17].
The low-field vortex-core structure further provides valu-
able insight into the general electronic structure of Bi2212.
For example, the checkerboard and SGS have been linked
FIG. 4. Angular dependence of the low-field vortex-core to the pseudogap in previous studies [12]. Here, we demon-
structure at 0.16 Tesla. (a) Four-quadrant averaged STS con- strate that even in the absence of a pseudogap [23], a low-
ductance map σðr; 0 mVÞ of vortex 2 in Fig. 3. (b) Differential energy modulation of about 4a0 × 4a0 and SGS are present
tunneling conductance spectra along the (110) crystallographic when vortex-vortex interactions are significant.
direction in panel (a). (c) Differential tunneling conductance
spectra along the (100) crystallographic direction in panel (a). VI. SUMMARY
(d) Differential tunneling conductance spectra along the arc from
(100) to (110) depicted in panel (a). All the spectra are four- The key result of the detailed, low-field, STS spectros-
quadrant averaged. Conductance scales correspond to bottom copy discussed here is the experimental demonstration
spectra in panels (b)–(d); other spectra are offset for clarity. of the vortex-core structure predicted by Wang and
031040-4
WANG-MACDONALD d-WAVE VORTEX CORES OBSERVED IN … PHYS. REV. X 11, 031040 (2021)
MacDonald for a d-wave superconductor [4]. This finding [8] B. W. Hoogenboom, C. Renner, B. Revaz, I. Maggio-Aprile,
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in detail), whereas the checkerboard was predominantly
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