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result(s) for
"Davis, C J"
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Discovery of orbital-selective Cooper pairing in FeSe
The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the G = (0, 0) and X = (p/aFe, 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the dyz orbitals of the iron atoms.
Journal Article
Magnetic field–induced pair density wave state in the cuprate vortex halo
High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N(r) within the halo surrounding Bi₂Sr₂CaCu₂O₈ vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N(r) modulations with wave vectors QP
and 2QP
, with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO₂ unit-cell periodicity and coexisting with its secondary CDWs.
Journal Article
Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe
Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high-temperature superconductivity. By contrast, the parent phase of an iron-based high-temperature superconductor is never a correlated insulator. However, this distinction may be deceptive because Fe has five actived d orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund’s metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations, producing orbitally selective strong correlations. The spectral weights Zm of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle Zm appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that \\[Z_{xy} < Z_{xz} \\ll Z_{yz}\\], consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based high-temperature superconductivity in FeSe.
Journal Article
Detection of a pair density wave state in UTe2
Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe
2
may embody such bulk topological superconductivity
1
–
11
, its superconductive order parameter Δ(
k
) remains unknown
12
. Many diverse forms for Δ(
k
) are physically possible
12
in such heavy fermion materials
13
. Moreover, intertwined
14
,
15
density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating
14
,
15
superconductive order parameter Δ(
r
), electron-pair density
16
–
19
and pairing energy gap
17
,
20
–
23
. Hence, the newly discovered CDW state
24
in UTe
2
motivates the prospect that a PDW state may exist in this material
24
,
25
. To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips
26
–
31
. We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors
P
i
=1,2,3
that are indistinguishable from the wavevectors
Q
i
=1,2,3
of the prevenient
24
CDW. Concurrent visualization of the UTe
2
superconductive PDWs and the non-superconductive CDWs shows that every
P
i
:
Q
i
pair exhibits a relative spatial phase
δϕ
≈ π. From these observations, and given UTe
2
as a spin-triplet superconductor
12
, this PDW state should be a spin-triplet PDW
24
,
25
. Although such states do exist
32
in superfluid
3
He, for superconductors, they are unprecedented.
A spin-triplet pair density wave is discovered in the candidate topological superconductor UTe
2
using superconductive scanning tunnelling microscopy tips.
Journal Article
Evidence for a vestigial nematic state in the cuprate pseudogap phase
The CuO₂ antiferromagnetic insulator is transformed by hole-doping into an exotic quantum fluid usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states D(E) for energies |E| < Δ*, where Δ* is the PG energy. Unanticipated broken-symmetry phases have been detected by a wide variety of techniques in the PG regime, most significantly a finite-Q density-wave (DW) state and a Q = 0 nematic (NE) state. Sublattice-phase-resolved imaging of electronic structure allows the doping and energy dependence of these distinct broken-symmetry states to be visualized simultaneously. Using this approach, we show that even though their reported ordering temperatures TDW
and TNE
are unrelated to each other, both the DW and NE states always exhibit theirmaximumspectral intensity at the same energy, and using independent measurements that this is the PG energy Δ*. Moreover, no new energy-gap opening coincides with the appearance of the DW state (which should theoretically open an energy gap on the Fermi surface), while the observed PG opening coincides with the appearance of the NE state (which should theoretically be incapable of opening a Fermi-surface gap). We demonstrate how this perplexing phenomenology of thermal transitions and energy-gap opening at the breaking of two highly distinct symmetries may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi₂Sr₂CaCu₂O₈.
Journal Article
Momentum-resolved superconducting energy gaps of Sr₂RuO₄ from quasiparticle interference imaging
Sr₂RuO₄ has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap Δ
i
(k) on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the Δ
i
(k) of Sr₂RuO₄. Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband Δ
i
(k). At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors q
j
: j = 1−5 consistent with eight gap nodes/minima that are all closely aligned to the (±1, ± 1) crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72–75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr₂RuO₄ appears most consistent with Δ
i
(k) having
d
x
2
−
y
2
(
B
1
g
)
symmetry.
Journal Article
Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO ₂ unit cell, segregating the results into three separate electronic structure images containing only the Cu sites [ Cu (r)] and only the x / y axis O sites [ O ₓ(r) and O y(r)]. Phase-resolved Fourier analysis reveals directly that the modulations in the O ₓ(r) and O y(r) sublattice images consistently exhibit a relative phase of π . We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials-specific systematics. These observations demonstrate by direct sublattice phase-resolved visualization that the density wave found in underdoped cuprates consists of modulations of the intraunit-cell states that exhibit a predominantly d- symmetry form factor.
Journal Article
Imaging the energy gap modulations of the cuprate pair-density-wave state
The defining characteristic
1
,
2
of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap
Δ
(
r
), where
r
is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)
3
,
4
. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling
5
, the distinctive signature in single-electron tunnelling of a periodic
Δ
(
r
) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong
Δ
(
r
) modulations in the canonical cuprate Bi
2
Sr
2
CaCu
2
O
8+
δ
that have eight-unit-cell periodicity or wavevectors
Q
≈ (2π/
a
0
)(1/8, 0) and
Q
≈ (2π/
a
0
)(0, 1/8) (where
a
0
is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states
N
(
r
,
E
) (where
E
is the energy) reveals electronic modulations with wavevectors
Q
and 2
Q
, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these
N
(
r
,
E
) density waves at 2
Q
, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state
6
,
7
. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi
2
Sr
2
CaCu
2
O
8+
δ
.
Using a spectroscopic technique based on scanning tunnelling microscopy, the superconducting energy gap modulations in a copper oxide are visualized, demonstrating that a pair-density-wave state coexists with superconductivity.
Journal Article