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"Norman, M. R."
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Quantum spin liquids
Materials with interacting quantum spins that nevertheless do not order magnetically down to the lowest temperatures are candidates for a materials class called quantum spin liquids (QSLs). QSLs are characterized by long-range quantum entanglement and are tricky to study theoretically; an even more difficult task is to experimentally prove that a material is a QSL. Broholm et al. take a broad view of the state of the field and comment on the upcoming challenges. Science , this issue p. eaay0668 Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including “fractionalization”—elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area.
Journal Article
From quantum matter to high-temperature superconductivity in copper oxides
A review of the phases of copper oxides (especially the ‘strange metal’), discussing their high-temperature superconductivity and their various forms of quantum matter, and the implications for fundamental theory.
High-
T
c
superconductors reviewed
Since the discovery of high temperature copper oxide superconductors nearly thirty years ago, much has been learned about the nature of the superconducting state and the novel forms of quantum matter involved. This Review concentrates on the related issues that have not been resolved, notably the complexity of the phase diagram for the copper oxides, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.
The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.
Journal Article
Intertwined density waves in a metallic nickelate
Nickelates are a rich class of materials, ranging from insulating magnets to superconductors. But for stoichiometric materials, insulating behavior is the norm, as for most late transition metal oxides. Notable exceptions are the 3D perovskite LaNiO
3
, an unconventional paramagnetic metal, and the layered Ruddlesden-Popper phases R
4
Ni
3
O
10
, (R = La, Pr, Nd). The latter are particularly intriguing because they exhibit an unusual metal-to-metal transition. Here, we demonstrate that this transition results from an incommensurate density wave with both charge and magnetic character that lies closer in its behavior to the metallic density wave seen in chromium metal than the insulating stripes typically found in single-layer nickelates like La
2-
x
Sr
x
NiO
4
. We identify these intertwined density waves as being Fermi surface-driven, revealing a novel ordering mechanism in this nickelate that reflects a coupling among charge, spin, and lattice degrees of freedom that differs not only from the single-layer materials, but from the 3D perovskites as well.
Layered Ruddlesden-Popper structure nickelates
R
4
Ni
3
O
10
(
R
= La,Pr) show an unusual metal-to-metal transition, but its origin has remained elusive for more than two decades. Here, the authors show that this transition results from intertwined density waves that arise from a coupling between charge and spin degrees of freedom
Journal Article
Large orbital polarization in a metallic square-planar nickelate
High-temperature cuprate superconductivity remains a defining problem in condensed-matter physics. Among myriad approaches to addressing this problem has been the study of alternative transition metal oxides with similar structures and 3
d
electron count that are suggested as proxies for cuprate physics. None of these analogues has been superconducting, and few are even metallic. Here, we report that the low-valent, quasi-two-dimensional trilayer compound Pr
4
Ni
3
O
8
avoids a charge-stripe-ordered phase previously reported for La
4
Ni
3
O
8
, leading to a metallic ground state. X-ray absorption spectroscopy shows that metallic Pr
4
Ni
3
O
8
exhibits a low-spin configuration with significant orbital polarization and pronounced
d
x
2
-
y
2
character in the unoccupied states above the Fermi energy, a hallmark of the cuprate superconductors. Density functional theory calculations corroborate this finding, and reveal that the
d
x
2
-
y
2
orbital dominates the near-
E
f
occupied states as well. Belonging to a regime of 3
d
electron count found for hole-doped cuprates, Pr
4
Ni
3
O
8
thus represents one of the closest analogues to cuprates yet reported and a singularly promising candidate for high-
T
c
superconductivity if electron doping could be achieved.
A careful study of the low-valent, quasi-two-dimensional trilayer metallic nickelate Pr
4
Ni
3
O
8
is presented, revealing this system to be a close analogue of cuprate systems, and offering tantalizing hope that it may superconduct if appropriate electron doping can be achieved.
Journal Article
Electronic Character of Charge Order in Square-Planar Low-Valence Nickelates
Charge order is a central feature of the physics of cuprate superconductors and is known to arise from a modulation of holes with primarily oxygen character. Low-valence nickelate superconductors also host charge order, but the electronic character of this symmetry breaking is unsettled. Here, using resonant inelastic x-ray scattering at the NiL2edge, we identify intertwined involvements of Ni3dx2−y2,3d3z2−r2, and O2pσorbitals in the formation of diagonal charge order in an overdoped low-valence nickelateLa4Ni3O8. The Ni3dx2−y2orbitals, strongly hybridized with planar O2pσ, largely shape the spatial charge distribution and lead to Ni site-centered charge order. The3d3z2−r2orbitals play a small, but non-negligible role in the charge order as they hybridize with the rare-earth5dorbitals. Our results reveal that the low-energy physics and ground-state character of these nickelates are more complex than those in cuprates.
Journal Article
Stacked charge stripes in the quasi-2D trilayer nickelate La4Ni3O8
SignificanceCompetition between localized and itinerant electrons in highly correlated materials can lead to myriad insulating ground states, including spatially inhomogeneous but ordered charge superlattices. In layered transition metal oxides, such charge order can take the form of stripes, which typically arrange themselves in staggered formations to reduce Coulomb repulsion. Having achieved single-crystal growth of the layered nickelate La4Ni3O8, we show that its heretofore incompletely understood phase transition is associated with charge stripe ordering. We find that the stripes are stacked directly on top of one another within nickel oxide trilayers but staggered between successive trilayers. A unique, paradoxical ground state results, in which the electrostatic building principle is respected at long range but violated at short range.
The quasi-2D nickelate La4Ni3O8 (La-438), consisting of trilayer networks of square planar Ni ions, is a member of the so-called T′ family, which is derived from the Ruddlesden–Popper (R-P) parent compound La4Ni3O10−x by removing two oxygen atoms and rearranging the rock salt layers to fluorite-type layers. Although previous studies on polycrystalline samples have identified a 105-K phase transition with a pronounced electronic and magnetic response but weak lattice character, no consensus on the origin of this transition has been reached. Here, we show using synchrotron X-ray diffraction on high-pO2 floating zone-grown single crystals that this transition is associated with a real space ordering of charge into a quasi-2D charge stripe ground state. The charge stripe superlattice propagation vector, q = (2/3, 0, 1), corresponds with that found in the related 1/3-hole doped single-layer R-P nickelate, La5/3Sr1/3NiO4 (LSNO-1/3; Ni2.33+), with orientation at 45° to the Ni-O bonds. The charge stripes in La-438 are weakly correlated along c to form a staggered ABAB stacking that reduces the Coulomb repulsion among the stripes. Surprisingly, however, we find that the charge stripes within each trilayer of La-438 are stacked in phase from one layer to the next, at odds with any simple Coulomb repulsion argument.
Journal Article
Quantum oscillations in a biaxial pair density wave state
There has been growing speculation that a pair density wave state is a key component of the phenomenology of the pseudogap phase in the cuprates. Recently, direct evidence for such a state has emerged from an analysis of scanning tunneling microscopy data in halos around the vortex cores. By extrapolation, these vortex halos would then overlap at a magnetic-field scale where quantum oscillations have been observed. Here, we show that a biaxial pair density wave state gives a unique description of the quantum oscillation data, bolstering the case that the pseudogap phase in the cuprates may be a pair density wave state.
Journal Article
Emergence of coherence in the charge-density wave state of 2H-NbSe2
A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature
T
cdw
. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2
H
-NbSe
2
intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at
T
cdw
marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.
Charge density waves are described by a complex order parameter whose amplitude is expected to vanish at the transition temperature. This study shows that the transition in 2
H
-NbSe
2
is driven by fluctuations of the phase of the order parameter, with a finite amplitude surviving in the disordered state.
Journal Article