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Computed materials data using density functional theory calculations. These calculations determine the electronic structure of bulk materials by solving approximations to the Schrodinger equation. For more information, see https://materialsproject.org/docs/calculations
The primordial ingredient of cuprate superconductivity is the CuO 2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d 9 and 3d 10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p 6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p 6 and 3d 10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO 2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO 2 .
Significance The pairing mechanism of high-temperature superconductivity, especially in cuprates, remains as the most challenging issue in condensed matter physics. The antiferromagnetic (AF) order/correlation is supposed to be important for inducing pairing and superconductivity. In this paper, we report the observation of a static incommensurate AF order by spin-polarized scanning tunneling microscope in Fe-doped Bi2212 with a nearly optimally doped state of superconductivity. The local incommensurate AF order can be directly visualized in regions with some Fe impurities. Our measurements provide a basis to study the interplay between superconductivity and AF spin fluctuations in cuprates.
Although phase diagrams can be leveraged to investigate high transition temperature (high-T c ) superconductivity, the issue has not been discussed thoroughly. In this study, we elucidate the phase diagram of the overdoped side of high-T c cuprates via systematic anisotropic transport measurements for Pb-doped Bi-2212 single crystals. We demonstrate that the characteristic temperatures of the “weak” pseudogap opening and electronic coherence cross each other at a critical doping level, while those of the “strong” pseudogap merges into that of superconducting fluctuations above the critical doping level. Her the results indicate the importance of Mottness in high-T c superconductivity.
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The evidence for proximity-induced superconductivity in heterostructures of topological insulators and high- T c cuprates has been intensely debated. We use molecular-beam epitaxy to grow thin films of topological insulator Bi 2 Te 3 on a cuprate Bi 2 Sr 2 CaCu 2 O 8+x , and study the surface of Bi 2 Te 3 using low-temperature scanning tunneling microscopy and spectroscopy. In few unit-cell thick Bi 2 Te 3 films, we find a V-shaped gap-like feature at the Fermi energy in d I /d V spectra. By reducing the coverage of Bi 2 Te 3 films to create nanoscale islands, we discover that this spectral feature dramatically evolves into a much larger hard gap, which can be understood as a Coulomb blockade gap. This conclusion is supported by the evolution of d I /d V spectra with the lateral size of Bi 2 Te 3 islands, as well as by topographic measurements that show an additional barrier separating Bi 2 Te 3 and Bi 2 Sr 2 CaCu 2 O 8+x . We conclude that the prominent gap-like feature in d I /d V spectra in Bi 2 Te 3 films is not a proximity-induced superconducting gap. Instead, it can be explained by Coulomb blockade effects, which take into account additional resistive and capacitive coupling at the interface. Our experiments provide a fresh insight into the tunneling measurements of complex heterostructures with buried interfaces.
The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in cuprates. Although the signature of a cuprate PDW has been detected in Cooperpair tunneling, the distinctive signature in single-electron tunneling of a periodic Δ(r) modulation has never been observed. Here, using a new approach, we discover strong Δ(r) modulations in Bi 2 Sr 2 CaCu 2 O 8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8). Simultaneous imaging of the localdensity- of-states N(r, E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by !, as predicted by the theory of half-vortices in a PDW state. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi 2 Sr 2 CaCu 2 O 8+δ .
Mesa-shaped structures of the high critical temperature (high-T c ) superconductor Bi 2 Sr 2 CaCu 2 O 8+δ ; contain stacked intrinsic Josephson junctions. As such, they are a promising source of coherent radiation in the "terahertz gap" range, spanning from approximately 0.3 to 2.0 THz. Technological applications of these devices become far more practical if they can be operated at a cryogenic bath temperature of 77 K or higher. Previous works have reported emission from this type of device at high terahertz power levels at lower operating temperatures, 40-60 K, while at T bath >= 77 K observed power levels have generally been low. Here we report generation of 130 mu W of coherent power at 0.456 THz from a mesa of Bi 2 Sr 2 CaCu 2 O 8+δ ; doped with 0.16 holes per Cu atom, at a bath temperature of 77.4 K. Here, we find that the device radiates terahertz power when clearly identifiable cavity modes are excited, and that the frequency and bias voltage corresponding to each of these modes is almost independent of temperature. This is consistent with these modes having terahertz-frequency electric fields with very little dependence on vertical position within the mesa. We also find that the terahertz power radiated from any given mode decreases monotonically as the mesa temperature is increased. On the other hand, the low-frequency modes become inaccessible at low temperatures due to retrapping of the intrinsic Josephson junctions, and the maximum radiation power for the emitting mode is typically achieved at the temperature at which the retrapping voltage reaches the resonance voltage for this mode.
Superconducting quantum interferometer device (SQUID) plays a key role in understanding electromagnetic properties and emergent phenomena in quantum materials. The technological appeal of SQUID is that its detection accuracy for the electromagnetic signal can precisely reach the quantum level of a single magnetic flux. However, conventional SQUID techniques normally can only be applied to a bulky sample and do not have the capability to probe the magnetic properties of micro-scale samples with small magnetic signals. Here, in this paper, it is demonstrated that, based on a specially designed superconducting nano-hole array, the contactless detection of magnetic properties and quantized vortices in micro-sized superconducting nanoflakes is realized. An anomalous hysteresis loop and a suppression of Little–Parks oscillation are observed in the detected magnetoresistance signal, which originates from the disordered distribution of the pinned vortices in Bi 2 Sr 2 CaCu 2 O 8+δ . Therefore, the density of pinning centers of the quantized vortices on such micro-sized superconducting samples can be quantitatively evaluated, which is technically inaccessible for conventional SQUID detection. The superconducting micro-magnetometer provides a new approach to exploring mesoscopic electromagnetic phenomena of quantum materials.
Artificially engineered twisted van der Waals (vdW) heterostructures have unlocked new pathways for exploring emergent quantum phenomena and strongly correlated electronic states. Many of these phenomena are highly sensitive to the twist angle, which can be deliberately tuned to tailor the interlayer interactions. This makes the twist angle a critical tunable parameter, emphasizing the need for precise control and accurate characterization during device fabrication. In particular, twisted cuprate heterostructures based on Bi 2 Sr 2 CaCu 2 O 8 + x (BSCCO) have demonstrated angle-dependent superconducting properties, positioning the twist angle as a key tunable parameter. However, the twisted interface is highly unstable under ambient conditions and vulnerable to damage from conventional characterization tools such as electron microscopy or scanning probe techniques. In this work, a fully non-invasive, polarization-resolved Raman spectroscopy approach is introduced for determining twist angles in artificially stacked BSCCO heterostructures. By analyzing twist-dependent anisotropic vibrational Raman modes, particularly utilizing the out-of-plane A 1g vibrational mode of Bi/Sr at ≈116 cm −1 , clear optical fingerprints of the rotational misalignment between cuprate layers are identified. The high-resolution confocal Raman setup, equipped with polarization control and RayShield filtering down to 10 cm −1 , allows for reliable and reproducible measurements without compromising the material's structural integrity.
Controlled fabrication of twisted van der Waals heterostructures is essential to unlock the full potential of moiré materials. However, achieving reproducibility remains a major challenge, particularly for air-sensitive materials such as Bi 2 Sr 2 CaCu 2 O 8 + δ (BSCCO), where it is crucial to preserve the intrinsic and delicate superconducting properties of the interface throughout the entire fabrication process. Here, a dry, inert and cryogenic assembly method is presented that combines silicon nitride nanomembranes (NMBs) with pre-patterned electrodes and the cryogenic stacking technique (CST) to fabricate high-quality twisted BSCCO Josephson junctions (JJs). This protocol prevents thermal and chemical degradation during both interface formation and electrical contact integration. It is also found that asymmetric membrane designs, such as a double cantilever, effectively suppress vibration-induced disorder due to wire bonding, resulting in sharp and hysteretic current–voltage characteristics. The junctions exhibit a twist-angle-dependent Josephson coupling with magnitudes comparable to the highest-performing devices reported to date, but achieved through a straightforward and versatile contact method, offering a scalable and adaptable platform for future applications. These findings highlight the importance of both interface and contact engineering in addressing reproducibility in superconducting van der Waals heterostructures.
An additional insulating layer between the electrode and semiconductor is beneficial to reduce the interfacial coupling and build two-dimensional (2D) Schottky contacts. Here, an intralayer strategy was proposed by using metallic 2D Bi 2 Sr 2 CaCu 2 O 8+δ (BSCCO) as contacts on 2D semiconductors. Inside a BSCCO monolayer, a conductive layer is sandwiched between insulating layers. Thus, the BSCCO contact has its own insulating layer, which is ultra-thin, single crystalline, and of high quality. This native layer could reduce the metal-induced gap state and thus weaken the interfacial Fermi level pinning effect. Such 2D Schottky diodes thus have barrier heights of 300 mV and a rectification ratio of 104. Furthermore, 2D metal-semiconductor field-effect transistors with BSCCO Schottky gate have a high on-off ratio, low leakage current, and low subthreshold swing value near the theoretical limit. The intralayer structure offers a new approach to improve the 2D Schottky junctions and has prospects in 2D electronics and optoelectronics.
The Ce(Co 1 -Fe ) 4.4 Cu 0.6 (0 ≤ x ≤ 0.19) is a composite, hard magnetic system that is based on the CaCu 5 -type structure (1:5). It shows both, unique magnetic and microstructural features that are essential for permanent magnets, e.g., exceptional squareness of the 2nd. quadrant of the magnetization loops and microstructural features typically needed for pinning. Samples solidified in alumina crucibles are coarse-grained and often clearly faceted and readily align in a magnetic field. X-ray, SEM, and TEM analyses show a 1:5-type single-phase material when quenched from high temperature, which, after heat treatment, transforms into a laminar coherent nanostructure through the formation of a dense array of extended intercalated regions. Furthermore, these extended intercalated regions are comprised of segments of the Ce 2 Ni 7 –type structure (2:7) which segregate into various closely related precipitates forming a nanostructure similar to the SmCo 5 - Sm 2 Co 17 composites seen in Sm-Co permanent magnets. Based on TEM and Lorentz microscopy of well-aligned single grain particles, the magnetic domains’ reversal mechanism is regulated by anisotropy fluctuations occurring along the easy direction of magnetization and strong exchange interactions between the matrix and defects (e.g.: stacking faults). Lorentz microscopy suggests the domain wall is not physically pinned by the defect, but rather is offset/deflected when it interacts with the defect. The Lorentz and magnetization data suggest that defects cause a bending of the moment away from the c axis inside the grains.
Twisted van derWaals (vdW) heterostructures offer a unique platform for engineering the efficient Josephson coupling between cuprate thin crystals harboring the nodal superconducting order parameter. Preparing the vdW heterostructures-based Josephson junction comprising stacked cuprates requires maintaining an ordered interface with preserved surface superconductivity. Here, we report the preparation of the Josephson junction out of the stacked Bi 2 Sr 2 CaCu 2 O 8+d crystals using the cryogenic dry transfer technique and encapsulating the junction with an insulating layer, that protects the interface during the electrical contacts evaporation at the 1×10 -6 mbar base pressure. We find that the Josephson critical current $I$ c has a maximum at low twist angles, comparable to that of the bulk intrinsic Josephson junctions, and is reduced by two orders of magnitude at twist angles close to 45°. In conclusion, the reduction of $I$ c occurs due to a mismatch between superconducting $d$-wave order parameters, which suppresses the direct Cooper pair tunneling.
Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems.
The density-density response in optimally doped Bi 2 Sr 2 CaCu 2 O 8+$x$ has recently been shown to exhibit conformal symmetry. Using, the experimentally inferred conformal dynamic susceptibility, we compute the resultant quantum Fisher information (QFI), a witness to multi-partite entanglement. For a Fermi liquid, we find that the QFI grows quadratically as the temperature increases, consistent then with the phase space available for scattering in the standard theory of metals. By contrast, the QFI in a strange metal increases as a power law at as the temperature decreases, but ultimately extrapolates to a constant at T=0. The constant is of the form, ω$^{2Δ}_g$, where Δ is the conformal dimension and ω g is the UV cutoff which is on the order of the pseudogap. As this constant depends on both UV and IR properties, it illustrates that multipartite entanglement in a strange metal exhibits UV-IR mixing, a benchmark feature of doped Mott insulators as exemplified by dynamical spectral weight transfer. We conclude with a discussion of the implication of our results for low-energy reductions of the Hubbard model.