Phase-sensitive determination of nodal d-wave order parameter in single-band and multiband superconductors

PHYSICAL REVIEW B 101 (2020) ARTN 214505

J Boeker, MA Sulangi, A Akbari, JCS Davis, PJ Hirschfeld, IM Eremin

Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity.

Proceedings of the National Academy of Sciences of the United States of America 117 (2020) 14805-14811

P Choubey, SH Joo, K Fujita, Z Du, SD Edkins, MH Hamidian, H Eisaki, S Uchida, AP Mackenzie, J Lee, JCS Davis, PJ Hirschfeld

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

Imaging the energy gap modulations of the cuprate pair-density-wave state.

Nature 580 (2020) 65-70

Z Du, H Li, SH Joo, EP Donoway, J Lee, JCS Davis, G Gu, PD Johnson, K Fujita

The defining characteristic1,2 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 tunnelling5, 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 Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8) (where a0 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 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 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 state6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+δ.

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging.

Proceedings of the National Academy of Sciences of the United States of America 117 (2020) 5222-5227

R Sharma, SD Edkins, Z Wang, A Kostin, C Sow, Y Maeno, AP Mackenzie, JCS Davis, V Madhavan

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 [Formula: see text] 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 [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] 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 [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond


DF Agterberg, JCS Davis, SD Edkins, E Fradkin, DJ Van Harlingen, SA Kivelson, PA Lee, L Radzihovsky, JM Tranquada, Y Wang

Magnetic field-induced pair density wave state in the cuprate vortex halo.

Science (New York, N.Y.) 364 (2019) 976-980

SD Edkins, A Kostin, K Fujita, AP Mackenzie, H Eisaki, S Uchida, S Sachdev, MJ Lawler, E-A Kim, JC Séamus Davis, MH Hamidian

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 2Q P , 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.

Visualizing electronic quantum matter

in Springer Handbooks, (2019) 1369-1390

K Fujita, MH Hamidian, PO Sprau, SD Edkins, JCS Davis

© Springer Nature Switzerland AG 2019. Modern quantum materials support a wide variety of exotic and unanticipated states of quantum matter and differ radically in phenomenology from conventional systems such as metals, semiconductors, band insulators, and ferromagnets. For example, quantum materials exhibit states such as electron liquid crystals, fluids of fractionalized quantum particles, quantum-entangled spin liquids, and topologically protected composite quantum particles. However, predictive theory is not fully developed for these forms of electronic quantum matter (EQM) and exploratory empirical research is required to discover and understand their properties. One of the most powerful and productive new techniques to achieve this is direct visualization of EQM at the atomic scale. For EQM, as with many highly complex systems in nature, seeing is believing and understanding. Here we describe the experimental, theoretical and analysis techniques of atomic-resolution spectroscopic imaging scanning tunneling microscopy (SI-STM) that allow such complex and enigmatic electronic/magnetic states to be directly visualized, identified, and understood.

Atomic and electronic structure of an epitaxial Nb2O3 honeycomb monolayer on Au(111)

Physical Review B American Physical Society 100 (2019) 125408

S Wang, J Goniakowski, C Noguera, M Castell

Machine learning in electronic-quantum-matter imaging experiments.

Nature 570 (2019) 484-490

Y Zhang, A Mesaros, K Fujita, SD Edkins, MH Hamidian, K Ch'ng, H Eisaki, S Uchida, JCS Davis, E Khatami, E-A Kim

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena1. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science2-5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)6-16, the next challenge is to apply this approach to experimental data-for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals18,19 are consistent with these observations.

Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

PHYSICAL REVIEW B 100 (2019) ARTN 224511

D Chakraborty, M Grandadam, MH Hamidian, JCS Davis, Y Sidis, C Pepin

Evidence for a vestigial nematic state in the cuprate pseudogap phase.

Proceedings of the National Academy of Sciences of the United States of America 116 (2019) 13249-13254

S Mukhopadhyay, R Sharma, CK Kim, SD Edkins, MH Hamidian, H Eisaki, S-I Uchida, E-A Kim, MJ Lawler, AP Mackenzie, JCS Davis, K Fujita

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| < [Formula: see text], where [Formula: see text] 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 T DW and T NE are unrelated to each other, both the DW and NE states always exhibit their maximum spectral intensity at the same energy, and using independent measurements that this is the PG energy [Formula: see text] 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.

Influence of the support on stabilizing local defects in strained monolayer oxide films

Nanoscale Royal Society of Chemistry 11 (2019) 2412-2422

S Wang, X Hu, J Goniakowski, C Noguera, M Castell

Two-dimensional materials with a honeycomb lattice, such as graphene and hexagonal boron nitride, often contain local defects in which the hexagonal elements are replaced by four-, five-, seven-, and eight-membered rings. An example is the Stone-Wales (S-W) defect, where a bond rotation causes four hexagons to be transformed into a cluster of two pentagons and two heptagons. A further series of similar defects incorporating divacancies results in larger structures of non-hexagonal elements. In this paper, we use scanning tunneling microscopy (STM) and density functional theory (DFT) modeling to investigate the structure and energetics of S-W and divacancy defects in a honeycomb (2 × 2) Ti2O3 monolayer grown on an Au(111) substrate. The epitaxial rumpled Ti2O3 monolayer is pseudomorphic and in a state of elastic compression. As a consequence, divacancy defects, which induce tension in freestanding films, relieve the compression in the epitaxial Ti2O3 monolayer and therefore have significantly lower energies when compared with their freestanding counterparts. We find that at the divacancy defect sites there is a local reduction of the charge transfer between the film and the substrate, the rumpling is reduced, and the film has an increased separation from the substrate. Our results demonstrate the capacity of the substrate to significantly influence the energetics, and hence favor vacancy-type defects, in compressively strained 2D materials. This approach could be applied more broadly, for example to tensile monolayers, where vacancy-type defects would be rare and interstitial-type defects might be favored.

Magnetic monopole noise

Nature Springer Nature 571 (2019) 234-239

R Dusad, F Kirschner, JC Hoke, BR Roberts, A Eyal, F Flicker, GM Luke, S Blundell, J Davis

Magnetic monopoles1-3 are hypothetical elementary particles with quantized magnetic charge. In principle, a magnetic monopole can be detected by the quantized jump in magnetic flux that it generates upon passage through a superconducting quantum interference device (SQUID)4. Following the theoretical prediction that emergent magnetic monopoles should exist in several lanthanide pyrochlore magnetic insulators5,6, including Dy2Ti2O7, the SQUID technique has been proposed for their direct detection6. However, this approach has been hindered by the high number density and the generation-recombination fluctuations expected of such thermally generated monopoles. Recently, theoretical advances have enabled the prediction of the spectral density of magnetic-flux noise from monopole generation-recombination fluctuations in these materials7,8. Here we report the development of a SQUID-based flux noise spectrometer and measurements of the frequency and temperature dependence of magnetic-flux noise generated by Dy2Ti2O7 crystals. We detect almost all of the features of magnetic-flux noise predicted for magnetic monopole plasmas7,8, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence. Moreover, comparisons of simulated and measured correlation functions of the magnetic-flux noise indicate that the motions of magnetic charges are strongly correlated. Intriguingly, because the generation-recombination time constant for Dy2Ti2O7 is in the millisecond range, magnetic monopole flux noise amplified by SQUID is audible to humans.

Maximising the resolving power of the scanning tunneling microscope

Advanced Structural and Chemical Imaging SpringerOpen 4 (2018) 7-

L Jones, S Wang, X Hu, S ur Rahman, M Castell

The usual way to present images from a scanning tunneling microscope (STM) is to take multiple images of the same area, to then manually select the one that appears to be of the highest quality, and then to discard the other almost identical images. This is in contrast to most other disciplines where the signal to noise ratio (SNR) of a data set is improved by taking repeated measurements and averaging them. Data averaging can be routinely performed for 1D spectra, where their alignment is straightforward. However, for serial-acquired 2D STM images the nature and variety of image distortions can severely complicate accurate registration. Here, we demonstrate how a significant improvement in the resolving power of the STM can be achieved through automated distortion correction and multi-frame averaging (MFA) and we demonstrate the broad utility of this approach with three examples. First, we show a sixfold enhancement of the SNR of the Si(111)-(7 × 7) reconstruction. Next, we demonstrate that images with sub-picometre height precision can be routinely obtained and show this for a monolayer of Ti2O3 on Au(111). Last, we demonstrate the automated classification of the two chiral variants of the surface unit cells of the (4 × 4) reconstructed SrTiO3(111) surface. Our new approach to STM imaging will allow a wealth of structural and electronic information from surfaces to be extracted that was previously buried in noise.

Common glass-forming spin-liquid state in the pyrochlore magnets Dy2Ti2 O7 and Ho2Ti2 O7

Physical Review B 98 (2018)

AB Eyvazov, R Dusad, TJS Munsie, HA Dabkowska, GM Luke, ER Kassner, JCS Davis, A Eyal

© 2018 American Physical Society. Despite a well-ordered pyrochlore crystal structure and strong magnetic interactions between the Dy3+ or Ho3+ ions, no long-range magnetic order has been detected in the pyrochlore titanates Ho2Ti2O7 and Dy2Ti2O7. To explore the actual magnetic phase formed by cooling these materials, we measure their magnetization dynamics using toroidal, boundary-free magnetization transport techniques. We find that the dynamical magnetic susceptibility of both compounds has the same distinctive phenomenology, which is indistinguishable in form from that of the dielectric permittivity of dipolar glass-forming liquids. Moreover, Ho2Ti2O7 and Dy2Ti2O7 both exhibit microscopic magnetic relaxation times that increase along the super-Arrhenius trajectories analogous to those observed in glass-forming dipolar liquids. Thus, upon cooling below about 2 K, Dy2Ti2O7 and Ho2Ti2O7 both appear to enter the same magnetic state exhibiting the characteristics of a glass-forming spin liquid.

Phase diagram of Bi2Sr2CaCu2O8+δ revisited.

Nature communications 9 (2018) 5210-

IK Drozdov, I Pletikosić, C-K Kim, K Fujita, GD Gu, JCS Davis, PD Johnson, I Božović, T Valla

In cuprate superconductors, the doping of carriers into the parent Mott insulator induces superconductivity and various other phases whose characteristic temperatures are typically plotted versus the doping level p. In most materials, p cannot be determined from the chemical composition, but it is derived from the superconducting transition temperature, Tc, using the assumption that the Tc dependence on doping is universal. Here, we present angle-resolved photoemission studies of Bi2Sr2CaCu2O8+δ, cleaved and annealed in vacuum or in ozone to reduce or increase the doping from the initial value corresponding to Tc = 91 K. We show that p can be determined from the underlying Fermi surfaces and that in-situ annealing allows mapping of a wide doping regime, covering the superconducting dome and the non-superconducting phase on the overdoped side. Our results show a surprisingly smooth dependence of the inferred Fermi surface with doping. In the highly overdoped regime, the superconducting gap approaches the value of 2Δ0 = (4 ± 1)kBTc.

Imaging orbital-selective quasiparticles in the Hund's metal state of FeSe.

Nature materials 17 (2018) 869-874

A Kostin, PO Sprau, A Kreisel, YX Chong, AE Böhmer, PC Canfield, PJ Hirschfeld, BM Andersen, JCS Davis

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 [Formula: see text], 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.

In-situ angle-resolved photoemission spectroscopy of copper-oxide thin films synthesized by molecular beam epitaxy

Journal of Electron Spectroscopy and Related Phenomena (2018)

CK Kim, IK Drozdov, K Fujita, JCS Davis, I Božović, T Valla

© 2018 Elsevier B.V. Angle-resolved photoemission spectroscopy (ARPES) is the key momentum-resolved technique for direct probing of the electronic structure of a material. However, since it is highly surface-sensitive, it has been applied to a relatively small set of complex oxides that can be easily cleaved in ultra-high vacuum. Here we describe a new multi-module system at Brookhaven National Laboratory (BNL) in which an oxide molecular beam epitaxy (OMBE) is interconnected with an ARPES and a spectroscopic-imaging scanning tunneling microscopy (SI-STM) module. This new capability largely expands the range of complex-oxide materials and artificial heterostructures accessible to these two most powerful and complementary techniques for studies of electronic structure of materials. We also present the first experimental results obtained using this system — the ARPES studies of electronic band structure of a La2-xSrxCuO4 (LSCO) thin film grown by OMBE.

Pair density waves in superconducting vortex halos

PHYSICAL REVIEW B 97 (2018) ARTN 174510

Y Wang, SD Edkins, MH Hamidian, JCS Davis, E Fradkin, SA Kivelson

Single-layer TiOx reconstructions on SrTiO3 (111): (√7 × √7)R19.1°, (√13 × √13)R13.9°, and related structures

Surface Science Elsevier 675 (2018) 36-41

TK Andersen, S Wang, M Castell, DD Fong, LD Marks

The atomic structures of two reconstructions, (√7 × √7)R19.1° and (√13 × √13)R13.9°, on the SrTiO3 (111) surface were determined using a combination of density functional theory and scanning tunneling microscopy data and APW + lo density functional theory minimizations and simulations. These reconstructions belong to the same structural family made up of an interconnected, single layer of edge-sharing TiO6 and TiO5[] octahedra. This family of reconstructions between 0.5 and 1.5 excess TiO2, representing the lowest-reported TiO2 coverages for reconstructions on this surface. This family is found to include the previously-solved (2 × 2)a reconstruction. They all follow a simple rule for surface composition, which serves as a tool for better understanding and predicting the structure of other reconstructions of arbitrary surface unit cell size on SrTiO3 (111). This reconstruction family and the calculations of surface energies for different hypothesis structures also shed light on the structure of Schottky defects observed on these reconstructed SrTO3 (111) surfaces.