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		A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories thus explaining the anomalous color of magnetic monopole noise spectra. Applying these novel concepts to field-driven magnetic monopole currents predicts a characteristic dichotomy in both their DC and AC dynamics. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy₂Ti₂O₇, we measure φ(t), the time-dependence of magnetic flux threading the sample when a net monopole current J(t)=φ(t)/μ₀ is generated by applying an external magnetic field B₀(t). These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time-constants before and after t∼600 μs from monopole current initiation. Application of sinusoidal magnetic fields B₀(t)=Bcos(ωt) generates oscillating monopole currents whose loss angle θ(f) exhibits a characteristic transition at frequency f≈1.8 kHz over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t∼600 μs. An accurate atomic-scale understanding of the mechanisms of magnetic monopole currents in spin-ice is thereby established. This complex phenomenology represents a new form of heterogeneous dynamics generated by the interplay of fractionalization and local spin configurational symmetry.

		published article (Proc. Nat'l Acad. Sci. 121, 2320384121 - May 2024)


		No state of matter can be defined categorically by what it is not; yet spin liquids are often conjectured to exist based on the nonexistence of magnetic order as T→0. An emerging concept designed to circumvent this ambiguity is to categorically identify each spin liquid type by using its spectrum of spontaneous spin noise. Here we introduce such a spectroscopy to spin liquid studies by considering Ca₁₀Cr₇O₂₈. This is a spin liquid, but whether classical or quantum and in which specific state, are unknown. By enhancing the flux-noise spectrometry techniques introduced for magnetic monopole noise studies, here we measure the time and temperature dependence of spontaneous flux φ(t,T) and thus magnetization M(t,T) of Ca₁₀Cr₇O₂₈ samples. The resulting power spectral density of magnetization noise S_M(ω,T) along with its correlation function C_M(t,T), reveal intense spin fluctuations spanning frequencies 0.1Hz ≤ ω/2π ≤ 50kHz, and that S_M(ω,T)∝ω^-α(T) with 0.84<α(T)<1.04. Predictions for quantum spin liquids yield a frequency-independent spin-noise spectrum, clearly inconsistent with this phenomenology. However, when compared to Monte Carlo simulations for a 2D spiral spin liquid state that are accurately parameterized to describe Ca₁₀Cr₇O₂₈, comprehensive quantitative correspondence with the data including S_M(ω,T), C_M(t,T) and magnetization variance σ_M²(T) fingerprint the state of Ca₁₀Cr₇O₂₈ as a spiral spin liquid.

		published article (arXiv 2405.02075 - May 2024)


		The primordial ingredient of cuprate superconductivity is the CuO₂ unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d⁹ and 3d¹⁰ configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p⁶ 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 2p⁶ and 3d¹⁰ orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO₂ 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 ∼50meV, in underdoped CuO₂.

		published article (Nature Materials 23, 492 - April 2024)


		The properties of superconducting materials, their perfectly dissipationless electronics, perfect diamagnetism, and macroscopic quantum mechanical dynamics are all the products of the formation of a macroscopic quantum fluid of electron pairs. To better understand this, we have developed the first scanned Josephson/Andreev tunneling microscopes (SJTM/SATM) which provide direct access to the macroscopic quantum electron pair condensate. Since the 1960s the possibility of a crystalline superconducting phase within the overall fluid has been discussed with great interest in the superconducting community. Such a state should manifest itself as a spatially periodic electron-pair crystal; we call this state a Pair Density Wave (PDW). For years the superconducting community had suggested that such a PDW state might exist in the high-temperature superconductor Bi₂Sr₂CaCu₂O_8+x. In 2016 our group developed our first SJTM system and subsequently detected this long predicted PDW state. Since then we have discovered PDWs in several other materials including in the transition metal dichalcogenide superconductor NbSe₂. Recently our focus of study has been the spin-triplet topological superconductor UTe₂. This class of superconductor should exhibit many unprecedented electronic properties including fractionalized electronic states relevant to quantum information processing. In UTe₂ we searched for a PDW state, by visualizing the pairing energy-gap with μeV-scale energy-resolution made possible by a superconducting SATM tip. We discovered three PDWs at incommensurate wavevectors P_i = 1,2,3 that are indistinguishable from the wavevectors Q_i = 1,2,3 of the prevenient CDW. From these observations and given UTe₂ as a spin-triplet superconductor, this PDW state appears to be the first known spin-triplet pair density wave.

		published article (Nature 618, 921 - June 2023)


		A Kondo lattice is often electrically insulating at low temperatures. However, several recent experiments have detected signatures of metallicity within this Kondo insulating phase. In this study, we visualized the real-space charge landscape within a Kondo lattice with atomic resolution using a scanning tunneling microscope. We discovered nanometer-scale puddles of metallic conduction electrons centered around uranium-site substitutions in the heavy-fermion compound uranium ruthenium silicide (URu₂Si₂) and around samarium-site defects in the topological Kondo insulator samarium hexaboride (SmB₆). These defects disturbed the Kondo screening cloud, leaving behind a fingerprint of the metallic parent state. Our results suggest that the three-dimensional quantum oscillations measured in SmB₆ arise from Kondo-lattice defects, although we cannot exclude other explanations.

		published article (Science 379, 1214-1218 - March 2023)


		The elementary CuO₂ plane sustaining cuprate high-temperature superconductivity occurs typically at the base of a periodic array of edge-sharing CuO₅ pyramids. Virtual transitions of electrons between adjacent planar Cu and O atoms, occurring at a rate t/ℏ and across the charge-transfer energy gap ε, generate “superexchange” spin–spin interactions of energy J ≈ 4t⁴/ε³ in an antiferromagnetic correlated-insulator state. However, hole doping this CuO₂ plane converts this into a very-high-temperature superconducting state whose electron pairing is exceptional. A leading proposal for the mechanism of this intense electron pairing is that, while hole doping destroys magnetic order, it preserves pair-forming superexchange interactions governed by the charge-transfer energy scale ε. To explore this hypothesis directly at atomic scale, we combine single-electron and electron-pair (Josephson) scanning tunneling microscopy to visualize the interplay of ε and the electron-pair density n_p in Bi₂Sr₂CaCu₂O_8+x. The responses of both ε and n_p to alterations in the distance δ between planar Cu and apical O atoms are then determined. These data reveal the empirical crux of strongly correlated superconductivity in CuO₂, the response of the electron-pair condensate to varying the charge-transfer energy. Concurrence of predictions from strong-correlation theory for hole-doped charge-transfer insulators with these observations indicates that charge-transfer superexchange is the electron-pairing mechanism of superconductive Bi₂Sr₂CaCu₂O_8+x.

		published article (Proc. Nat'l Acad. Sci. 119, 2207449119 - September 2022)


		Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi₂Sr₂CaCu₂O_8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi₂Sr₂CaCu₂O_8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

		published article (Proc. Nat'l Acad. Sci. 119, 2206481119 - July 2022)


		An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO₂ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap Δ_P(r) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature Λ_P(q) in wavevector space. By studying strongly underdoped Bi₂Sr₂CaDyCu₂O₈ at hole-density ~0.08 in the superconductive phase, we detect the 8a₀-periodic Δ_P(r) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find evolution of the scattering interference signature Λ(q) that is predicted specifically for the temperature dependence of an 8a₀-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi₂Sr₂CaDyCu₂O₈ pseudogap phase.

		published article (Nature Communications 12, 6087 - Oct 2021)


		Pair density wave (PDW) states are defined by a spatially modulating superconductive order parameter. To search for such states in transition-metal dichalcogenides (TMDs), we used high-speed atomic- resolution scanned Josephson-tunneling microscopy. We detected a PDW state whose electron-pair density and energy gap modulate spatially at the wave vectors of the preexisting charge density wave (CDW) state. The PDW couples linearly to both the s-wave superconductor and the CDW and exhibits commensurate domains with discommensuration phase slips at the boundaries, conforming those of the lattice-locked commensurate CDW. Nevertheless, we found a global δΦ ≈ ±2π/3 phase difference between the PDW and CDW states, possibly owing to the Cooper-pair wave function orbital content. Our findings presage pervasive PDW physics in the many other TMDs that sustain both CDW and superconducting states.

		published article (Science 372, 1447 - June 2021)


		Although rapid advances have occurred in quantum fluid flow imaging, the velocity field v(r) of a charged superfluid - a superconductor - had never been visualized. We used superconductive–tip scanning tunneling microscopy to image the electron-pair density ρ_s(r) and velocity v_s(r) fields of the flowing electron-pair fluid in superconducting NbSe₂. Imaging v_s(r) surrounding a quantized vortex finds speeds reaching 10,000 km/hr. Together with independent imaging of ρ_s(r) via Josephson tunneling, we visualize the supercurrent density j_s(r)≡ ρ_s(r)v_s(r), which peaks above 3×10⁷ A/cm². The spatial patterns in electron-pair fluid flow and magneto-hydrodynamics reveal hexagonal structures co-aligned to the crystal lattice and quasiparticle bound states, as long anticipated from NbSe₂ crystal symmetry. This demonstration of atomic-scale imaging of v_s(r) for charged superfluid paves the way for electronic fluid flow visualization in other quantum fluids.

		published article (Nature Materials 20, 1480 - August 2021)


		The quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTIs) when a Dirac mass gap opens in the spectrum of the topological surface states (SSs). Unaccountably, although the mean mass gap can exceed 28 meV (or ~320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ to that of its nonmagnetic parent (Bi_0.1Sb_0.9)₂Te₃, to explore the cause. In (Bi_0.1Sb_0.9)₂Te₃, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr_0.08(Bi_0.1Sb_0.9)_1.92Te₃ with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 µeV for nanoscale regions separated by <1 µm. This fundamentally limits the fully quantized anomalous Hall effect in Sb₂Te₃-based FMTI materials to very low temperatures.

		published article (Nano Lett. 2020, 20, 8001-8007 - Nov 2020)


		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 high temperature superconducting cuprates (ARCMP 11, 231 (2020) ). Although the existence of a PDW in cuprates was discovered by using Cooper-pair tunneling (Nature 532, 343 (2016) ), its signature in single-electron tunneling of periodic Δ(r) modulations, proved elusive. Now, by using a new approach, we detect strong Δ(r) modulations in Bi₂Sr₂CaCu₂O_8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ 2π/a₀ (1/8,0); 2π/a₀ (0,1/8). Simultaneous imaging of the local-density-of-states N(r,E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated for a coexisting superconductor and PDW. Overall, this provides strong confirmation that a PDW state coexists with superconductivity in the canonical cuprate Bi₂Sr₂CaCu₂O_8+δ. These results were published in Nature 580, 65-70 (April 2020)..

		published article - download PDF (Nature 580, 6570 - April 2020)


		Magnetic monopoles are highly elusive elementary particles exhibiting quantised magnetic charge. The prospect for studying them has brightened in recent years with the theoretical realisation that, in certain classes of magnetic insulators, the thermally excited states exhibit all the characteristics of magnetic monopoles. Specifically, recent theories predicted that these magnetic insulators should spontaneously generate wildly and randomly fluctuating magnetic fields as the monopoles move around, but with a magnitude near one billionth of the Earth’s field. Using an exquisitely sensitive magnetic-field-noise spectrometer based on a superconducting quantum interference device (SQUID), we detected from crystals of Dy₂Ti₂O₇ virtually all the predicted features of the magnetic noise coming from a dense fluid of magnetic monopoles. Extraordinarily, because this magnetic monopole noise occurs in the frequency range below 20kHz, when amplified by the SQUID it is actually audible to humans as exemplified in this video clip.

		published article - download PDF (Nature 571, 234 - Jul 2019) See also - Oxford Science Blog / Phys.org


		A collaboration of experimental physicists led by Prof. JC Séamus Davis (University of Oxford), theoretical physicists led by Prof. Eun-Ah Kim (Cornell University), and computer scientists led by Prof. E. Kathami (San Jose State University), developed and trained a new Machine Learning (ML) protocol, based on a suite of artificial neural networks (ANN), that is designed to recognize different types of electronic ordered states which are hidden within electronic quantum matter image-arrays. Electronic quantum matter studies using automated scientific instrumentation and large-scale data acquisition are now generating data sets of such volume and complexity as to defy human analysis. For example modern scanning tunneling microscopy (STM) visualization of electronic quantum matter (EQM) yields dense arrays of atomic-scale, electronic-structure images, that are often astonishingly complex. The ANN suite analyzed one of the Davis Group experimental EQM image archives, spanning a wide range of electron densities and energies, in carrier-doped cuprate Mott insulators. The ANN suite discovered, throughout all the noisy and complex data, the features of a very specific ordered state of EQM: a Vestigial Nematic State. This is a milestone for general scientific technique in that ANN’s can process and identify specific broken symmetries of highly complex image-arrays from non-synthetic experimental EQM data. It opens the immediate prospect of additional ML-driven scientific discovery in EQM studies.

		published article - download PDF (Nature 570, 484 - Jun 2019) See also - Phys.org / Science Daily / EE News Analog EE journal / Silicon Republic / Science Codex


		Superconductivity occurs when electrons form pairs of opposite spin and opposite momentum, and these "Cooper pairs" condense into a homogeneous electronic fluid. However, theorists have recently realized that these electron pairs might also crystallize into a “pair density wave” (PDW) state where the density of pairs modulates periodically in space. Intense theoretical interest has emerged in whether such a PDW is the competing phase in cuprates. To search for evidence of such a PDW state we suppress the homogeneous superconductivity using high magnetic field and visualize the electronic structure of the new phase which appears. Under these circumstances we discovered modulations in the density of electronic states containing multiple signatures of a PDW state. The phenomena are in detailed and excellent agreement with theoretical predictions for a field-induced primary PDW state. These data indicate that it is a PDW state which competes with superconductivity in cuprates and that it dominates in the high-field regime.

		published article - download PDF (Science 364, 976 - Jun 2019) See also - Phys.org / Science Daily / EurekaAlert



		In the cuprate pseudogap phase, an energy gap of unknown mechanism opens, and both an electronic nematic phase (NE) and a density-wave (DW) phase appear. Perplexingly, the DW, which should generate an energy gap, appears without any new gap opening; and the NE, which should be incapable of opening an energy gap, emerges coincident with the pseudogap opening. Recently, however, it was demonstrated theoretically that a disordered unidirectional DW can generate a vestigial nematic (VN) phase. If the cuprate pseudogap phase were in such a VN state, the energy gap of the NE and DW should be identical to each other and to the pseudogap. We report discovery of such a phenomenology throughout the phase diagram of underdoped Bi₂Sr₂CaCu₂O₈. (click the image for enlarged version)

		published article - download PDF (Proc. Nat'l Aacd. Sci. 116, 13249 - Jul 2019) Commentary by Kivelson & Lederer (PDF)


		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 active 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 Z_m appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that Z_xy<Z_xz<<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.

		published article - download PDF (Nature Materials 17, 869 - Oct 2018) News and Views article by Massimo Capone (PDF) See also - BNL News


		The cuprate pseudogap exhibits an unidentified unconventional density modulation, which is widely believed to be charge density wave (CDW). Recent theory indicates that it could actually be an electron-pair density wave (PDW) state. Here we demonstrate theoretically that a biaxial PDW state with 8a₀ periodicity may provide a compelling quantitative explanation for much of the observed quantum oscillation data.

		published article - download PDF (Proc. Nat'l Aacd. Sci. 115, 5389 - 22 May 2018)


		In Cu-based HTS materials, the undoped phase is a robust Mott insulator while, in Fe-based HTS materials, the undoped phase is generally not an insulator at all. Thus, proximity to a Mott insulator appears neither indispensable nor universal to HTS. However, theory predicts that Fe-based materials could still be governed by strong electronic correlations proximate to a Mott insulator if an orbital selective Mott phase (OSMP) exists. A key signature of OSMP would be orbital selective Cooper pairing wherein electrons of a specific orbital character predominantly form the Cooper pairs. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry and the corresponding superconducting energy gaps of the famous iron-based superconductor FeSe. We show that both gaps are extremely anisotropic but nodeless, and they exhibit gap maxima oriented orthogonally in momentum space. By introducing 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. (click the image for enlarged version)

		published article - download PDF (Science 357, 75 - 7 Jul 2017) See also - BNL News / Phys.org / Science Daily Next Big Future / Irish Times / Chemie.de Journal Club for Condensed Matter Physics


		Phase-optimization analysis of the phase-resolved electronic structure reveals a virtually doping-independent locking of the local charge density modulation with four crystal unit cell periodicity throughout the underdoped phase diagram of the canonical cuprate Bi₂Sr₂CaCu₂O_8+x.

		published article - download PDF (Proc. Nat'l Acad. Sci. 113, 12661 - 8 Nov 2016)


		Theory predicts that the cuprate pseudogap phase should contain a spatially modulating Cooper-pair density wave (PDW) state. This would be akin to the famous FFLO state of spatially modulated conventional superconductivity, but generated by strong correlations instead of high magnetic fields. To search for a cuprate PDW, we developed a millikelvin scanned Josephson tunneling microscope (SJTM) system that can image Cooper-pair tunneling from a d-wave superconducting STM tip to the Cooper-pair condensate of Bi₂Sr₂CaCu₂O₈. Nanometer resolution condensate visualization then revealed a Cooper-pair density wave modulating along the Cu-O bond directions at wavevectors Q_p ~ (1/4,0)2π/a₀; (0,1/4)2π/a₀.

		published article - download PDF (Nature 532, 343 - 21 Apr 2016) See also - BNL news / Cornell Chronicle / Phys.org EurekaAlert / Newswise / Science Daily / Sci-news Lainformacion / TechnoBuffalo / Ooyuz Headlines & Global news / Kavli Foundation The Science Explorer * On Korean media : Chosun / NocutNews / Yohhap


		Energy-resolved sublattice visualization of the electronic structure reveals that the d-form-factor density wave states in underdoped cuprate involve particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in momentum space where the pseudogap opens.

		published article - download PDF (Nature Physics 12, 150 - Feb 2016) See also - BNL news / Nanowerk / Phys.org EurekaAlert / Newswise / Electronics weekly


		A classic "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Such liquids have specific identifiers including microscopic relaxation times diverging on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function, and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the magnetic state of the frustrated pyrochlore Dy₂Ti₂O₇ has become of wide interest. By introducing novel magnetization transport measurement techniques, an improved understanding of the time- and frequency-dependent magnetization dynamics of Dy₂Ti₂O₇ is achieved. We find that this system exhibits a virtually universal HN form for the magnetic susceptibility, a general KWW form for the real-time magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with the VTF trajectory. Low-temperature Dy₂Ti₂O₇ therefore exhibits all the characteristics expected of a supercooled classical spin-liquid; we propose that this is the correct description of its magnetic state.

		published article - download PDF (Proc. Nat'l. Acad. Sci. 112, 8549 - Jul 2015)


		SI-STM study visualizes the atomic-scale effects of irradiating Fe(Se,Te) superconductor with high-energy heavy ions. Simultaneous imaging of defects, superconducting order parameter and vortex configuration reveals how columnar and point defects pin quantum vortices allowing high critical current density.

		published article - download PDF (Sci. Adv. 1, e1500033 - May 2015) See also - BNL news / Nanowerk / Phys.org Eurekalert / Newswise / Laboratory Equipment


		By introducing the Dirac-mass 'gapmap' technique, i.e. simultaneously visualizing the mass gap Δ(r) and the ferromagnetic dopant atoms in the atomic-scale, we discover intense nanoscale disorder in the Dirac-mass and demonstrate that this is directly related to fluctuations in the magnetic-dopant atom density n(r). (click the image for expanded version with scale bars)

		published article - download PDF - movie [wmv] (Proc. Nat'l Acad. Sci. 112, 1316 - Feb 2015) See also - BNL news / Cornell Chronicle Phys.org / Eurekalert / Newswise Topological Insulator Today / ScienceSeeker New Materials News / Nanowerk Controlled Environments Magazine


		Quasiparticle Interference (QPI) imaging technique reveals that electron-boson interaction in LiFeAs superconductivity has momentum-space anisotropic self-energy 'fingerprint' of anti-ferromagnetic spin fluctuations.

		published article - download PDF (Nature Physics 11, 177 - Feb 2015) See also - Phys.org / R&D Magazine Cornell Chronicle


		Direct sublattice-phase-resolved imaging of the electronic structure in both Bi₂Sr₂CaCu₂O_8+δ and Ca_2-xNa_xCuO₂Cl₂ reveals that the cuprate pseudogap phase exhibits a previously unknown electronic state: a d-symmetry form factor density wave. (click the image for enlarged version)

		published article - download PDF (Proc. Nat'l. Acad. Sci. 111, E3026 - Jul 2014) See also - Phys.org / Quanta Magazine


		Quasiparticle interference imaging of heavy fermions reveals the momentum-space structure of the f-electron magnetism in CeCoIn₅. Using this novel information, we then demonstrate directly and quantitatively that the Cooper pairing in this heavy fermion superconductor is mediated by the f-electron magnetic interactions.

		published article - download PDF (Proc. Nat'l. Acad. Sci. 111, 11663 - Aug 2014) See also - Science Editor's choice Superconductor Week (pg. 13) / Red Orbit Int'l Business Times / Science Codex Cornell Chronicle / Next big future


		Abrupt transition in Bi₂Sr₂CaCu₂O_8+δ Fermi surface topology from broken 'arc' to full closed contour is visualized with SI-STM to occur at the same critical doping level where d-form factor density wave disappears. (Click the image for enlarged version)

		published article - download PDF (Science 344, 612 - May 201 4) See also - DoE headliner (click to see captured image) (click here for the illustration only) / 2014's top ten achievements at BNL BNL news / Phys.org / Eurekalert / Nanowerk Nanotechnology Now / Science Codex / Wired ScienceDaily / Newswise / Lab. Equipment OneNewsPage / News.nom.co / StarDrive Lab Manager / DailyFusion / SC Week (pg. 8)


		Rich ordering phenomena with distinct symmetry observed in proximity to the superconductivity of Cu-based / Fe-based / heavy-fermion compounds are explained in a unified theory based on antiferromagnetic interaction. (Click the image for enlarged version)

		published article - download PDF (Proc. Nat'l. Acad. Sci. 110, 17623 - Oct 2013) See also - BNL headliner BrightSurf / Ocnus / ScienceDaily / Phys.org DemocraticUnderground / Blodic.us / Nanotechnology Now / ECN magazine / Press-News / Red Orbit / R&D magazine/


		Complex band structure and the Fermi surface of CeCoIn₅ is revealed in detail with QPI. Also visualized for the first time in heavy fermion superconductor compound is the superconducting energy gaps, shown to be consistent with d_x2-y2 symmetry.

		published article - download PDF (Nature Physics 9, 468 - Aug 2013) See also - News and Views by Taillefer DoE headliner (click to see captured image) Phys.org / ScienceDaily / EurekAlert / Eureka! Science News / ScienceCodex / Newswise / Nanotechnology Now


		Dopant-induced impurity states in underdoped iron-based superconductor Ca(Fe_1-xCo_x)₂As₂, resulting quasiparticle scattering, and its relation to the nematic transport of the parent phase are studied with SI-STM and ARPES.

		published article - download PDF (Nature Physics 9, 220 - Apr 2013) See also - TechConnect / Product Design & Development / Science Newsline / Phys.org / ECN magazine / LabSpaces.net / Innovations report / Red orbit / Nanotechnology now / R & D magazine


		Zinc impurity states inside Bi₂Sr₂CaCu₂O_8+δ are located to pico-meter scale, providing phase information for intra-unit-cell Bragg-peak Fourier analysis.

		published article - download PDF (New Journal of Physics 14, 053017 - May 2012)


		Anisotropic energy gaps of iron-based superconductor LiFeAs are determined from intra-band QPI analysis.

		published article - download PDF (Science 336, 563 - May 2012) See also - Article on Cornell Chronicle Article on EurekaAlert Article on ScienceDaily


		Electronic structure of Kondo holes in the Th-doped heavy Fermion compound URu₂Si₂ is visualized with STM to find heterogeneous hybridization strength in nanoscale.

		published article - download PDF (Proc. Nat'l Acad. Sci. 108, 18233 - Nov 2011) See also - Commentary by J. D. Thompson Author Interview with Kavli Foundation Article on Physorg.com Article on Eurekaorg.com News on ScienceDaily


		The 2π topological defects in the pseudogap phase of underdoped Bi₂Sr₂CaCu₂O_8+δ and the relationship between the coexistent smectic and intra-unit-cell broken symmetries are studied.

		published article - download PDF (Science 333, 426 - Jul 2011) See also - News on R&D Magazine Binghamton University Research News Article on Physorg.com


		Interplay of rotational, relaxational and shear dynamics in solid ⁴He is investigated.

		published article - download PDF (Science 332, 821 - May 2011) See also - Nature NewsBlog by E. S. Reich ScienceDaily news Physics Today The Dayside by Charles Day (Physics Today online editor)


		Electronic nematicity within unit cell in Bi₂Sr₂CaCu₂O_8+δ was studied with SI-STM.

		published article - download PDF (Nature 466, 347 - July 2010)


		Heavy-fermion compound URu₂Si₂ is investigated in both real and momentum space with spectroscopic imaging (SI) - STM.

		published article - download PDF (Nature 465, 570 - June 2010) See also - News and Views by A. J. Schofield (Nature 465, 553)


		Nematic electronic structure in the parent state of the iron-based superconductor Ca(Fe_1-xCo_x)₂As₂ is revealed by spectroscopic imaging (SI) STM measurements in both real-space and momentum-space.

		published article - download PDF (Science 327, 181 - January 2010) See also - Perspectives by E. Fradkin & S. A. Kivelson (Science 327, 155) Article on NewScientist by Colin Barras


		Heavy d-electron quasiparticle interferenc(QPI) patterns in k-space and sub-atomic electronic structure in r-space are revealed by spectroscopic imaging(SI) STM measurements on Sr₃Ru₂O₇. A relevant band is also identified from the complicated band structure of Sr₃Ru₂O₇ by inverting dispersing QPI patterns.

		published article - download pdf (Nature Physics 5, 800 - September 2009)


		Quasiparticle interference imaging in the cuprate pseudogap state (T>Tc) reveals the spectro-scopic 'fingerprint' of phase incoherent d-wave superconductivity. (Click image to enlarge)

		published article - download PDF (Science 325, 1099 - August 2009) See also - Perspectives by Michael R. Norman (Science 325, 1080) Press release by Cornell University


		Relaxation study of ⁴He in the solid phase reveals ultraslow dynamics, evidencing the formation of superglass state.

		published article - download PDF (Science 324, 632 - May 2009) See also - Perspectives by John Saunders (Science 324, 601) News by Jon Cartwright (Physics World, Apr 30 2009) Commentary by Tony Leggett (Journal Club for Conensed matter Physics) Article on Physics Today (8 Jun 2009)


		Investigation of the vanishing pattern of Cooper pairs in Bi₂Sr₂CaCu₂O_8+δ, approaching the Mott insulator.

		published article - download PDF (Nature 454, 1072 - Aug 2008) See also - Review by Tetsuo Hanaguri (Nature 454, 1062) Editor's summary


		Evolution of the electronic excitation spectrum with strongly diminishing hole density in superconducting Bi₂Sr₂CaCu₂O_8+δ.

		published article - download PDF (Nature Physics 4, 319 - Apr 2008) See also - review by Eric Hudson (Nature Physics 4, 271)


		Imaging the impact on cuprate superconductivity of varying the interatomic distances within individual crystal cells .

		published article - download PDF (Proc. Nat'l Acad. Sci. Vol. 105, no. 9, 3203 - Mar 2008) See also - comment by Michael R. Norman (Proc. Nat'l Acad. Sci. Vol. 105, no. 9, 3173)


		Quasiparticle interference of nearly optimally doped Ca_2-xNa_xCuO₂Cl₂ was studied using STS.

		published article - download PDF (Nature Physics 3, 865 - Oct 2007)


		Atomic resolution tunneling asymmetry imaging: an intrinsic Cu-O-Cu bond-centered electronic glass with disperse 4a₀-wide unidirectional domains in underdoped Ca_1.88Na_0.12CuO₂Cl₂ and Bi₂Sr₂Dy_0.2Ca_0.8Cu₂O_8+δ

		published article - cover story - download PDF (Science 315, 1380 - Mar 2007) Click the left image to see the movie.


		The pseudogap state in cuprate superconductors La_2-xBa_xCuO₄ (x=1/8) was studied by ARPES and STM.

		published article - download PDF (Science 314, 1914 - Dec 2006)


		The influence of atomic scale electron-lattice interactions on high-T_c superconductivity was imaged by STM.

		published article - download PDF (Nature 442, 546 - Aug 2006)


		Atomic-scale sources and mechanism of nanoscale electronic disorder in Bi₂Sr₂CaCu₂O_8+δ were identified by STM.

		published article - download PDF (Science 309, 1048 - Aug 2005)


		The doping dependence of nanoscale electronic structure in superconducting Bi₂Sr₂CaCu₂O_8+δ was studied by STM.

		published article - download PDF (Phys. Rev. Lett. 94, 197005 - May 2005)


		'Checkerboard' electronic crystal state in the lightly hole-doped cuprate Ca_2-xNa_xCuO₂Cl₂.

		published article - download PDF (Nature 430, 1001 - Aug 2004) See also : Magnetic Material Laboratory site (RIKEN) Physics Today - cover figure by Curry Taylor


		The relationship between atomic-scale electronic phenomena and wave-like quasiparticle states in superconducting Bi₂Sr₂CaCu₂O_8+δ was explained in terms of an octet model of quasiparticle interference.

		published article - download PDF (Nature 422, 592 - Apr 2003)


		The granular structure of high-T_c superconductivity in underdoped Bi₂Sr₂CaCu₂O_8+δ was imaged with atomic resolution, revealing inherent heterogeneity.

		published article - download PDF (Nature 415, 412 - Jan 2002)


		A checkerboard-like Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi₂Sr₂CaCu₂O_8+δ was discovered.

		published article - download PDF (Science 295, 466 - Jan 2002)
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