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Articles 1 - 23 of 23
Full-Text Articles in Physics
Photoemission Investigation Of Topological Quantum Materials, Klauss M. Dimitri
Photoemission Investigation Of Topological Quantum Materials, Klauss M. Dimitri
Honors Undergraduate Theses
Topological insulators (TIs) are a class of quantum materials, which behave as insulators in the bulk, yet possess gapless spin-polarized surface states, which are robust against nonmagnetic impurities. The unique properties of TIs make them attractive not only for studying various fundamental phenomena in condensed matter and particle physics, but also as promising candidates for applications ranging from spintronics to quantum computation. Within the topological insulator realm, a great deal of focus has been placed on discovering new quantum materials, however, ideal multi-modal quantum materials have yet to be found. Here we study alpha-PdBi2, KFe2Te2, and DySb compounds including others …
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. Allred, N. Alidoust, Hsin Lin, R. Markiewicz, A. Bansil, R. Cava, M. Hasan
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. Allred, N. Alidoust, Hsin Lin, R. Markiewicz, A. Bansil, R. Cava, M. Hasan
Hsin Lin
We report a study of low-energy electronic structure and Fermi surface topology for the recently discovered iron-based superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅(the 10-3-8 phase, with Tc∼8 K), via angle-resolved photoemission spectroscopy (ARPES). Despite its triclinic crystal structure, ARPES results reveal a fourfold symmetric band structure with the absence of Dirac-cone-like Fermi dots (related to magnetism) found around the Brillouin zone corners in other iron-based superconductors. Considering that the triclinic lattice and structural supercell arise from the Pt₃As₈ intermediary layers, these results indicate that those layers couple only weakly to the FeAs layers in this new superconductor at least near the surface, which has …
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. M. Allred, N. Alidoust, Hsin Lin, R. S. Markiewicz, A. Bansil, R. J. Cava, M. Z. Hasan
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. M. Allred, N. Alidoust, Hsin Lin, R. S. Markiewicz, A. Bansil, R. J. Cava, M. Z. Hasan
Arun Bansil
We report a study of low-energy electronic structure and Fermi surface topology for the recently discovered iron-based superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅(the 10-3-8 phase, with Tc∼8 K), via angle-resolved photoemission spectroscopy (ARPES). Despite its triclinic crystal structure, ARPES results reveal a fourfold symmetric band structure with the absence of Dirac-cone-like Fermi dots (related to magnetism) found around the Brillouin zone corners in other iron-based superconductors. Considering that the triclinic lattice and structural supercell arise from the Pt₃As₈ intermediary layers, these results indicate that those layers couple only weakly to the FeAs layers in this new superconductor at least near the surface, which has …
Electronic Structure Of The Metallic Ground State Of La2−2xsr1+2xmn2o7 For X≈0.59 And Comparison With X=0.36,0.38 Compounds As Revealed By Angle-Resolved Photoemission, Z. Sun, J. F. Douglas, Q. Wang, D. S. Dessau, A. V. Fedorov, H. Lin, S. Sahrakorpi, B. Barbiellini, R. S. Markiewicz, A. Bansil, H. Zheng, J. F. Mitchell
Electronic Structure Of The Metallic Ground State Of La2−2xsr1+2xmn2o7 For X≈0.59 And Comparison With X=0.36,0.38 Compounds As Revealed By Angle-Resolved Photoemission, Z. Sun, J. F. Douglas, Q. Wang, D. S. Dessau, A. V. Fedorov, H. Lin, S. Sahrakorpi, B. Barbiellini, R. S. Markiewicz, A. Bansil, H. Zheng, J. F. Mitchell
Bernardo Barbiellini
Using angle-resolved photoemission spectroscopy, we present the electronic structure of the metallic ground state of La₂₋₂ₓSr₁₊₂ₓMn₂O₇ (x≈0.59) and interpret the results in terms of first-principles band-structure computations, of which the generalized gradient approximation yields the best agreement with the experimental data. No bilayer-split bands are found in this compound, indicating the near degeneracy of electronic states in the neighboring MnO₂ layers due to its A-type antiferromagnetic structure. The d₃z2₋r2 states near the zone center were not observed, which is also consistent with its A-type antiferromagnetic structure. Near the Fermi level, a kink in the dispersion reveals an important electron-phonon many-body …
Influence Of The Third Dimension Of Quasi-Two-Dimensional Cuprate Superconductors On Angle-Resolved Photoemission Spectra, A. Bansil, M. Lindroos, S. Sahrakorpi, R. S. Markiewicz
Influence Of The Third Dimension Of Quasi-Two-Dimensional Cuprate Superconductors On Angle-Resolved Photoemission Spectra, A. Bansil, M. Lindroos, S. Sahrakorpi, R. S. Markiewicz
Robert Markiewicz
Angle-resolved photoemission spectroscopy (ARPES) presents significant simplifications in analyzing strictly two-dimensional (2D) materials, but even the most anisotropic physical systems display some residual three-dimensionality. Here we demonstrate how this third dimension manifests itself in ARPES spectra of quasi-2D materials by considering the example of the cuprate Bi₂Sr₂CaCu₂O₈ (Bi2212). The intercell, interlayer hopping, which is responsible for kz dispersion of the bands, is found to induce an irreducible broadening to the ARPES line shapes with a characteristic dependence on the in-plane momentum k‖. Our study suggests that ARPES line shapes can provide a direct spectroscopic window for establishing the existence of …
Evolution Of Midgap States And Residual Three Dimensionality In La₂₋ₓsrₓcuo₄, S. Sahrakorpi, M. Lindroos, R. Markiewicz, A. Bansil
Evolution Of Midgap States And Residual Three Dimensionality In La₂₋ₓsrₓcuo₄, S. Sahrakorpi, M. Lindroos, R. Markiewicz, A. Bansil
Robert Markiewicz
We carry out extensive first-principles doping-dependent computations of angle-resolved photoemission (ARPES) intensities in La₂₋ₓSrₓCuO₄ over a wide range of binding energies. Intercell hopping and the associated three dimensionality, which is usually neglected in discussing cuprate physics, is shown to play a key role in shaping the ARPES spectra. Despite the obvious importance of strong coupling effects (e.g., the presence of a lower Hubbard band coexisting with midgap states in the doped insulator), a number of salient features of the experimental ARPES spectra are captured to a surprising extent when kz dispersion is properly included in the analysis.
Bilayer Splitting And Coherence Effects In Optimal And Underdoped Bi₂Sr₂Cacu₂O₈+Δ, Y. D. Chuang, A. D. Gromko, A. V. Fedorov, Y. Aiura, K. Oka, Yoichi Ando, M. Lindroos, R. S. Markiewicz, A. Bansil, D. S. Dessau
Bilayer Splitting And Coherence Effects In Optimal And Underdoped Bi₂Sr₂Cacu₂O₈+Δ, Y. D. Chuang, A. D. Gromko, A. V. Fedorov, Y. Aiura, K. Oka, Yoichi Ando, M. Lindroos, R. S. Markiewicz, A. Bansil, D. S. Dessau
Robert Markiewicz
We have carried out extensive high-resolution angle-resolved photoemission (ARPES) experiments on Bi₂Sr₂CACu₂O₈₊δ samples, covering the entire doping range from the overdoped to the optimally and underdoped regimes in the normal state. Our focus is on delineating the doping dependence of the bilayer splitting which is associated with the intracell coupling of electrons between the two CuO₂ planes. We exploit the photon energy of 47 eV, where strong ARPES matrix element effects are found to provide a tremendous enhancement of the antibonding to bonding component of the bilayer split bands near (π,0), in good agreement with the predictions of corresponding first-principles …
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. M. Allred, N. Alidoust, Hsin Lin, R. S. Markiewicz, A. Bansil, R. J. Cava, M. Z. Hasan
Fermi-Surface Topology And Low-Lying Electronic Structure Of The Iron-Based Superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅, Madhab Neupane, Chang Liu, Su-Yang Xu, Yung-Jui Wang, Ni Ni, J. M. Allred, N. Alidoust, Hsin Lin, R. S. Markiewicz, A. Bansil, R. J. Cava, M. Z. Hasan
Robert Markiewicz
We report a study of low-energy electronic structure and Fermi surface topology for the recently discovered iron-based superconductor Ca₁₀(Pt₃As₈)(Fe₂As₂)₅(the 10-3-8 phase, with Tc∼8 K), via angle-resolved photoemission spectroscopy (ARPES). Despite its triclinic crystal structure, ARPES results reveal a fourfold symmetric band structure with the absence of Dirac-cone-like Fermi dots (related to magnetism) found around the Brillouin zone corners in other iron-based superconductors. Considering that the triclinic lattice and structural supercell arise from the Pt₃As₈ intermediary layers, these results indicate that those layers couple only weakly to the FeAs layers in this new superconductor at least near the surface, which has …
Special Photon Energies For Extracting The Bosonic Spectral Function Mediating Superconductivity In Bi₂Sr₂Cacu₂O₈ Via Angle-Resolved Photoemission Spectroscopy, M. Lindroos, R. S. Markiewicz, A. Bansil
Special Photon Energies For Extracting The Bosonic Spectral Function Mediating Superconductivity In Bi₂Sr₂Cacu₂O₈ Via Angle-Resolved Photoemission Spectroscopy, M. Lindroos, R. S. Markiewicz, A. Bansil
Robert Markiewicz
We delineate the complex nature of the angle-resolved photoemission spectroscopy (ARPES) matrix element in Bi₂Sr₂CaCu₂O₈ and identify photon energies where the matrix element is insensitive to wave vector and/or frequency. These special photon energies provide a unique route for extracting the spectral function of the bosonic glue mediating superconductivity and for obtaining self-energies more generally via ARPES experiments.
Fermi Surface Evolution And Collapse Of The Mott Pseudogap In Nd2-Xcexcuo4±Δ, C. Kusko, R. S. Markiewicz, M. Lindroos, A. Bansil
Fermi Surface Evolution And Collapse Of The Mott Pseudogap In Nd2-Xcexcuo4±Δ, C. Kusko, R. S. Markiewicz, M. Lindroos, A. Bansil
Robert Markiewicz
Fermi surface (FS) maps and spectral intensities obtained recently in Nd₂₋ₓCeₓCuO₄±δ via high resolution ARPES measurements are analyzed using mean-field Hartree Fock and self-consistent renormalization computations within the framework of the one-band t-t′-t″-U Hubbard model Hamiltonian. We show that the remarkable observed crossover of the FS from small to large sheets reflects a reduction in the value of the effective Hubbard U with increasing electron doping and the collapse of the correlation induced Mott pseudogap just above optimal doping.
Site-Selectivity Properties Of The Angle-Resolved Photoemission Matrix Element In Bi₂Sr₂Cacu₂O₈, S. Sahrakorpi, M. Lindroos, A. Bansil
Site-Selectivity Properties Of The Angle-Resolved Photoemission Matrix Element In Bi₂Sr₂Cacu₂O₈, S. Sahrakorpi, M. Lindroos, A. Bansil
Arun Bansil
We show that the angle-resolved photoemission (ARPES) spectra for emission from the bonding as well as the antibonding Fermi-surface sheet in Bi₂Sr₂CaCu₂O₈ possess remarkable site, selectivity properties, in that the emission for photon energies less than 25 eV is dominated by pd excitations from just the O sites in the CuO₂ planes. There is little contribution from Cu electrons to the ARPES intensity, even though the initial states at the Fermi energy contain an admixture of Cu-d and O-p electrons. We analyze the origin of this effect by considering the nature of the associated dipole matrix element in detail and …
Matrix Element Effects In Angle-Resolved Photoemission From Bi₂Sr₂Cacu₂O₈: Energy And Polarization Dependencies, Final State Spectrum, Spectral Signatures Of Specific Transitions, And Related Issues, M. Lindroos, S. Sahrakorpi, A. Bansil
Matrix Element Effects In Angle-Resolved Photoemission From Bi₂Sr₂Cacu₂O₈: Energy And Polarization Dependencies, Final State Spectrum, Spectral Signatures Of Specific Transitions, And Related Issues, M. Lindroos, S. Sahrakorpi, A. Bansil
Arun Bansil
We have carried out extensive simulations of the angle-resolved photoemission (ARPES) intensity in Bi2212 within the one-step- and three-step-type models using a first-principles band theory framework. The focus is on understanding the behavior of emissions from the antibonding and bonding bands arising from the CuO₂ bilayers around the M̅ (π,0) symmetry point. The specific issues addressed include: Dependencies of the photointensity on the energy and polarization of the incident light; character of the initial and final states involved as well as the spectrum of the relevant final states; and changes in the spectral intensity as a function of the perpendicular …
Angle-Resolved Photoemission Spectra, Electronic Structure, And Spin-Dependent Scattering In Ni1-Xfex Permalloys, P. E. Mijnarends, S. Sahrakorpi, M. Lindroos, A. Bansil
Angle-Resolved Photoemission Spectra, Electronic Structure, And Spin-Dependent Scattering In Ni1-Xfex Permalloys, P. E. Mijnarends, S. Sahrakorpi, M. Lindroos, A. Bansil
Arun Bansil
We present the all-electron charge and spin self-consistent electronic structure of Ni₁₋ₓFeₓ Permalloys for a range of Fe concentrations. using the first-principles Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) scheme to treat disorder and the local spin density approximation to incorporate exchange-correlation effects. Recent high-resolution angle-resolved photoemission spectroscopy (ARPES) experiments on Ni0.90Fe0.10 and Ni0.80Fe0.20 Permalloys are analyzed in terms of the spectral density function, ABkⅡ, k⊥ = 0, EF), computed from the KKR-CPA Green function for kⅡ values varying along the Γ-K direction in the Brillouin zone. The widths of the majority as well as the minority spin peaks in the theoretical …
Influence Of The Third Dimension Of Quasi-Two-Dimensional Cuprate Superconductors On Angle-Resolved Photoemission Spectra, A. Bansil, M. Lindroos, S. Sahrakorpi, R. S. Markiewicz
Influence Of The Third Dimension Of Quasi-Two-Dimensional Cuprate Superconductors On Angle-Resolved Photoemission Spectra, A. Bansil, M. Lindroos, S. Sahrakorpi, R. S. Markiewicz
Arun Bansil
Angle-resolved photoemission spectroscopy (ARPES) presents significant simplifications in analyzing strictly two-dimensional (2D) materials, but even the most anisotropic physical systems display some residual three-dimensionality. Here we demonstrate how this third dimension manifests itself in ARPES spectra of quasi-2D materials by considering the example of the cuprate Bi₂Sr₂CaCu₂O₈ (Bi2212). The intercell, interlayer hopping, which is responsible for kz dispersion of the bands, is found to induce an irreducible broadening to the ARPES line shapes with a characteristic dependence on the in-plane momentum k‖. Our study suggests that ARPES line shapes can provide a direct spectroscopic window for establishing the existence of …
Evolution Of Midgap States And Residual Three Dimensionality In La₂₋ₓsrₓcuo₄, S. Sahrakorpi, M. Lindroos, R. S. Markiewicz, A. Bansil
Evolution Of Midgap States And Residual Three Dimensionality In La₂₋ₓsrₓcuo₄, S. Sahrakorpi, M. Lindroos, R. S. Markiewicz, A. Bansil
Arun Bansil
We carry out extensive first-principles doping-dependent computations of angle-resolved photoemission (ARPES) intensities in La₂₋ₓSrₓCuO₄ over a wide range of binding energies. Intercell hopping and the associated three dimensionality, which is usually neglected in discussing cuprate physics, is shown to play a key role in shaping the ARPES spectra. Despite the obvious importance of strong coupling effects (e.g., the presence of a lower Hubbard band coexisting with midgap states in the doped insulator), a number of salient features of the experimental ARPES spectra are captured to a surprising extent when kz dispersion is properly included in the analysis.
Surface States And Angle-Resolved Photoemission Spectra From Nd₂₋ₓceₓcuo₄, M. Lindroos, A. Bansil
Surface States And Angle-Resolved Photoemission Spectra From Nd₂₋ₓceₓcuo₄, M. Lindroos, A. Bansil
Arun Bansil
By carrying out first-principles angle-resolved photoemission (ARPES) computations within the local-density-approximation-based band theory framework, we predict the existence of surface states on the (001) surface of the superconductor Nd₂₋ₓCeₓCuO₄ (NCCO). Two surface state bands are identified in the vicinity of the Fermi energy. The associated states possess quite different characteristics in terms of their binding energy, dispersion with k∥, and the polarization and photon energy dependence. Our theoretical predictions offer new insight into the existing ARPES data on NCCO with which they are consistent.
High-Resolution Angle-Resolved Photoemission Spectra From Ni(100): Matrix Element Effects And Spin-Resolved Initial And Final State Bands, S. Sahrakorpi, M. Lindroos, A. Bansil
High-Resolution Angle-Resolved Photoemission Spectra From Ni(100): Matrix Element Effects And Spin-Resolved Initial And Final State Bands, S. Sahrakorpi, M. Lindroos, A. Bansil
Arun Bansil
We have carried out extensive one- and three-step angle-resolved photoemission spectroscopy (ARPES) intensity computations on Ni(100) within the band theory framework based on the local spin-density approximation. The results show a good overall level of accord with the recent high-resolution ARPES experiments on Ni(100) which probe the majority- and minority-spin Σ₁ band along the Γ-K direction near the Fermi energy (EF), uncertainties inherent in our first-principles approach notwithstanding. The k‖ and energy dependencies of various spectral features are delineated in terms of the interplay between changes in the initial- and final-state bands and the associated transition matrix elements. The remarkable …
Electronic Structure Of The Metallic Ground State Of La2−2xsr1+2xmn2o7 For X≈0.59 And Comparison With X=0.36,0.38 Compounds As Revealed By Angle-Resolved Photoemission, Z. Sun, J. F. Douglas, Q. Wang, D. S. Dessau, A. V. Fedorov, H. Lin, S. Sahrakorpi, B. Barbiellini, R. S. Markiewicz, A. Bansil, H. Zheng, J. F. Mitchell
Electronic Structure Of The Metallic Ground State Of La2−2xsr1+2xmn2o7 For X≈0.59 And Comparison With X=0.36,0.38 Compounds As Revealed By Angle-Resolved Photoemission, Z. Sun, J. F. Douglas, Q. Wang, D. S. Dessau, A. V. Fedorov, H. Lin, S. Sahrakorpi, B. Barbiellini, R. S. Markiewicz, A. Bansil, H. Zheng, J. F. Mitchell
Arun Bansil
Using angle-resolved photoemission spectroscopy, we present the electronic structure of the metallic ground state of La₂₋₂ₓSr₁₊₂ₓMn₂O₇ (x≈0.59) and interpret the results in terms of first-principles band-structure computations, of which the generalized gradient approximation yields the best agreement with the experimental data. No bilayer-split bands are found in this compound, indicating the near degeneracy of electronic states in the neighboring MnO₂ layers due to its A-type antiferromagnetic structure. The d₃z2₋r2 states near the zone center were not observed, which is also consistent with its A-type antiferromagnetic structure. Near the Fermi level, a kink in the dispersion reveals an important electron-phonon many-body …
Special Photon Energies For Extracting The Bosonic Spectral Function Mediating Superconductivity In Bi₂Sr₂Cacu₂O₈ Via Angle-Resolved Photoemission Spectroscopy, M. Lindroos, R. S. Markiewicz, A. Bansil
Special Photon Energies For Extracting The Bosonic Spectral Function Mediating Superconductivity In Bi₂Sr₂Cacu₂O₈ Via Angle-Resolved Photoemission Spectroscopy, M. Lindroos, R. S. Markiewicz, A. Bansil
Arun Bansil
We delineate the complex nature of the angle-resolved photoemission spectroscopy (ARPES) matrix element in Bi₂Sr₂CaCu₂O₈ and identify photon energies where the matrix element is insensitive to wave vector and/or frequency. These special photon energies provide a unique route for extracting the spectral function of the bosonic glue mediating superconductivity and for obtaining self-energies more generally via ARPES experiments.
Importance Of Matrix Elements In The Arpes Spectra Of Bisco, A. Bansil, M. Lindroos
Importance Of Matrix Elements In The Arpes Spectra Of Bisco, A. Bansil, M. Lindroos
Arun Bansil
We have carried out extensive first-principles angle-resolved photointensity (ARPES) simulations in Bi2212 wherein the photoemission process is modeled realistically by taking into account the full crystal wave functions of the initial and final states in the presence of the surface. The spectral weight of the ARPES feature associated with the CuO₂ plane bands is found to undergo large and systematic variations with k∥ as well as the energy and polarization of the incident photons. These theoretical predictions are in good accord with the corresponding measurements, indicating that the remarkable observed changes in the spectral weights in Bi2212 are essentially a …
Fermi Surface Evolution And Collapse Of The Mott Pseudogap In Nd2-Xcexcuo4±Δ, C. Kusko, R. Markiewicz, M. Lindroos, A. Bansil
Fermi Surface Evolution And Collapse Of The Mott Pseudogap In Nd2-Xcexcuo4±Δ, C. Kusko, R. Markiewicz, M. Lindroos, A. Bansil
Arun Bansil
Fermi surface (FS) maps and spectral intensities obtained recently in Nd₂₋ₓCeₓCuO₄±δ via high resolution ARPES measurements are analyzed using mean-field Hartree Fock and self-consistent renormalization computations within the framework of the one-band t-t′-t″-U Hubbard model Hamiltonian. We show that the remarkable observed crossover of the FS from small to large sheets reflects a reduction in the value of the effective Hubbard U with increasing electron doping and the collapse of the correlation induced Mott pseudogap just above optimal doping.
Competing Order Scenario Of Two-Gap Behavior In Hole-Doped Cuprates, Tanmoy Das, R. Markiewicz, A. Bansil
Competing Order Scenario Of Two-Gap Behavior In Hole-Doped Cuprates, Tanmoy Das, R. Markiewicz, A. Bansil
Arun Bansil
Angle-dependent studies of the gap function provide evidence for the coexistence of two distinct gaps in hole doped cuprates, where the gap near the nodal direction scales with the superconducting transition temperature Tc, while that in the antinodal direction scales with the pseudogap temperature. We present model calculations which show that most of the characteristic features observed in the recent angle-resolved photoemission spectroscopy (ARPES) as well as scanning tunneling microscopy (STM) two-gap studies are consistent with a scenario in which the pseudogap has a non-superconducting origin in a competing phase. Our analysis indicates that, near optimal doping, superconductivity can quench …
Competing Order Scenario Of Two-Gap Behavior In Hole-Doped Cuprates, Tanmoy Das, R. S. Markiewicz, A. Bansil
Competing Order Scenario Of Two-Gap Behavior In Hole-Doped Cuprates, Tanmoy Das, R. S. Markiewicz, A. Bansil
Robert Markiewicz
Angle-dependent studies of the gap function provide evidence for the coexistence of two distinct gaps in hole doped cuprates, where the gap near the nodal direction scales with the superconducting transition temperature Tc, while that in the antinodal direction scales with the pseudogap temperature. We present model calculations which show that most of the characteristic features observed in the recent angle-resolved photoemission spectroscopy (ARPES) as well as scanning tunneling microscopy (STM) two-gap studies are consistent with a scenario in which the pseudogap has a non-superconducting origin in a competing phase. Our analysis indicates that, near optimal doping, superconductivity can quench …