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1. Two superconducting states with broken time-reversal symmetry in FeSe 1−x S x

   https://doi.org/10.1073/pnas.2208276120  

   Matsuura, Kohei ; Roppongi, Masaki ; Qiu, Mingwei ; Sheng, Qi ; Cai, Yipeng ; Yamakawa, Kohtaro ; Guguchia, Zurab ; Day, Ryan P. ; Kojima, Kenji M. ; Damascelli, Andrea ; et al ( May 2023 , Proceedings of the National Academy of Sciences)

   Iron-chalcogenide superconductors FeSe_1−xS_xpossess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe_1−xS_xsuperconductors for0≤x≤0.22covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperatureT_cfor all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-fieldμSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x>0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe_1−xS_x, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

    

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

   https://doi.org/10.1073/pnas.1821454116  

   Mukhopadhyay, Sourin ; Sharma, Rahul ; Kim, Chung Koo ; Edkins, Stephen D. ; Hamidian, Mohammad H. ; Eisaki, Hiroshi ; Uchida, Shin-ichi ; Kim, Eun-Ah ; Lawler, Michael J. ; Mackenzie, Andrew P. ; et al ( July 2019 , Proceedings of the National Academy of Sciences)

   The CuO 2 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 | < Δ * , where Δ * 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 Δ * . 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 Bi 2 Sr 2 CaCu 2 O 8 . 

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3. A crystallographic approach to the short-range ordering problem in V 1−x Mo x O 2 (0.50 ≤ x ≤ 0.60)

   https://doi.org/10.1039/d0tc01173h  

   Davenport, Matthew A. ; Allred, Jared M. ( January 2020 , Journal of Materials Chemistry C)

   The V 1−x Mo x O 2 phase diagram has high structural and electronic complexity that is driven by strong, short-range correlations that compete with the long-range rutile crystal structure. The substitution regime near 50% Mo occupancy is no exception, but there has so far been no significant progress in determining the actual structure. Reported here is a combined study using single crystal X-ray diffraction, powder X-ray diffraction, and representational analysis to examine both the local and crystallographically averaged atomic structures simultaneously near x = 0.50. Between about x = 0.50 and 0.60, the average structure of V 1−x Mo x O 2 is the parent rutile phase, but the local symmetry is broken by atomic displacements that are best described using the orthorhombic subgroup Fmmm . This model is locally similar to the two-dimensionally ordered 2D-M2 phase recently reported in the compositional range 0.19 ≤ x ≤ 0.30, except the correlation length is much shorter in the 2D plane, and longer in the frustrated one, making it more isotropic. This work also extends the 2D-M2 phase regime up to x = 0.43, and suggests that the local- Fmmm phase observed here can be seen as the end result of the continued suppression of the 2D-M2 phase through enhanced geometric frustration between the intrinsic order parameters. This suggests that other doped-rutile phases with elusive structures may also be dominated by similar short-range correlations that are hidden in the diffuse scattering. 

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4. Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh 3 ) 2 X 2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling

   https://doi.org/10.1002/chem.202100705  

   Bone, Alexandria N. ; Widener, Chelsea N. ; Moseley, Duncan H. ; Liu, Zhiming ; Lu, Zhengguang ; Cheng, Yongqiang ; Daemen, Luke L. ; Ozerov, Mykhaylo ; Telser, Joshua ; Thirunavukkuarasu, Komalavalli ; et al ( August 2021 , Chemistry – A European Journal)

   Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single‐molecule magnets (SMMs). Spin‐phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin‐phonon coupling in molecules is challenging. We have found that far‐IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂(Co‐X; X=Cl, Br, I) reveal rarely observed spin‐phonon coupling as avoided crossings between magnetic andu‐symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero‐field split (ZFS) levels of theS=3/2 electronic ground state were probed by INS, high‐frequency and ‐field EPR (HFEPR), FIRMS, and frequency‐domain FT terahertz EPR (FD‐FT THz‐EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) andgvalues. Ligand‐field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities inCo‐X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin‐phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

    

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5. Global perspectives of the bulk electronic structure of URu 2 Si 2 from angle-resolved photoemission

   https://doi.org/10.1088/2516-1075/ac4315  

   Denlinger, J. D. ; Kang, J-S ; Dudy, L. ; Allen, J. W. ; Kim, Kyoo ; Shim, J-H ; Haule, K. ; Sarrao, J. L. ; Butch, N. P. ; Maple, M. B. ( January 2022 , Electronic Structure)

   Previous high-resolution angle-resolved photoemission (ARPES) studies of URu₂Si₂have characterized the temperature-dependent behavior of narrow-band states close to the Fermi level (E_F) at low photon energies near the zone center, with an emphasis on electronic reconstruction due to Brillouin zone folding. A substantial challenge to a proper description is that these states interact with other hole-band states that are generally absent from bulk-sensitive soft x-ray ARPES measurements. Here we provide a more globalk-space context for the presence of such states and their relation to the bulk Fermi surface (FS) topology using synchrotron-based wide-angle and photon energy-dependent ARPES mapping of the electronic structure using photon energies intermediate between the low-energy regime and the high-energy soft x-ray regime. Small-spot spatial dependence,f-resonant photoemission, Si 2pcore-levels, x-ray polarization, surface-dosing modification, and theoretical surface slab calculations are employed to assist identification of bulk versus surface state character of theE_F-crossing bands and their relation to specific U- or Si-terminations of the cleaved surface. The bulk FS topology is critically compared to density functional theory (DFT) and to dynamical mean field theory calculations. In addition to clarifying some aspects of the previously measured high symmetry Γ,ZandXpoints, incommensurate 0.6a* nested Fermi-edge states located alongZ–N–Zare found to be distinctly different from the DFT FS prediction. The temperature evolution of these states aboveT_HO, combined with a more detailed theoretical investigation of this region, suggests a key role of theN-point in the hidden order transition.

    

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