Identification of a nematic pair density wave state in Bi ₂ Sr ₂ CaCu ₂ O _8+x

Abstract

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 Bi 2 Sr 2 CaCu 2 O 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 Bi 2 Sr 2 CaCu 2 O 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].

Magnetic Interaction in Doped 2D Perovskite Cuprates with Nanoscale Inhomogeneity: Lattice Nonlocal Effects vs. Superexchange

“…, where 0.5 ≤ v 2 (α D ) ≤ 1 and J U ij ≈ 0.15 eV. The strip signatures noticeably weaken with the decreasing temperature, but they are still detected as density waves of the hole pairs [43][44][45][46].…”

“…Actual research on the properties of a quantum spin liquid in the double perovskite oxides with the general formula of A 2 Me 2 O 6 [40][41][42] does not provide a direct answer to this question, since there is no anion substitution in the CuO 2 layer of HTSC cuprates. However, the dynamical charge and spin nanoinhomogeneities are identified and discussed in current neutron and STM experiments [43][44][45][46]. Based on the large isotope effect in high-Tc superconductors with the stripe nanostructure [47][48][49], here we study superexhange interaction taking into account the phonon nature of the stripe structure in high-Tc cuprates.…”

Detection of a pair density wave state in UTe2

“…Recent experimental advances have demonstrated two techniques for visualizing a PDW state. In the first [16][17][18][19] , the condensed electron-pair density at location r, n(r), can be visualized by measuring the tip-sample Josephson critical-current squared I ( ) in which R N (r) is the normal-state junction resistance. In the second PDW visualization technique 17,[20][21][22][23] , the magnitude of the energy gap in the sample, Δ(r), is defined as half the energy separation between the two superconductive coherence peaks in the density of electronic states N(E).…”

“…Many diverse forms for Δ(k) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14,15 superconductive order parameter Δ(r), electron-pair density [16][17][18][19] and pairing energy gap 17,[20][21][22][23] . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24,25 .…”

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3

“…Topological defects are defined as singularities that appear in the order parameter space . They have been important in condensed matter physics due to their key role in understanding the emergence of exotic quantum phases in materials, such as those involving superconductivity, − ferroicity, − charge density waves (CDWs), − and so on. In general, they appear when a system undergoes phase transitions that change its charge (or spin) order or symmetry. , Their proliferation often gives rise to phenomena different from those inherent in the pristine lattice .…”