Charge Order Driven by Fermi-Arc Instability in Bi ₂ Sr _{2− x} La _x CuO _6+δ

Abstract

An understanding of the nature of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. Here we combine resonant X-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, as well as momentum and real space, with the Bi2Sr2−xLaxCuO 6+δ cuprate family. The observed wavevector rules out simple antinodal nesting in the single particle limit, but matches well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates, and uncover its connection to the pseudogap regime. PACS numbers:Since the discovery of cuprate high-temperature superconductors, several unconventional phenomena have been observed in the region of the phase diagram located between the strongly localized Mott insulator at zero doping and the itinerant Fermi-liquid state that emerges beyond optimal doping [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The so-called 'pseudogap' opens at the temperature T * and obliterates the Fermi surface at the antinodes (AN) of the d-wave superconducting gap function, leaving behind disconnected "Fermi arcs" centered around the nodes. In addition, charge order has been observed on the surface of Bi-and Clbased compounds [4][5][6][7][8], in the bulk of La-based compounds [9][10][11], and most recently in YBa 2 Cu 3 O 6+δ (YBCO) [17][18][19][20], indicating this might be the leading instability in underdoped cuprates. The similarity between the observed charge ordering wavevector and the antinodal nesting vector of the hightemperature Fermi surface has prompted suggestions that a conventional Peierls-like charge-density-wave (CDW) might be responsible for the opening of the pseudogap [7,8,12,19]. We use complementary bulk/surface techniques to examine the validity of this scenario, and explore the connection between charge ordering and fermiology.By applying a suite of complementary tools to a single cuprate material, Bi 2 Sr 2−x La x CuO 6+δ (Bi2201), we reveal that the charge order in this system emerges just below T * , and that its wavevector corresponds to the Fermi arc tips rather than the antinodal nesting vector. We quantify the Fermi surface using ARPES, and we look for charge modulations along the Cu-O bond directions in both real-and reciprocalspace, using STM and REXS. The single-layer Bi2201 is well suited to this purpose owing to: (i) its two-dimensionality and high degree of crystallinity [22,23], and (ii) the possibility of probing the temperature evolution across T * , which is bettercharacterized [15,16] and more accessible than in bilayer sys-

Amperean Pairing and the Pseudogap Phase of Cuprate Superconductors

“…Angle-resolved photoemission (ARPES) shows that the pseudogap opens in the antinodal region near ð0; πÞ (we set the lattice constant a to unity), leaving behind ungapped "Fermi arcs" centered around the nodes. Recent x-ray scattering data [2][3][4][5] reveal that the pseudogap is likely to be a distinct phase, characterized by the onset of a charge density wave (CDW) with wave vectors at ð0; AEδÞ and ðAEδ; 0Þ, where δ decreases with increasing doping, thus confirming evidence for charge order found earlier by scanning tunneling microscope (STM) [6][7][8][9] and nuclear magnetic resonance (NMR) experiments [10]. Recent advances include STM and x-ray studies on the same Bi 2 Sr 2 CaCu 2 O 8þx (Bi-2212) samples [11].…”

Ideal charge-density-wave order in the high-field state of superconducting YBCO

“…high-temperature superconductors | charge-density-wave order | high magnetic field X-ray scattering | vestigial nematic order | competing order C harge-density-wave (CDW) order has been found to exist universally in the hole-doped superconducting cuprates (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), and the common characteristics at zero magnetic field include bidirectionality, quasi-2D and short-ranged correlations (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). More specifically, the CDW diffraction patterns are found in both directions of Cu-O bonds in the CuO2 plane (Fig.…”

“…More specifically, the CDW diffraction patterns are found in both directions of Cu-O bonds in the CuO2 plane (Fig. 1A), and the CDW correlation lengths parallel and perpendicular to the planes (i.e., along the a-or b-axes and the c axis) are less than ∼ 20 and ∼ 1 lattice constants, respectively (7)(8)(9)(10)(11)(12)(13)(14)(15)(16), corresponding to a correlation volume of order 10 2 unit cells (UCs). Thus, the properties of the quasi-2D CDW are likely strongly affected by disorder and only indirectly represent the true nature of the underlying CDW correlations.…”

“…Thus, the properties of the quasi-2D CDW are likely strongly affected by disorder and only indirectly represent the true nature of the underlying CDW correlations. Indeed, X-ray scattering shows that the onset of the quasi-2D order is gradual without a sharp transition (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), consistent with the influence of quenched disorder on an incommensurate CDW (19)(20)(21). Furthermore, whereas Y-based and La-based cuprates exhibit a clear competition between CDW and superconductivity (7,8,(12)(13)(14)(15), such competition is not apparent in the families of Bi-based and Hg-based cuprate compounds (9-11)-a discrepancy that probably reflects different degrees of quenched disorder among cuprate families.…”

Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

“…An incommensurate CDW order has been observed in La-based cuprates a while ago 1,2 , and recently was found to be ubiquitous in the cuprates [3][4][5][6][7][8][9][10][11][12][13] . The CDW order is incommensurate, with momentum Q along X and/or Y directions, where Q ∼ (0.2 − 0.3) × 2π.…”