Quasiparticle interference and charge order in a heavily overdoped non-superconducting cuprate

One of the key issues in unraveling the mystery of high Tc superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi,Pb)2Sr2CuO6+x cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with sqrt(2)*sqrt(2) periodicity. Both the dispersive quasiparticle interference and static charge order can be qualitatively explained by theoretical calculations, which reveal the unique electronic structure of strongly overdoped cuprate.

The superconducting (SC) state of high TC cuprates exists within a "dome" in the phase diagram and disappears both in the severely underdoped and heavily overdoped limits. Because the cuprates are widely believed to be doped Mott insulators [1], the underdoped regime near the parent compound has been extensively studied by various experimental techniques, which have revealed highly unusual phenomena such as the pseudogap phase [2] and complex charge/spin orders [3][4][5][6][7][8][9][10][11][12][13][14]. On the contrary, the heavily overdoped regime is much less explored because it is generally considered to be a rather conventional Fermi liquid (FL) state. This point has been illustrated by the crossover from a non-FL-like linear temperature (T) dependent resistivity at optimal doping to the T 2 dependent resistivity characteristic of Landau FL in the heavily overdoped regime [15][16][17][18][19], as well as quantum oscillation experiments revealing a single hole-like Fermi surface (FS) [20,21]. Because the physics of the FL is well-understood, the heavily overdoped limit can actually serve as another valid starting point, presumably more accessible than the Mott insulator limit, for understanding the origin of superconductivity in cuprates.
Previous experiments on overdoped cuprates have revealed a number of important features regarding the electronic structure. Angle-resolved photoemission spectroscopy (ARPES) shows a FS topology transition from a (π,π)-centered hole-like pocket to a (0,0)-centered electron-like pocket [22][23][24]. In single band tight binding model [25,26], the change of FS topology in two-dimension should be accompanied by a logarithmic divergence of electron density of states (DOS) known as the Van Hove singularity (VHS) [27]. Recent scanning tunneling microscopy (STM) experiments provide direct evidence for VHS in heavily overdoped cuprate, as well as the existence of pseudogap [26]. However, it is still unclear what the main difference is, from the electronic structure and electronic order point of view, between the FL and SC states across the phase boundary in the overdoped side. Especially, the charge order phenomenon, which is ubiquitous in underdoped cuprates and entangles intricately with superconductivity [7, [28][29][30], has been mostly neglected in the heavily overdoped non-SC regime of the phase diagram.
In order to elucidate the electronic structure and electronic order in the overdoped regime outside the SC dome, here we perform STM studies on a heavily overdoped, non-SC Bi2-xPbxSr2CuO6+δ (Pb-Bi2201) cuprate. Tunneling spectroscopy reveals the VHS feature and its evolution into the pseudogap phase, and the dispersive quasiparticle interference (QPI) patterns reveal the change of FS topology. More remarkably, we observe nanoscale patches of static charge orders with √2 × √2 periodicity. The possible origin of the charge order and its implications to the superconductivity will be discussed.

Results
Spatially resolved tunneling spectroscopy.
The Pb doped Bi2201 is chosen because it can be overdoped into the non-SC regime and has an ideal cleaved surface. High-quality Pb-Bi2201 single crystals are grown by the traveling solvent floating zone method and the TC of the as-grown sample is about 3 K [31]. The non-SC sample studied in this work is obtained by annealing the as-grown sample in high pressure O2 (~ 80 atm) at 500 °C for 7 days to further increase the hole density. It exhibits no sign of superconductivity down to 2 K. Figure 1(a) depicts the schematic electronic phase diagram, and the red arrow shows the approximate location of the non-SC sample. The Pb-Bi2201 crystal is cleaved in the ultrahigh vacuum chamber at T = 77 K, and is then transferred into the STM chamber with the sample stage cooled to T = 5 K. STM topography is taken in the constant current mode with an electro-chemically etched tungsten tip, which has been treated and calibrated on a clean Au(111) surface [32]. The dI/dV (differential conductance) spectra are collected by using a standard lock-in technique with modulation frequency f = 423 Hz. All the data reported here are taken at T = 5 K. Fig. 1(b) is the exposed (Bi,Pb)O surface topography of a non-SC sample, which shows a regular square lattice. The structural supermodulation usually observed in Bi-based cuprates is suppressed by Pb doping [28,33]. Around 13% of the atomic sites are bright spots, which is consistent with the 12.2% Pb substitution of Bi determined by the sample growth condition [28,33]. There are spatial inhomogeneities with typical size around a few nanometers, which presumably result from the non-uniform distribution of local hole density [34,35].

Shown in
The local electronic structure is probed by dI/dV spectroscopy, which is approximately proportional to the electron DOS. Figure 1(c) displays a series of representative spectra taken at various locations indicated by the corresponding colored dots in Figure 1(b). The spectra exhibit significant but yet systematic variations. Roughly speaking there are two types of spectra, one with a prominent peak near the Fermi energy (EF) and the other with a DOS suppression around EF that is reminiscent of the pseudogap. In Fig. 1(d) we show that the peaks in dI/dV can be fitted well by a simple function a + b log |E-EVHS| with EVHS denoting the peak position, which is consistent with the spectrum due to the presence of VHS [36]. The spectra with DOS suppression are quite similar to that in OD cuprate with lower hole density in the overdoped SC regime [37,38]. The spatially averaged dI/dV spectrum in Fig. 1(e) exhibits a DOS peak around EF, revealing that statistically the dominant spectral feature in this sample is the VHS-type. The spatial variations of the spectra reflect that the VHS-type spectra gradually evolve into the pseudogap-type with reduced doping, which is consistent with the expected band structure evolution of overdoped cuprates.
The dI/dV maps and dispersive QPI patterns.
Next we will focus on the electronic structure and electronic order in this sample. The static √ × √ charge order structure.
In addition to the dispersive QPI features, a more important, and totally unexpected feature revealed by the dI/dV maps are the existence of non-dispersive structure when we examine the low energy dI/dV maps. As displayed by the dashed squares in Fig. 3(a), the DOS map at zero bias exhibits nanoscale patches of short-range charge orders with a 45-degree rotation with respect to the atomic lattice. This feature has never been observed in cuprates before [7, 26,29,38]. The dI/dV maps obtained at different bias energies indicate that the charge order is more pronounced around EF, and is visible over the entire energy range. To inspect its fine structures, we show in Figs. 4(b) and 4(c) the zoomed-in topographic and dI/dV maps acquired at Vb = 0 mV on the area enclosed by the green dashed square in Fig. 3(a). It is clearly illustrated from the comparison of these two maps that the charge order locally imposes a commensurate √2 × √2 superstructure on the original atomic lattice. Moreover, the charge order patterns of different patches in Fig. 3(a) do not align with each other. The lack of long-range order indicates that the charge order may be affected by local impurities or inhomogeneous distribution of hole concentration.
We gain more insight into the charge order by investigating its dependence on the bias voltage. Depicted in Figs. 4(d)-4(g) are the dI/dV maps of a small charge ordered patch (marked by the red dashed square in Figs. 4(b) and 4(c)) acquired at Vb = 0 mV, -5 mV, -10 mV and -20 mV, demonstrating that this charge order keeps a commensurate periodicity without any dispersion within the energy range from -20 mV to 0 mV. This suggests that the √2 × √2 pattern is a static charge order, in sharp contrast to the dispersive QPI patterns.

Discussion
Previous STM studies in underdoped cuprates have revealed the ubiquitous existence of charge order with wavevector around 4 a0 along the Cu-Cu bond direction [7,30]. However, the √2 × √2 charge order reported here has never been observed before in cuprates. In fact, the issue of charge order in heavily overdoped cuprates has been mostly neglected so far, and previous study on an overdoped Bi2201 with TC = 15 K did not observe such charge order [38].
Therefore, the √2 × √2 charge order could be a unique feature of the non-SC regime of the cuprate phase diagram, and may reveal key information regarding how superconductivity is suppressed by strong overdoping. The main questions regarding the observed charge order are its origin and implications to the SC phase. Below we present a possible mechanism to account for the √2 × √2 charge order in the strongly overdoped regime.
A likely cause for the charge order is the competition between onsite Coulomb repulsion U and nearest-neighbor interaction V, in combination with the proximity to the VHS. In the simplest classical picture, or if the kinetic energy of electrons is neglected, the potential energy per site for the √2 × √2 charge configuration in Fig. 4(a) is: