Discerning electronic fingerprints of nodal and antinodal nestings and their phase coherences in doped cuprate superconductors

The complexity of competing orders in cuprates has recently been multiplied by a number of bulk evidences of charge ordering with wave vector that connects the antinodal region of the Fermi surface. This result contradicts many spectroscopic results of the nodal nesting. To resolve this issue, we carry out a unified study of the resulting electronic fingerprints of both nodal and antinodal nestings (NNs/ANs) and compare with angle-resolved photoemission, scanning tunneling spectroscopic data, as well as bulk-sensitive Hall-effect measurements. Our result makes several definitive distinctions between them in that while both nestings gap out the antinodal region, AN induces an additional quasiparticle gap below the Fermi level along the nodal direction, which is so far uncharted in spectroscopic data. Furthermore, we show that the Hall coefficient in the AN state obtains a discontinuous jump at the phase transition from an electronlike nodal pocket (negative value) to a large holelike Fermi surface (positive value), in contrast to a continuous transition in the available data. We conclude that individual NNs and ANs have difficulties in explaining all of the data. In this spirit, we study a possibility of coexisting NN and AN phases within a Ginsburg-Landau functional formalism. An interesting possibility of disorder pinned “chiral” charge ordering is finally discussed.

Figure 1

(a) Schematic FS evolution for the NN at ${\mathit{Q}}_n\to (\pi ,\pi )$. (b) Same as (a), but for the AN at ${\mathit{Q}}_a\to (\pm \pi /2,0),(0,\pm \pi /2)$. (c), (d) Electronic dispersion along the nodal direction for the two cases discussed in (a), (b), respectively.

Figure 2

(a) Computed FS for the NN at ${\mathit{Q}}_n$. (b) Same as (a), but for the AN at ${\mathit{Q}}_a$ (see text). (d), (e) Computed dispersion along the nodal direction for the two cases discussed in (a) and (b), respectively. ARPES (c) FS and (f) dispersion along nodal line for underdoped YBCO${}_{6.3}$.[16]

Figure 3

Computed DOS for AN and NN cases (solid thick lines) are compared with STM results for two different hole-doped systems. The data for Ca${}_{1.88}$Na${}_{0.12}$CuO${}_2$Cl${}_2$ (Na-CCOC) and Bi${}_2$Sr${}_2$Dy${}_{0.2}$Ca${}_{0.8}$Cu${}_2$O${}_{8+\delta }$ (Bi2212) (normal state) are obtained from Ref. 22. The two horizontal arrows dictate the antinodal gap (AG) and nodal gap (NG) for the AN case.

Figure 4

Computed Hall coefficient $R_H$ as a function of $T$ for the AN and NN cases. Symbols give experimental data for YBCO${}_{6.51}$ at doping $x=0.1$ and magnetic field $B=55$ T, taken from Ref. 18. In both cases, the phase transition is assumed to occur at the same $T=55$ K. NN gives positive $R_H$ and connects smoothly to its paramagnetic value, whereas $R_H$ for the AN case is negative (coming from electronlike FS) below $T_a$, and, at the transition, it shows a discontinuous jump (dashed line) to the positive value for the paramagnetic holelike FS. We note, however, that although the Boltzmann approach is applicable in the low-field region as compared to high-field experimental data, the results are pertinent.

Figure 5

(a) Phase diagram in the ($x,T$) plane for the AN ($T_a$) and NN ($T_n$) phases. The shaded area represents a possible phase coexistence region. $T^{*}$ is a common critical point of present interest. The doping axis is rescaled with respect to the VHS doping at which AN nesting is strongest. (b1), (b2) The bare susceptibilities, plotted in two-dimensional momentum space at zero energy, show NN and AN at underdoped and optimally doped regions, respectively. (c1), (c2) Corresponding RPA susceptibilities. (d1), (d2) Self-consistent susceptibilities in the corresponding gap states.