Melting of stripe phases and its signature in the single-particle spectral function

Motivated by the recent experimental data [J. Fink, E. Schierle, E. Weschke, J. Geck, D. Hawthorn, V. Soltwisch, H. Wadati, H.-H. Wu, H. A. Dürr, N. Wizent, B. Büchner, and G. A. Sawatzky, Phys. Rev. B 79, 100502 (2009)] indicating the existence of a pure stripe charge order over unprecedently wide temperature range in ${\text{La}}_{1.8-x}{\text{Eu}}_{0.2}{\text{Sr}}_x{\text{CuO}}_4$, we investigate the temperature-induced melting of the metallic stripe phase. In spite of taking into account local dynamic correlations within a real-space dynamical mean-field theory of the Hubbard model, we observe a mean-field-like melting of the stripe order irrespective of the choice of the next-nearest-neighbor hopping. The temperature dependence of the single-particle spectral function shows the stripe induced formation of a flat band around the antinodal points accompanied by the opening a gap in the nodal direction.

Figure 1

(Color online) Temperature dependence of the [(a) and (b)] local charge density $n_i$, [(c) and (d)] magnetization $\left|S_i^z\right|$, as well as [(e) and (f)] double occupancies $D_i$ at the inequivalent sites in the SC (left) and BC (right) stripe phases at doping $x=1/8$. Filled symbols at $\beta t=50$ were obtained with $t^{\prime }=-t/3$.

Figure 2

(Color online) Intensity of the (a) charge $C\left(\mathit{q}\right)$ and (b) spin $S\left(\mathit{q}\right)$ structure factor maxima at the wave vectors corresponding to the SC stripe phase with the charge (spin) unit cell containing 4 (8) atoms, respectively. For clarity, $C\left(\mathit{q}\right)$ was multiplied by a factor of 4.

Figure 3

(Color online) Evolution of the low-energy part of the single-particle spectral function $A\left(\mathit{k},\omega \right)$ in the SC stripe phase (a) $\beta t=12$, (b) $\beta t=16$, and (c) $\beta t=50$; the SC and BC stripe phases are dynamically indistinguishable. Panel (d) shows $A\left(\mathit{k},\omega \right)$ in the PM phase at $\beta t=50$.

Figure 4

(Color online) Temperature dependence of the low-energy part of the spectral function $A\left(\mathit{k},\omega \right)$ in the SC stripe phase in the vicinity of [(a)–(c)] the nodal $S=\left(\pi /2,\pi /2\right)$ and [(d)–(f)] antinodal $X=\left(\pi ,0\right)$ points. For comparison, dashed line in panels (c) and (f) shows $A\left(\mathit{k},\omega \right)$ in the PM phase.

Figure 5

(Color online) (a) Temperature dependence of the density of states $N\left(\omega \right)$ in the SC stripe phase and (b) imaginary part of the self-energy at the DW. Dashed line in panel (a) shows $N\left(\omega \right)$ in the PM phase while in panel (b) depicts the result of a linear fitting of data points at the smallest Matsubara frequency ${\omega }_m=\pi T$.