Fermi surface dichotomy in systems with fluctuating order

We investigate the effect of a dynamical collective mode coupled with quasiparticles at specific wave vectors only. This coupling describes the incipient tendency to order and produces shadow spectral features at high energies while leaving essentially untouched the low-energy quasiparticles. This allows interpretation of seemingly contradictory experiments on underdoped cuprates, where many converging evidences indicate the presence of charge (stripe or checkerboard) order, which remains instead elusive in the Fermi surface obtained from angle-resolved photoemission experiments.

Figure 1

Schematic view of heavy-fermion system with a Kondo-type resonance arising at the Fermi energy $E_F$ from the mixing of a deep narrow $f$ level (not shown) and the conduction band (dashed line). Two QP bands arise $E^{1,2}\left(k\right)$. The corresponding momentum distribution function $n_k$ is shown below with a true Fermi momentum $k_F^{\text{QP}}$ and a fictitious Fermi surface at $k_F^c$.

Figure 2

(Color online) Upper panel: two-pole band structure in one dimension for $g=0.5t$, ${\omega }_0=0$, and particle density $n=0.67$. The width of the curve is proportional to the weight of the state, and energies are measured with respect to $E_F$. Lower panel: momentum distribution curve.

Figure 3

(Color online) Upper panel: two-pole band structure in one dimension for $g^2/{\omega }_0=0.5$, ${\omega }_0=0.3$, and electron density $n=0.57$. The width of the curve is proportional to the weight of the state, and energies are measured with respect to $E_F$. Lower panel: momentum distribution curve. For $k>2$ the occupation number $n_k$ has been scaled by a factor of 5 to enhance the visibility.

Figure 4

(Color online) Schematic electronic structure for $g=0$.

Figure 5

(Color online) Upper panel: six-pole band structure in one dimension for $g^2/{\omega }_0=0.5$ and ${\omega }_0=0.2$. The electron density is $n=0.55$. The width of the curve is proportional to the weight of the state, and energies are measured with respect to $E_F$. Lower panel: momentum distribution curve. For $k>2$ the occupation number $n_k$ has been scaled by a factor of 5 to enhance the visibility.

Figure 6

(Color online) Two-pole band structure in one dimension for $g^2/{\omega }_0=2$ and ${\omega }_0=0.3$. The electron density is $n=0.83$. The width of the curve is proportional to the weight of the state, and energies are measured with respect to $E_F$. Lower panel: momentum distribution curve.

Figure 7

Two-pole band structure in one dimension for $g^2/{\omega }_0=0.5$ and ${\omega }_0=0.3$ at half-filling $n=1$. In (a) the bare vertex $g$ is used, while in (b) the phenomenological vertex $\tilde{g}$ of Eq. (13) is used.

Figure 8

Two-pole band structure in one dimension for $g^2/{\omega }_0=0.5$ and ${\omega }_0=0.3$ at generic filling $n=0.57$. Here a finite inverse coherence length $\gamma =0.02$ and time $\Gamma =0.1$ are used.

Figure 9

Two-pole band structure in one dimension for $g^2/{\omega }_0=0.5$ and ${\omega }_0=0.3$ at generic filling $n=0.4$. Here a finite inverse coherence length $\gamma =0.02$ and time $\Gamma =0.1$ are used as well as a finite pairing gap $\Delta =0.1$.

Figure 10

Two-dimensional FS obtained from the momentum distribution function $n_{\mathbf{k}}$ in Eq. (1). The spectral function has been integrated over: (a) a low-energy range $W_l=10\text{meV}$; (b) a high-energy range $W_l=100\text{meV}$.