Dynamical electronic nematicity from Mott physics

Very large anisotropies in transport quantities have been observed in the presence of very small in-plane structural anisotropy in many strongly correlated electron materials. By studying the two-dimensional Hubbard model with dynamical-mean-field theory for clusters, we show that such large anisotropies can be induced without static stripe order if the interaction is large enough to yield a Mott transition. Anisotropy decreases at large frequency. The maximum effect on conductivity anisotropy occurs in the underdoped regime, as observed in high-temperature superconductors.

Figure 1

(Color online) Spectral function at the Fermi level $A\left(\mathbf{k},\omega =0\right)$ in the first quadrant of the Brillouin zone obtained with CDMFT, $U=10$, $t^{\prime }=-0.3t$. The self-energy is computed directly in real frequency with a small imaginary part $i\eta$ with $\eta =0.1t$. The carrier density is (a) $N=0.62$, (b) 0.81, (c) 0.89, and (d) 0.93. The maximum of the spectral intensity $A_{max}$ is given by (a) 0.9, (b) 0.6, (c) 0.4, and (d) 0.3 in units of $1/t$. The thin white lines indicate the location of the maxima of $A\left(\mathbf{k},\omega =0\right)$ that define the Fermi surface. The band anisotropy is ${\delta }_0=0.04$.

Figure 2

(Color online) Angle-resolved spectral function $A\left(\mathbf{k},\omega \right)$ near the Fermi level obtained from CDMFT with the same parameters as Fig. 1. (a) $N=0.81$ and (b) $N=0.93$. Spectral intensity is given in units of $1/t$. The Fermi level $\omega =0$ is indicated by a broken line. In the insets, the vertical axis near the Fermi level is blown up.

Figure 3

(Color online) Anisotropy in the CDMFT conductivity ${\delta }_{\sigma }=2\left[{\sigma }_x\left(0\right)-{\sigma }_y\left(0\right)\right]/\left[{\sigma }_x\left(0\right)+{\sigma }_y\left(0\right)\right]$ as a function of filling $N$ for various values of $U$ and $\eta =0.1t$, ${\delta }_0=0.04$.

Figure 4

(Color online) Anisotropy in the DCA conductivity for ${\delta }_0=0.04$ as a function of filling $N$ for various values of $U$ and $\eta =0.1t$. Open symbols do not include vertex corrections, filled symbols do.