Hysteresis and Noise from Electronic Nematicity in High-Temperature Superconductors

An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model. Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network and use what is known about the random field Ising model to predict new ways to test for local electronic nematic order (nematicity) using noise and hysteresis. In particular, we have uncovered a remarkably robust linear relation between the orientational order and the resistance anisotropy which holds over a wide range of circumstances.

Figure 1

Mapping of nematic patches to random resistor networks. (a) Configurations of nematic patches generated by the random field Ising model. (b) Corresponding resistor network, modeling local anisotropic conduction in each nematic patch. Solid lines are small resistors, and dotted lines are large ones.

Figure 2

Hysteresis and comparison of the macroscopic resistance anisotropy to the orientational order for size $L\times L=100\times 100$, disorder strength $\Delta =3J$, temperature $T=0$, microscopic resistance anisotropy $r=2$, and external field sweep rate $\Omega =J/N$, where $N=L\times L$. (a) Hysteresis of the resistance anisotropy $R_a$ (see text) vs the symmetry-breaking field $h$. (b) Resistance anisotropy $R_a$ vs orientational order parameter $m$. The resistance anisotropy is a remarkably good indicator of orientational order.

Figure 3

(a) Field ramp-up from a disordered configuration at $T=0$, with hysteresis subloops, for system size $L\times L=100\times 100$ and disorder strength $\Delta =3J$. The arrows indicate the order in which the external field sweep is taken. Subloops $A$ and $B$ are both taken between the same extremal orienting fields $h=1.5J$ and $h=2.1J$ but with different histories. (b) Incongruency of subloops $A$ and $B$, due to the presence of interactions. Here the orientational order parameter has been shifted to compare the shape of the two subloops. Subloop $A$, executed at lower $m$, has a higher slope than subloop $B$, executed at higher $m$.

Figure 4

(a) Telegraph noise in a confined geometry. Resistance $R_{xx}$ vs time of a small system of size $L\times L=6\times 6$ with disorder strength $\Delta =2J$, at temperature $T=0.5J$, in zero applied field, $H=0$. An initial random state is allowed to thermalize for 10 000 Monte Carlo steps before measurements are taken. The local microscopic conductivity anisotropy in the resistor network is $r=2$. Small fluctuations are due to a single nematic patch fluctuating. Large switches are due to the thermal fluctuations of a single correlated cluster of nematic patches. (b) Histogram of the time series. $N$ is the number of occurrences of a particular resistance. There are two main states, one for which the correlated cluster is up, and the other for which it is down.