Elastoconductivity as a probe of broken mirror symmetries

We propose the possible detection of broken mirror symmetries in correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the“shear conductivity” ${\mathrm{\Gamma }}_{xx,xy}$, defined as the linear change of the longitudinal conductivity ${\sigma }_{xx}$ due to a shear strain ${\epsilon }_{xy}$. This quantity can only be nonvanishing when in-plane mirror symmetries are broken and we discuss how candidate states in the cuprate pseudogap regime (e.g., various loop current or charge orders) may exhibit a finite shear conductivity. We also provide a realistic experimental protocol for detecting such a response.

Figure 1

(Left) A real-space picture of a square lattice in the presence of a CDW and BDW in both $x$ and $y$ directions. Darker points indicate a higher electron density and darker lines an increased hopping between neighboring sites. (Right) A real-space picture of the ${\mathrm{CuO}}_2$ plane showing the ${\mathrm{\Theta }}_2$ planar loop order phase, which produces a finite shear conductivity. Orange circles represent copper sites, green circles are oxygen sites, and arrows indicate the direction of spontaneously formed microscopic current loops.

Figure 2

Ratio ${\mathrm{\Gamma }}_{xx,xy}/{\sigma }_{xx}$ of shear conductivity over longitudinal conductivity for checkerboard charge and bond order (scattering time ${\tau }_{\text{sc}}=10/t$). Blue dashed curve as a function of ${\varphi }_x$ for a finite and fixed value of the other three order parameters: ${\varphi }_y={\mathrm{\Delta }}_x=-{\mathrm{\Delta }}_y=0.1t$ and red curve as a function of ${\mathrm{\Delta }}_x$ for similarly fixed ${\varphi }_x={\varphi }_y=-{\mathrm{\Delta }}_y=0.1t$.

Figure 3

Ratio ${\mathrm{\Gamma }}_{xx,xy}/{\sigma }_{xx}$ for the loop current states ${\mathrm{\Theta }}_1$ (brown dashes) and ${\mathrm{\Theta }}_2$ (blue) as afunction of the order parameter magnitudes $R/t$, where $t$ the tight-binding hopping parameter of the copper-oxygen bond. The response is parametrically larger than for charge order since it is quadratic in the magnitude of the small, dimensionless order parameters, $R/t$, and not quartic as in the case of charge order.

Figure 4

Experimental setup for the detection of shear resistance similar to Refs. [20, 21].

Figure 5

Unstrained and sheared Bravais lattice and corresponding first Brillouin zone of square lattices.

Figure 6

Fermi surface of the original (left) and downfolded (right) Brillouin zone for charge and bond order ($N=2$) with gaps opening at the hot spots of the Fermi surface that are connected by ${\mathit{Q}}_{x/y}=\pi {\mathit{e}}_{x/y}$. Note that the figure on the right is the reduced Brillouin zone shown here as the upper right corner of the original Brillouin zone.

Figure 7

The first example of an experimental setup, where samples which have the same alignment of their crystalline $a-b$ axes are glued at several different angles to a piezoelectric stack.

Figure 8

A second possible experimental setup, where crystals with different alignment of their crystalline axes can be glued onto the piezoelectric stack.