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Strain apparatus
This protocol is extracted from research article:
Evidence for a strain-tuned topological phase transition in ZrTe5

Procedure

Uniaxial stress was applied to single crystals using a homebuilt three-piezostack device (shown in fig. S1). Three piezoelectric actuators are aligned in parallel with each other. A U-shaped titanium block was glued to the outer two piezoelectric actuators, and a small titanium block was glued to the middle actuator, forming a small gap between these blocks. Applying a voltage to the outer piezostacks while applying an equal and opposite voltage to the middle piezostack will strain the piezostacks and change the gap size.

A crystal is glued across this apparatus gap. Tuning this gap with the piezostack voltage will apply uniaxial stress to the crystal. For a similar apparatus, Hicks et al. (29) showed that gluing only the bottom surface of the crystal to these plates can lead to strain gradients between the top and bottom surfaces of the crystal. These gradients can be suppressed by submerging the crystal in glue, as we did. Hicks et al. showed that the strain gradients are small when the ratio of t/LG (sample thickness to gap size) is small. For our measurements, this ratio is small, ranging from 0.02 to 0.08. We simulated the strain distribution with finite element analysis. Our finite element analysis does show that there are still some small strain gradients along the vertical axis of the crystal, mostly confined to the bottom quarter of the crystal. The strain along the a axis ϵaa is equal to α∆L/L, where the change of the gap size ∆L/L is estimated by a strain gauge glued on the piezostacks. The constant α takes into account a strain relaxation effect, which is estimated by finite element analysis and is typically about 0.8. The strain along the b axis and c axis are determined by the Poisson’s ratio. The resistance-strain dependence identified in this work is a smoothly varying function. Because of this, these small strain gradients have minimal impact on our interpretation of the spatially average resistance.

Care was taken during the construction of the three-piezo apparatus to ensure fine alignment of the piezostacks, minimizing any stress in the secondary axes. First, a “scaffolding” piece was machined with indents the exact dimensions of the piezoelectric actuators and the titanium blocks. The actuators and blocks were placed in these indents and then glued together while secured in precise alignment. The scaffolding block was then removed after the glue dried. Second, the middle titanium block and the outer titanium block were machined with a thin flexor plate connecting them. This flexor plate restricts motion between the blocks in any axis except the primary strain axis.

Strain was measured by a foil strain gauge glued to one of the piezostacks, measuring ϵpiezo. The displacement strain of the device was estimated as this strain multiplied by the mechanical advantage of the apparatus, $ϵxxdisp=2Lp/LGϵpiezo$, where Lp is the length of the piezostack, LG is the length of the gap the sample is glued across, and $ϵxxdisp$ is the displacement of the apparatus. Because of a low signal-to-noise ratio associated with the strain gauge measurement, we presented data plotted against piezostack voltage rather than plotted directly against the measured strain. We then calibrated this with a strain per volt calibration fitted from the strain measurement. We carefully minimized the amplitude of the voltage sweeps applied to the piezostacks, staying centered around ϵmin to minimize any hysteresis effect in the piezostacks.

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