Determination of the Fine-Structure Constant Using GaAs-AlxGa1−xAsHeterostructures

The fine-structure constant $\alpha$ has been determined from precision measurements of quantized Hall resistances $R_{\mathrm{H}}$ of three different GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures. The result, ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}968\left(23\right)\mathrm{}$ (0.17 ppm), is in excellent agreement with the 0.11-ppm value obtained from the gyromagnetic ratio of the proton, ${{\gamma }_p}^{\prime }$, and $\frac{2e}{h}$ via the Josephson effect. Our $R_{\mathrm{H}}$ value can be combined with ${{\gamma }_p}^{\prime }$ and $\frac{2e}{h}$ to yield a more accurate value of ${\alpha }^{-1\mathrm{}}$ independent of the ohm: ${\alpha }^{-1\mathrm{}}=137.035\mathrm{}965\left(12\right)\mathrm{}$ (0.089 ppm).