Fig. 1: Description of the proposed method.
From: Quantized valley Hall response from local bulk density variations
Measuring the variation of the particle density, upon varying the strength of the applied strain τ, leads to a quantized bulk response, \({\mathfrak{S}}({{{{{{{\bf{r}}}}}}}})\), reflecting the underlying valley Hall effect. a Number of particles \(\tilde{n}({{{{{{{\bf{r}}}}}}}})\) within a unit cell at position r when applying trigonal strain to the sample (arrows). b Local valley Hall marker \({\mathfrak{S}}({{{{{{{\bf{r}}}}}}}})\) [Eq. (14)] in units of the conductivity quantum σ0 = e2/h, displaying a plateau at a quantized value \({\mathfrak{S}}({{{{{{{\boldsymbol{r}}}}}}}})/{\sigma }_{0}\in {\mathbb{Z}}\) deep in the bulk. In the present case, \({\mathfrak{S}}({{{{{{{\bf{r}}}}}}}})/{\sigma }_{0}\simeq 1\), as emphasized in the zoomed region. This local bulk response exists irrespective of the sample’s edge termination. For more details on the system parameters used, see the Results subsection “Trigonal strain in a finite hexagonal flake''.
