Cryogenic focused-ion-beam microstructuring enabling quantitative $c$-axis transport measurements in Tl$_2$Ba$_2$CuO$_{6+δ}$

Absolute transport measurements in correlated quantum materials are often limited by disorder, inhomogeneity, geometric uncertainty, and small crystal size. Focused ion beam (FIB) technology offers a route to overcome many of these limitations by enabling transport devices with precisely defined geometry to be fabricated from lamellae extracted from carefully selected regions of a crystal, but its application to cuprate superconductors has been hindered by ion-beam-induced damage. Here we study the clean overdoped cuprate Tl2201 and show that conventional FIB processing causes thermally driven oxygen loss, while cryogenic FIB microstructuring largely suppresses this degradation and preserves the crystal structure from the bulk to the atomic scale. Microstructured devices quantitatively reproduce established in-plane resistivity and Hall carrier density measurements without rescaling. Applying this approach to $c$-axis transport, we obtain absolute $\rho_c(T)$ values approximately three times larger than previously reported, bringing the transport anisotropy into quantitative agreement with the known Fermi surface geometry within an isotropic relaxation-time approximation. These results resolve a long-standing discrepancy between transport and quantum oscillation measurements in overdoped Tl2201 and establish cryogenic FIB microstructuring as a route to reliable quantitative transport measurements in quantum materials where disorder, inhomogeneity, geometry, or small crystal size have previously limited experimental accuracy.