Fig. 2: Critical field, weak antilocalization, and the extent of disorder.
a Temperature dependence of out of plane upper critical field (\({B}_{{{{{{{{{\rm{C}}}}}}}}}_{\perp }}\)) for I along [\(11\bar{2}\)] and [\(1\bar{1}0\)]. The solid line denotes fitting with Ginzburg-Landau theory. b Temperature dependence of in-plane upper critical field (\({B}_{{{{{{{{{\rm{C}}}}}}}}}_{\parallel }}\)) for I along [\(11\bar{2}\)] and [\(1\bar{1}0\)]. Further, B is parallel to the current direction. The solid line denotes fitting with Tinkham’s model. c. Sheet conductance difference (Δσ = σ(B)-σ(B = 0), σ = 1/RS (B)) in the units of e2/πh for the Hall bar with I along [\(11\bar{2}\)]. The black solid curves show the fitting with ILP (Iordanskii, Lyanda-Geller, and Pikus) theory70,71 (without considering linear Rashba term) including a classical B2 term (also see Supplementary Note 2 and Supplementary Fig. 7 for fitting details). d. Phase diagram of several superconducting compounds categorized by their extent of 2D character and cleanliness. 2D character is resembled by the anisotropy of critical field defined by (\({B}_{{{{{{{{{\rm{C}}}}}}}}}_{\perp }}/{B}_{{{{{{{{{\rm{C}}}}}}}}}_{\parallel }}\)) and extent of disorder is quantified by the ratio between phase coherence length and electronic mean free path (ξ0/lmfp). Assuming a single isotropic band in 2D, lmfp is given by lmfp = h/(e2kFRS), where \({k}_{{{{{{{{\rm{F}}}}}}}}}={(2\pi {n}_{{{{{{{{\rm{s}}}}}}}}})}^{1/2}\) is the Fermi wave vector and ns is the sheet carrier density. From the measured ns (at 5 K) and RS (at 5 K), the lmfp is estimated to be ~12 nm for the present case. The value of all the parameters for other compounds have been largely taken from the reference56 except for the LaTiO3/SrTiO3 interface which has been taken from reference37. As evident, AlOx/KTaO3 (111) is located very near to the boundary between clean and dirty limits, denoted by a horizontal solid line.
