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We study the temperature flow of conductivities in a gated GaAstwo-dimensional electron gas (2DEG) containing self-assembled InAs dots andcompare the results with recent theoretical predictions. By changing the gatevoltage, we are able to tune the 2DEG density and thus vary disorder andspin-splitting. Data for both the spin-resolved and spin-degenerate phasetransitions are presented, the former collapsing to the latter with decreasinggate voltage and/or decreasing spin-splitting. The experimental results supporta recent theory, based on modular symmetry, which predicts how the criticalHall conductivity varies with spin-splitting.

Probing temperature-driven flow lines in a gated two-dimensional electron gas with tunable spin-splitting