enhancement of the 2D carrier mean free path, although much less well-known than the celebrated Moore’s law in the Si electronics industry, is actually quantitatively on par with Moore’s law increase in the microprocessor performance. Unlike Moore’s law in Si microelectronics performance, where the motivation has been technological, however, the drive for the mobility enhancement in 2D GaAs structures has been motivated entirely by fundamental physics considerations. Indeed, this increase in the 2D mobility has been accompanied by some of the most spectacular experimental discoveries in modern physics including, for example, the fractional quantum Hall effect (FQHE) [@tsuiprl1982], the even-denominator FQHE [@willettprl1987], the bilayer half-filled FQHE [@shayeganprl1992], the anisotropic stripe and bubble phases [@lillyprl], and many other well-known novel 2D phenomena. (As an aside we point out that, qualitatively similar to the situation in the Moore’s law, the exponential enhancement in the 2D mobility of semiconductor heterostructures has slowed down considerably in the recent years with only a 30% increase in the mobility during the $2003-2013$ period, from $\sim 3\times 10^7$ to $\sim 4 \times 10^7$ cm$^2$/Vs, after roughly a factor of 1,000 increases during $1978-2003$.)

We mention right in the beginning that our interest here is obviously the $T=0$ 