Discovery of an insulating ferromagnetic phase of electrons in two dimensions

The two dimensional electron gas (2DEG) realized in semiconductor hetero-structures has been the focus of fruitful study for decades. It is, in many ways, the paradigmatic system in the field of highly correlated electrons. The list of discoveries that have emerged from such studies and have opened new fields of physics is extraordinary, including discoveries related to the integer and fractional quantum Hall effects, weak localization, metal-insulator transitions, Wigner crystalization, mesoscopic quuantum transport phenomena, etc. Now, a set of recent studies [1, 2] on ultra-clean modulation-doped AlAs quantum wells have uncovered a new set of ordering transitions associated with the onset of ferrromagnetism and electron nematicity (or orbital ordering). The 2DEG in the current generation of “ultra-clean” AlAs quantum wells have been gate-tuned over a range of electron density from n = 1.1×1010cm−2 to n = 2×1011cm−2. The electrons occupy two valleys one located about the (0, π) and the other about the (π, 0) point in the 2D Brillouin zone so in addition to two spin-polarizations, the electrons carry a valley “pseudo-spin” index. In the absence of shear strain, the 2DEG has a discrete C4 rotational symmetry that interchanges the valleys. Older studies of the 2DEG in Si MOSFETs and modulation-doped GaAs quantum wells have explored the same general range of correlation strengths; while there is considerable overlap in results – for instance concerning the existence and character of a metal-insulator transition (MIT) – a number of aspects have been seen here for the first time. Since each realization of the 2DEG differs in some details – e.g. the character and strength of the disorder, the geometry of the device, the existence of a valley pseudo-spin, and the effective mass anisotropy of each valley – both the similarities and the differences in observed behaviors are significant. To facilitate such comparisons, it is useful to invoke the dimensionless parameter, rs ≡ 1/(aB √ πn), where n is the areal electron density, aB is the effective Bohr radius. rs = V̄ /K̄ is thus the ratio of a characteristic electronelectron interaction strength, V̄ , to a characteristic kinetic energy, K̄. Because the 2DEG is burried deep in a heterostructure, many experiments that one would like to perform are not possible the present studies depend entirely on measurements of the components of the resistivity tensor, ρab. However, these have been carried out with great precision as a function of the electron density, n (controlled by a remote gate 150μm from the 2DEG), applied magnetic field, both in-plane, B‖, and out-of-plane, B⊥, shear strain to controlably break the underlying C4 symmetry, and temperature, T . In an era in which local and/or time-resolved probes are opening new horizons, it is worth recalling that most discoveries concerning the physics of quantum materials have stemmed from measurements of the resistance. None-the-less, the absence of direct thermodynamic information means that much about the phase diagram has to be inferred from indirect arguments. Moreover, since the primary focus of