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Title: Does a two-dimensional metal survive to zero temperature?
Plain: Scaling theory says a thin disordered sheet of non-interacting electrons is always an insulator at absolute zero. The question is whether strong repulsion allows a true metal, or whether the observed metal turns insulating at temperatures not yet reached.
Precise: For 2D electrons with $1/r$ Coulomb repulsion and weak short-range disorder at $r_s >> 1$, determine whether $\sigma(T \to 0) > 0$ in a finite density range $n > n_{c}$, implying a quantum phase transition at $n_{c}$ with scaling $\rho(n, T) = F(\mid n - n_{c}\mid / T^{(1/(z \nu))})$, or whether $\rho(T)$ eventually rises (logarithmically or faster) at every $n$. An answer gives the $T = 0$ phase diagram in $(n, \mathrm{disorder})$, or the crossover temperature $T*(n, \mathrm{disorder})$ below which localization appears.
Settled by: Transport down to T well below $0.01 E_{\mathrm{F}}$ in samples with independently calibrated weak-localization and interaction corrections, or a controlled theory of the disordered interacting 2D electron gas at $r_s >> 1$.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: contested
Status note: (empty)
Posed since: 1994