Nuclear quantum effects at metal-insulator transition of (Ga,Mn)As

Ga$_{1-x}$Mn$_x$As exhibits a Mott transition at the Mn concentration of $x_{\rm crit}\approx1\%$. We carry out self-interaction corrected density-functional calculations for this concentration regime, and in the find an insulator ground state $I$ for $x<0.5\%$, and a metal ground state $M$ for $x>1\%$. At $x=0.93\%$, however, $I$ and $M$ appear on a double well adiabatic potential energy curve, being separated only by a small energy barrier. Solving the Schr\"odinger eq.\ for nuclear motion along this adiabatic potential shows that, this energy barrier is smaller than the zero-point nuclear oscillations, i.e., the ground state must be described by the non-adiabatic superposition wavefunction $\Phi = c_M(Q;x) \phi^M + c_I(Q;x)\phi^I$, where $\phi^M$ and $\phi^I$ are the metallic and insulator states, respectively, and the expansion coefficients depend both on nuclear co-ordinates $Q$ and Mn concentration $x$. This implies that the Mott transition occurs continuously via a series of {\em excitonic phases}, as suggested by Kohn,\footnote{Kohn, Phys. Rev. Lett. {\bf 19}, 789 (1968).} but with the exception that the excitonic phase superposition states (charge density waves) can only be described after inclusion of nuclear quantum effects.