Quantum avalanche in higher dimensions.

Quantum Avalanche describes a mechanism of Insulator to Metal transition in which abrupt excited electronic occupation due to instability in the nonequilibrium conduction band under an electric field via the spontaneous phonon emission. The analytic theory[1][2] accounts for Quantum Avalanche was recently proposed predicting the switching fields of Insulator-Metal transition which are of the same order of magnitude as the experimental results for Mott insulators and CDW materials. Previous analytic thoery of Quantum Avalanche was discussed in one dimensional senario but the theory for higher dimensions can also be achieved using similar technique and the avalanche condition for two and three dimension can be established as well. Particularly in 2D senatio, the avlanche field (the critical value of E-field at which Quantum Avalanche occurs) is diverged when the dephasing of electron with the environment increases, which is supported by the numerical calculation for 2D tight binding lattice. In 3D, analytical theory shows no divergence in avalanche field as function of dephasing but avalanche is harder to occur.

[1] J. E. Han, C. Aron, X. Chen, I. Mansaray, J.-H. Han, K.-S. Kim, M. Randle, and J. P. Bird, Nat Commun 14, 2936 (2023).

[2] X. Chen and J. E. Han, Phy. Rev. B 109(5) (2024)