Hybrid Mode-Space–Real-Space Approximation for First-Principles Quantum Transport Simulation of Inhomogeneous Devices

We propose a robust strategy for transforming the Hamiltonian of a metallic structure expressed in a nonorthogonal density-functional-theory (DFT) basis into a low-dimensional space compatible with electron-transport simulations. This mode-space approximation is applied locally to inhomogeneous material stacks including amorphous phases and interfaces. The contacts and periodic parts of the device are transformed into the subspace created, while the active inhomogeneous regions remain represented in real space. The various regions are connected to each other through mode-space--real-space hybrid blocks of the Hamiltonian and overlap matrices. This approach allows harnessing of the full flexibility of DFT combined with the power of the nonequilibrium Green's function formalism at a moderate cost. In particular, for a realistic resistive random-access memory cell composed of 3390 atoms, a performance improvement by a factor of 136 compared with a pure real-space treatment is demonstrated, with an error of less than 2%.