Quantum Dynamical Simulation of Many Electron-Phonon Coupled Systems on Parallel Computers
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QUANTUM DYNAMICAL SIMULATION OF MANY ELECTRON-PHONON COUPLED SYSTEMS ON PARALLEL COMPUTERS AlICHIRO NAKANO, RAJIV K. KALIA, AND PRIYA VASHISHTA Concurrent Computing Laboratory for Materials Simulations, Department of Physics & Astronomy, and Department of Computer Science, Louisiana State University, Baton Rouge, LA 70803-4001
ABSTRACT A quantum dynamical simulation method is developed to investigate coupled many electron-phonon systems.
Both electron and phonon wave functions are numerically
propagated in time. The method is applied to the study of resonant tunneling of an electron through double quantum dots. Phonon-induced electron localization is observed. The spacesplitting Schrtdinger solver and dynamical-simulated-annealing Poisson solver are implemented on an 8,192-node MP-l computer from MasPar.
INTRODUCTfION Current technologies for very large-scale integrated-circuit (VLSI) are approaching their physical limits. There are growing efforts to extend the limits by utilizing quantum effects in semiconductor devices of nanometer size. For example, the interference effect is used in the quantum interference transistor[1], and tunneling is used in the resonant tunneling diode [2].
In single electron devices, tunneling is combined with the enhanced
charging effect in a small tunnel junction to control the flow of a single electron [3]. In polar semiconductors, longitudinal-optical (LO) phonons have a significant effect on the performance of nanodevices. Recently many researchers have focused on the carrier-LOphonon interaction in nanostructures to find ways to control mobility-degrading phonon scatterings by artificially tailored structures [4]. We have developed a quantum dynamical simulation scheme [5,6] for many electronphonon systems to study electron transport in nanodevices. Various physical effects have been investigated including: Plasmon-assisted tunneling in a resonant-tunneling diode [5] and spin-dependent Coulomb-blockade effect in a quantum-dot diode [6]. Recently, the simulation scheme has been applied to the study of resonant tunneling of an electron through double quantum dots. Phonon-induced electron localization has been observed [7]. The core computational kernel of our simulation scheme has two parts: Parabolic partial differential equations (the time-dependent Schrtidinger equation or time-dependent Kohn-Sham equation) for electrons and phonons and elliptic partial differential equations (the Poisson equation) for the long-range electron-electron interaction.
Space splitting
Schrtdinger solver [8] and dynamical-simulated-annealing (DSA) Poisson solver [9] are implemented on an 8,192-node MP- 1 computer from MasPar. Mat. Res. Soc. Symp. Proc. Vol. 291. C1993 Materials Research Society
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QUANTUM DYNAMICAL SIMULATION SCHEME In our quantum dynamical simulation scheme, the electron-electron interaction is included in the framework of the time-dependent density functional theory [10]. Accordingly we solve the time-dependent Kohn-Sham equations [10] for electron orbitals [5,6]. The Hart
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