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Register a new userAn efficient method for quantum transport simulations in the time domain
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An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. In this scheme, the density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier {em ab-initio} implementations of this formalism, the Hamiltonian is here approximated by a density expansion in the spirit of the density functional based tight-binding (DFTB) method without introducing empirical parameters. Results are presented for two prototypical molecular devices and compared to calculations at the full TDDFT level. The issue of non-existence of a steady state under certain conditions is also briefly touched on.
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Scaling of semiconductor devices has reached a stage where it has become absolutely imperative to consider the quantum mechanical aspects of transport in these ultra small devices. In these simulations, often one excludes a rigorous band structure treatment, since it poses a huge computational challenge. We have proposed here an efficient method for calculating full three-dimensionally coupled quantum transport in nanowire transistors including full band structure. We have shown the power of the method by simulating hole transport in p-type Ge nanowire transistors. The hole band structure obtained from our nearest neighbor sp3s* tight binding Hamiltonian agrees well qualitatively with more complex and accurate calculations that take third nearest neighbors into account. The calculated I-V results show how shifting of the energy bands due to confinement can be accurately captured only in a full band full quantum simulation.
We propose a first-principles method of efficiently evaluating electron-transport properties of very long systems. Implementing the recursive Greens function method and the shifted conjugate gradient method in the transport simulator based on real-space finite-difference formalism, we can suppress the increase in the computational cost, which is generally proportional to the cube of the system length to a linear order. This enables us to perform the transport calculations of double-walled carbon nanotubes~(DWCNTs) with 196,608 atoms. We find that the conductance spectra exhibit different properties depending on the periodicity of doped impurities in DWCNTs and they differ from the properties for systems with less than 1,000 atoms.
The quantum transport formalism based on tight-binding models is known to be powerful in dealing with a wide range of open physical systems subject to external driving forces but is, at the same time, limited by the memory requirements increasing with the number of atomic sites in the scattering region. Here we demonstrate how to achieve an accurate simulation of quantum transport feasible for experimentally sized bulk graphene heterojunctions at a strongly reduced computational cost. Without free tuning parameters, we show excellent agreement with a recent experiment on Klein backscattering [A. F. Young and P. Kim, Nature Phys. 5, 222 (2009)].
The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually involve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
The recent prediction, and subsequent discovery, of the quantum anomalous Hall (QAH) effect in thin films of the three-dimensional ferromagnetic topological insulator (MTI) (Cr$_y$Bi$_x$Sb$_{1-x-y}$)$_2$Te$_3$ has opened new possibilities for chiral-edge-state-based devices in zero external magnetic field. Like the $ u=1$ quantum Hall system, the QAH system is predicted to have a single chiral edge mode circulating along the boundary of the film. Backscattering of the chiral edge mode should be suppressed, as recently verified by the observation of well-quantized Hall resistivities $rho_{yx} = pm h/e^2$, along with longitudinal resistivities as low as a few ohms. Dissipationless 1D conduction is also expected along magnetic domain walls. Here, we intentionally create a magnetic domain wall in a MTI and study electrical transport along the domain wall. We present the first observation of chiral transport along domain walls, in agreement with theoretical predictions. We present further evidence that two modes equilibrate and co-propagate along the length of the domain wall.
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