Efficient method for the calculation of ballistic quantum transport

Mamaluy, Denis; Sabathil, M.; Vogl, P.

doi:10.1063/1.1560567

Cited by 79 publications

(85 citation statements)

References 31 publications

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“…Here we just mention that the traditional Dirichlet BC is in general poorly suited for opensystem problems, as it forces wave functions to zero at the device contacts, which is incompatible with the planewave-like open-system solutions. Moreover, utilization of generalized Neumann BC allows one to use a dramatically reduced set of eigenstates in the spectral representation of the closed system Green's function 14 . When applying the general 3D CBR approach to 1D quantum devices, we obtain a set of very simple equations.…”

Section: A 1d Cbr Formalismmentioning

confidence: 99%

“…In this paper, we focus on the details of the self-consistent 1D quantum transport code, which is based on adapting the general Contact Block Reduction (CBR) method [14][15][16][17] to 1D open systems. CBR provides a very efficient technique of implementing the non-equilibrium Green's function (NEGF) formalism 18,19 for quantum transport, and has been used successfully in simulating 2D and 3D quantum devices 15,16,20 .…”

Section: Introductionmentioning

confidence: 99%

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Efficient self-consistent quantum transport simulator for quantum devices

Gao¹,

Mamaluy²,

Nielsen³

et al. 2014

Journal of Applied Physics

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We present a self-consistent one-dimensional (1D) quantum transport simulator based on the Contact Block Reduction (CBR) method, aiming for very fast and robust transport simulation of 1D quantum devices. Applying the general CBR approach to 1D open systems results in a set of very simple equations that are derived and given in detail for the first time. The charge self-consistency of the coupled CBR-Poisson equations is achieved by using the predictor-corrector iteration scheme with the optional Anderson acceleration. In addition, we introduce a new way to convert an equilibrium electrostatic barrier potential calculated from an external simulator to an effective doping profile, which is then used by the CBR-Poisson code for transport simulation of the barrier under non-zero biases. The code has been applied to simulate the quantum transport in a double barrier structure and across a tunnel barrier in a silicon double quantum dot. Extremely fast self-consistent 1D simulations of the differential conductance across a tunnel barrier in the quantum dot show better qualitative agreement with experiment than non-self-consistent simulations.

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Section: A 1d Cbr Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient self-consistent quantum transport simulator for quantum devices

Gao¹,

Mamaluy²,

Nielsen³

et al. 2014

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…If the simulation-domain surface is within the material bulk region, a truly open BC or perfectly absorbing BC would be the best solution, as it does not introduce an artificial periodicity and would enable the simulation of carrier injection or transport. [1,2] However such a BC requires the inversion of a full matrix that is of the order of the number of atoms on the open surface. Therefore, the open BC can only be applied to relatively small open surfaces.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for the electronic structure of finite-extent embedded semiconductor nanostructures

et al. 2004

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The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires a proper boundary treatment for a finite simulation domain. For the study of a selfassembled InAs dot embedded in GaAs, three kinds of boundary conditions are examined within the empirical tight-binding model: (i) the periodic boundary condition, (ii) raising the orbital energies of surface atoms, and (iii) raising the energies of dangling bonds at the surface. The periodic boundary condition requires a smooth boundary and consequently a larger GaAs buffer than the two non-periodic boundary conditions. Between the non-periodic conditions, the dangling-bond energy shift is more numerically efficient than the orbital-energy shift, in terms of the elimination of non-physical surface states in the energy region of interest for interior states. A dangling-bond energy shift larger than 5 eV efficiently eliminates all of the surface states and leads to interior states that are highly insensitive to the choice of the energy shift.

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“…We begin this manuscript with a brief account of the numerical methods used for simulating the stationary (DC) transport properties of quantum systems. We focus on tight-binding models within the NEGF formalism 78 which has become, perhaps, the standard approach for this problem thanks to the development of recursive [38][39][40] and other advanced algorithms 41,79,80 . The basic objects obtained as the output of those numerical tools are the retarded Green's functions of the system which will be the input of the expressions for the AC observables derived later in this manuscript.…”

Section: Introductionmentioning

confidence: 99%

Numerical toolkit for electronic quantum transport at finite frequency

Shevtsov

Waintal

2013

Phys. Rev. B

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Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function of the system, i.e. the natural output of most DC numerical codes. Our framework allows to extend the simulations capabilities of existing codes to a large class of observables including, for instance, AC conductance, quantum capacitance, quantum pumping, spin pumping or photo-assisted shot noise. The theory is developed within the framework of Keldysh formalism and we provide explicit links with the alternative (and equivalent) scattering approach. We illustrate the formalism with a study of the AC conductance in a quantum point contact and an electronic Mach-Zehnder interferometer in the quantum Hall regime.

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Efficient method for the calculation of ballistic quantum transport

Cited by 79 publications

References 31 publications

Efficient self-consistent quantum transport simulator for quantum devices

Efficient self-consistent quantum transport simulator for quantum devices

Boundary conditions for the electronic structure of finite-extent embedded semiconductor nanostructures

Numerical toolkit for electronic quantum transport at finite frequency

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