Improvements on non-equilibrium and transport Green function techniques: the next-generation transiesta

Abstract: We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes ($N_e\ge1$) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour opti- mizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF post-processing code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, $N_e\ge1$ electrode capability, bond-currents, generalized interface for user-defined tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding $10^6$ atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems.

• The paper introduces a novel multi-electrode framework for quantum transport that expands beyond traditional two-terminal setups.
• The paper incorporates advanced algorithms like block-tri-diagonal matrix inversion, achieving computational speedups exceeding 100 times for large systems.
• The paper ensures realistic device simulations by addressing charge conservation and enabling scalable hybrid parallelization for efficient nanoscale analysis.

Improvements on Non-Equilibrium and Transport Green Function Techniques: The Next-Generation TranSiesta

The paper under consideration presents an extensive refinement and expansion of the TranSIESTA code, originally a DFT-NEGF implementation for simulating quantum transport phenomena at the atomic scale. This updated version aims to address various limitations and enhance several key aspects of the original framework, facilitating more efficient and accurate computations pertaining to electronic and phononic transport properties.

Methodological and Technical Advancements

The authors propose several novel methods within the NEGF code TranSIESTA, which utilize DFT to explore electronic transport. Significant improvements have been introduced in terms of computational efficiency, flexibility, and functionality:

1. Multi-Electrode Capability: The implementation of a framework allowing for devices with one or multiple electrodes, each equipped with separate chemical potentials and electronic temperatures, reflects a significant stride towards enabling complex transport scenarios beyond the typical two-terminal setups.
2. Electrostatic Gating and Contour Optimization: The introduction of novel methods for electrostatic gating and contour optimizations signifies a leap in accurately modeling the gate effects vital for nanoelectronic device simulations.
3. Efficient Matrix Inversion: A noteworthy enhancement in this paper is the optimized algorithms for sparse matrix inversion. By focusing on advanced techniques such as the block-tri-diagonal (BTD) inversion method, the authors claim an improvement in computational speedup by factors exceeding 100 times for larger systems, thus permitting simulations of unprecedented scale and complexity.
4. Charge Conservation and Thermoelectric Effects: Ensuring charge neutrality and accommodating non-equilibrium thermoelectric effects paves the way for more realistic device simulations under various operational conditions.
5. Flexible Post-Processing with TbTRANS: The paper also unveils a NEGF post-processing code for electron and phonon transport, allowing detailed examination of transport properties such as bond-currents and sub-partition eigenstate projections. A major feature is the ability to handle and simulate over millions of atoms efficiently.
6. Hamiltonian Interpolation for I-V Curves: To mitigate the heavy computational demands of full $I-V$ curve calculations, an interpolation scheme for Hamiltonians at different bias conditions is proposed, showcasing significant computational savings with maintained accuracy.
7. Scalable Hybrid Parallelization: With the incorporation of both OpenMP threading and MPI, the computational strategy adopted in this iteration ensures scalability on modern heterogeneous computing platforms.

Implications and Applications

The practical implications of these advancements are manifold. The enhanced methods allow for a more accurate and efficient exploration of charge transport at the nanoscale, critical for designing and understanding nanoscale electronic devices, including sensors, transistors, and more exotic quantum devices.

The inclusion of multi-electrode systems expands the range of practical device setups that can be simulated, facilitating a deeper understanding of complex junction interface behaviors and multi-terminal transport phenomena.

Future Outlook

While this paper undoubtedly advances the state of computational methodologies for quantum transport, it also sets the stage for future extensions and applications. The ability to simulate larger systems with increased accuracy and lower computational costs opens avenues for probing more intricate materials and device architectures.

Additionally, the introduced interpolation schemes and scalable computations may be further refined and adapted to integrate seamlessly with machine learning models, unlocking new frontiers in automated material discovery and device optimization.

In conclusion, the updates to TranSIESTA encapsulated in this paper represent a comprehensive enhancement to the DFT-NEGF framework, promising to drive further discoveries and optimizations in the field of quantum transport simulations.