*ANSWERS: Accelerating nano-device simulations with extreme-scale algorithms and software co-integration*

*PI: Mathieu Luisier (ETH Zurich)*

*Co-PIs: Anton Kozhevnikov, Lin Lin, Nicola Marzari, Olaf Schenk, Chao Yang*

*July 1, 2014 - December 31, 2016*

## Project Summary

The project aims at integrating general-purpose parallel numerical libraries and improved physical models to advance the state-of-the-art in electronic structure and quantum transport calculations of nanostructures. The treatment of larger atomic systems, the reduction of the simulation time, the improvement of the result accuracy, and the usage of novel computer architectures are the objectives of this project.

Nanosizing has revolutionized the design of electronic components to the point where their material properties and atomic configuration almost entirely determine their functionality. To accelerate the emergence of novel device concepts, advanced simulation tools relying on quantum mechanics and treating the different material regions at the atomic scale are needed. Electronic structure calculators and quantum transport simulators have established themselves as powerful engines to study the equilibrium and out-of-equilibrium properties of nanostructures. However, both approaches suffer from the same deficiencies: they are usually limited to small atomic systems and they are subject to lame compromises between short simulation times (empirical models) and accurate results (ab-initio approaches). These restrictions are mainly due to the underlying numerical algorithms, matrix diagonalizations for electronic structure calculations and sparse linear systems of equations for quantum transport problems, that do not scale well on large core numbers and poorly exploit the available computational resources.

As part of the ANSWERS project, we will address these issues by developing and releasing two parallel numerical libraries called SPI and SolQTP and by improving the capabilities of the existing Wannier90 software.

**SPI**: In ab-initio electronic structure calculations with a localized basis set, the diagonalization of Hamiltonian matrices can be replaced by an integration over a complex contour together with the selected inversion of a sparse matrix. Due to the narrow range of the basis components, not all the elements of the inverse matrix are needed, but only those corresponding to the original sparsity pattern. Hence, as first major innovation, a massively parallel algorithm to compute selected entries of the inverse of a matrix will be implemented and integrated into a package called SPI, which partially relies on the well-known computational math libraries Pardiso and SPIKE, which are both integrated into Intels math kernel library. As a proof of concept the selected inversion process will be coupled with CP2K, an ab-initio electronic structure solver, with Wannier90, and with OMEN, a quantum transport simulator.

**SolQTP**: Quantum transport problems differentiate themselves from electronic structure calculations by the presence of open boundary conditions (OBCs) and by the fact that linear systems of equations must be solved instead of diagonalizing a matrix. The Non-equilibrium Greens Function (NEGF) formalism is a very suitable technique for that purpose, but it usually does not scale well on large CPU counts, especially if an ab-initio basis is employed. As second major innovation we therefore propose to implement a versatile library called SolQTP to solve the NEGF and OBCs equations on hybrid architectures composed of CPUs and GPUs, irrespective of the Hamiltonian basis (kp, tight-binding, Wannier functions, or Gaussian orbitals) and device geometry. The quantum transport simulator OMEN will serve as a testbed for the solvers implemented in the SolQTP library.

**Wannier90**: Maximally-localizedWannier functions (MLWFs) provide a most compact, but still exact representation of the electronic structure of any given system, and a most transferable one since they depend only on the local chemical environment. For these reasons, they form an ideal building block to construct the Hamiltonians of very large nanostructures retaining full first-principles accuracy. These Hamiltonians can then be provided to SPI to calculate the desired part of the electronic spectrum or to SolQTP for quantum transport simulations. As part of this project, we will develop the infrastructure to construct Hamiltonians for large nanostructures, together with a database of Wannier functions, including inter-atomic matrix elements, for a wide variety of materials and chemical environments. This will leverage our on-going efforts in high-throughput calculations in inorganic materials. As a third major innovation we will implement the algorithm and procedure to construct the maximally-transferable Wannier functions into the Wannier90 package.

A team of scientists with different but complementary expertise has been assembled to successfully conduct the work proposed in the ANSWERS project.

The outcome of this research collaboration will not only benefit to the selected application tools, CP2K, OMEN, and Wannier90, but it will also be useful to the density-functional theory (DFT) and device modeling communities in general. For example, other DFT codes working directly with a localized basis, e.g. SIESTA, Onetep, Gaussian, or OpenMX, could greatly benefit from the capabilities of the SPI library. Similarly, the SolQTP library could bring significant speed-up to quantumtransport solvers such as NanoTCAD ViDES from the University of Pisa or NEMO5 from Purdue University. Finally, Wannier90 has already been interfaced to most electronic-structure codes in use in materials science (VASP, Quantum-ESPRESSO, Abinit, CASTEP, FLEUR, SIESTA, or Wien2K, to name a few) and thus represents an ideal interface to a broad user basis interested in large-scale electronic structure and quantum transport calculations.