arXiv subjects

Stephan Mohr

Publications and source records attributed to Stephan Mohr.

At least 19 recordsLinked to original sources

arXiv2022

Extending the coherence time of spin defects in hBN enables advanced qubit control and quantum sensing

Spin defects in hexagonal Boron Nitride (hBN) attract increasing interest for quantum technology since they represent optically-addressable qubits in a van der Waals material. In particular, negatively-charged boron vacancy centers (${V_B}^-$) in hBN have shown promise as sensors of temperature, pressure, and static magnetic fields. However, the short spin coherence time of this defect currently limits its scope for quantum technology. Here, we apply dynamical decoupling techniques to suppress magnetic noise and extend the spin coherence time by nearly two orders of magnitude, approaching the fundamental $T_1$ relaxation limit. Based on this improvement, we demonstrate advanced spin control and a set of quantum sensing protocols to detect electromagnetic signals in the MHz range with sub-Hz resolution. This work lays the foundation for nanoscale sensing using spin defects in an exfoliable material and opens a promising path to quantum sensors and quantum networks integrated into ultra-thin structures.

quant-ph↗

arXiv2022

Unveiling the Zero-Phonon Line of the Boron Vacancy Center by Cavity Enhanced Emission

Negatively charged boron vacancies ($V_B^-$) in hexagonal boron nitride (hBN) exhibit a broad emission spectrum due to strong electron-phonon coupling and Jahn-Teller mixing of electronic states. As such, the direct measurement of zero-phonon line (ZPL) of $V_B^-$ has remained elusive. Here, we measure the room-temperature ZPL wavelength to be $773\pm2$ nm by coupling the hBN layer to the high-Q nanobeam cavity. As the wavelength of cavity mode is tuned, we observe a pronounced intensity resonance, indicating the coupling to $V_B^-$. Our observations are consistent with the spatial redistribution of $V_B^-$ emission. Spatially resolved measurements show a clear Purcell effect maximum at the midpoint of the nanobeam, in accord with the optical field distribution of the cavity mode. Our results are in good agreement with theoretical calculations, opening the way to using $V_B^-$ as cavity spin-photon interfaces.

cond-mat.mes-hall↗

arXiv2022

Towards Electronic Structure-Based Ab-Initio Molecular Dynamics Simulations with Hundreds of Millions of Atoms

We push the boundaries of electronic structure-based \textit{ab-initio} molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine learning potentials. We achieve this breakthrough by combining innovations in linear-scaling AIMD, efficient and approximate sparse linear algebra, low and mixed-precision floating-point computation on GPUs, and a compensation scheme for the errors introduced by numerical approximations. The core of our work is the non-orthogonalized local submatrix method (NOLSM), which scales very favorably to massively parallel computing systems and translates large sparse matrix operations into highly parallel, dense matrix operations that are ideally suited to hardware accelerators. We demonstrate that the NOLSM method, which is at the center point of each AIMD step, is able to achieve a sustained performance of 324 PFLOP/s in mixed FP16/FP32 precision corresponding to an efficiency of 67.7% when running on 1536 NVIDIA A100 GPUs.

physics.comp-ph↗

arXiv2021

Lifetime effects and satellites in the photoelectron spectrum of tungsten metal

Tungsten is an important and versatile transition metal and has a firm place at the heart of many technologies. A popular experimental technique for the characterisation of tungsten and tungsten-based compounds is X-ray photoelectron spectroscopy (XPS), which enables the assessment of chemical states and electronic structure through the collection of core level and valence band spectra. However, in the case of metallic tungsten, open questions remain regarding the origin, nature, and position of satellite features that are prominent in the photoelectron spectrum. These satellites are a fingerprint of the electronic structure of the material and have not been thoroughly investigated, at times leading to their misinterpretation. The present work combines high-resolution soft and hard X-ray photoelectron spectroscopy (SXPS and HAXPES) with reflection electron energy loss spectroscopy (REELS) and a multi-tiered ab-initio theoretical approach, including density functional theory (DFT) and many-body perturbation theory (G0W0 and GW+C), to disentangle the complex set of experimentally observed satellite features attributed to the generation of plasmons and interband transitions. This combined experiment-theory strategy is able to uncover previously undocumented satellite features, improving our understanding of their direct relationship to tungsten's electronic structure. Furthermore, it lays the groundwork for future studies into tungsten based mixed-metal systems and holds promise for the re-assessment of the photoelectron spectra of other transition and post-transition metals, where similar questions regarding satellite features remain.

cond-mat.mtrl-sci↗

arXiv2021

Full operator preconditioning and the accuracy of solving linear systems

Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator equations with a large number of discrete variables. In this paper we show that the accuracy can be improved significantly if the equation is transformed before discretization, a process we call full operator preconditioning (FOP). It bears many similarities with traditional preconditioning for iterative methods but, crucially, transformations are applied at the operator level. We show that while condition-number improvements from traditional preconditioning generally do not improve the accuracy of the solution, FOP can. A number of topics in numerical analysis can be interpreted as implicitly employing FOP; we highlight (i) Chebyshev interpolation in polynomial approximation, and (ii) Olver-Townsend's spectral method, both of which produce solutions of dramatically improved accuracy over a naive problem formulation. In addition, we propose a FOP preconditioner based on integration for the solution of fourth-order differential equations with the finite-element method, showing the resulting linear system is well-conditioned regardless of the discretization size, and demonstrate its error-reduction capabilities on several examples. This work shows that FOP can improve accuracy beyond the standard limit for both direct and iterative methods.

math.NA↗

arXiv2021

Ranking the efficiency of gas hydrate anti agglomerants through molecular dynamic simulations

Using both computational and experimental methods, the capacity of four different surfactant molecules to inhibit the agglomeration of sII hydrate particles was assessed. The computational simulations were carried out using both steered and non-steered Molecular Dynamics (MD), simulating the coalescence process of a hydrate slab and a water droplet, both covered with surfactant molecules. The experimental work was based on rocking cell measurements, determining the minimum effective dose necessary to inhibit agglomeration. Overall, good agreement was obtained between the performance predicted by the simulations and the experimental measurements. Moreover, the simulations allowed to gain additional insights that are not directly accessible via experiments, such as an analysis of the mass density profiles, the diffusion coefficients, or the orientations of the long tails.

physics.chem-ph↗

arXiv2021

Thermal and Oxidation Stability of Ti$_x$W$_{1-x}$ Diffusion Barriers Investigated by Soft and Hard X-ray Photoelectron Spectroscopy

The binary alloy of titanium-tungsten (TiW) is an established diffusion barrier in high-power semiconductor devices, owing to its ability to suppress the diffusion of copper from the metallisation scheme into the surrounding silicon substructure. However, little is known about the response of TiW to high temperature events or its behaviour when exposed to air. Here, a combined soft and hard X-ray photoelectron spectroscopy (XPS) characterisation approach is used to study the influence of post-deposition annealing and titanium concentration on the oxidation behaviour of a 300~nm-thick TiW film. The combination of both XPS techniques allows for the assessment of the chemical state and elemental composition across the surface and bulk of the TiW layer. The findings show that in response to high-temperature annealing, titanium segregates out of the mixed metal system and upwardly migrates, accumulating at the TiW/air interface. Titanium shows remarkably rapid diffusion under relatively short annealing timescales and the extent of titanium surface enrichment is increased through longer annealing periods or by increasing the precursor titanium concentration. Surface titanium enrichment enhances the extent of oxidation both at the surface and in the bulk of the alloy due to the strong gettering ability of titanium. Quantification of the soft X-ray photoelectron spectra highlights the formation of three tungsten oxidation environments, attributed to WO$_2$, WO$_3$ and a WO$_3$ oxide coordinated with a titanium environment. This combinatorial characterisation approach provides valuable insights into the thermal and oxidation stability of TiW alloys from two depth perspectives, aiding the development of future device technologies.

cond-mat.mtrl-sci↗

arXiv2020

The CECAM Electronic Structure Library and the modular software development paradigm

First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, from the compiler up, with the exception of linear-algebra and message-passing libraries. This model has been quite successful for decades. The rapid progress in methodology, however, has resulted in an ever increasing complexity of those programs, which implies a growing amount of replication in coding and in the recurrent re-engineering needed to adapt to evolving hardware architecture. The Electronic Structure Library (\esl) was initiated by CECAM (European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure programs and redesign them as free, open-source libraries. They include "heavy-duty" ones with a high degree of parallelisation, and potential for adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by scientists when implementing new ideas. It is a community effort, undertaken by developers of various successful codes, now facing the challenges arising in the new model. This modular paradigm will improve overall coding efficiency and enable specialists (computer scientists or computational scientists) to use their skills more effectively. It will lead to a more sustainable and dynamic evolution of software as well as lower barriers to entry for new developers.

cond-mat.mtrl-sci↗

arXiv2020

SIESTA: recent developments and applications

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here we describe the more recent implementations on top of that core scheme, which include: full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, DFT+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient Van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as Wannier90 and the second-principles modelling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various postprocessing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low level libraries, as well as data standards and support for them, in particular the PSML definition and library for transferable pseudopotentials, and the interface to the ELSI library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.

physics.comp-ph↗

arXiv2020

Complexity Reduction in Density Functional Theory Calculations of Large Systems: System Partitioning and Fragment Embedding

With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments, and quantify inter-fragment interactions. The methodology proposed here requires no a priori information or user interaction, allowing a single workflow to be automatically applied to any system of interest. We apply this approach to a variety of different systems, and show how it allows for the derivation of new system descriptors, the design of QM/MM partitioning schemes, and the novel application of graph metrics to molecules and materials.

physics.chem-ph↗

arXiv2017

Linear scaling DFT calculations for large Tungsten systems using an optimized local basis

Density Functional Theory (DFT) has become the quasi-standard for ab-initio simulations for a wide range of applications. While the intrinsic cubic scaling of DFT was for a long time limiting the accessible system size to some hundred atoms, the recent progress with respect to linear scaling DFT methods has allowed to tackle problems that are larger by many orders of magnitudes. However, as these linear scaling methods were developed for insulators, they cannot, in general, be straightforwardly applied to metals, as a finite temperature is needed to ensure locality of the density matrix. In this paper we show that, once finite electronic temperature is employed, the linear scaling version of the BigDFT code is able to exploit this locality to provide a computational treatment that scales linearly with respect to the number of atoms of a metallic system. We provide prototype examples based on bulk Tungsten, which plays a key role in finding safe and long-lasting materials for Fusion Reactors. We believe that such an approach might help in opening the path towards novel approaches for investigating the electronic structure of such materials, in particular when large supercells are required.

cond-mat.mtrl-sci↗

arXiv2017

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

physics.chem-ph↗

arXiv2017

Complexity Reduction in Large Quantum Systems: Reliable Electrostatic Embedding for Multiscale Approaches via Optimized Minimal Basis Functions

Given a partition of a large system into an active quantum mechanical (QM) region and its environment, we present a simple way of embedding the QM region into an effective electrostatic potential representing the environment. This potential is generated by partitioning the environment into well defined fragments, and assigning each one a set of electrostatic multipoles, which can then be used to build up the electrostatic potential. We show that, providing the fragments and the projection scheme for the multipoles are chosen properly, this leads to an effective electrostatic embedding of the active QM region which is of equal quality as a full QM calculation. We coupled our formalism to the DFT code BigDFT, which uses a minimal set of localized in-situ optimized basis functions; this property eases the fragment definition while still describing the electronic structure with great precision. Thanks to the linear scaling capabilities of BigDFT, we can compare the modeling of the electrostatic embedding with results coming from unbiased full QM calculations of the entire system. This enables a reliable and controllable setup of an effective coarse-graining approach, coupling together different levels of description, which yields a considerable reduction in the degrees of freedom and thus paves the way towards efficient QM/QM and QM/MM methods for the treatment of very large systems.

physics.chem-ph↗

arXiv2017

Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis

We present, within Kohn-Sham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then show how within this framework simple generalizations of other well-known population analyses can be used to extract, from first principles, reliable electrostatic multipoles for the identified fragments. Our approach reduces arbitrariness in the fragmentation procedure, and enables the possibility to assess, quantitatively, whether the corresponding fragment multipoles can be interpreted as observable quantities associated to a system's moiety. By applying our formalism within the code BigDFT, we show that the use of a minimal set of in-situ optimized basis functions allows at the same time a proper fragment definition and an accurate description of the electronic structure.

physics.chem-ph↗

arXiv2017

A General Algorithm to Calculate the Inverse Principal $p$-th Root of Symmetric Positive Definite Matrices

We address the general mathematical problem of computing the inverse $p$-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary $p$-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter $q$ always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.

math.RA↗

arXiv2016

Challenges in Large Scale Quantum Mechanical Calculations

During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.

physics.chem-ph↗

arXiv2015

Fragment Approach to Constrained Density Functional Theory Calculations using Daubechies Wavelets

In a recent paper we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions is optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e. without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

cond-mat.mtrl-sci↗

arXiv2015

Accurate and efficient linear scaling DFT calculations with universal applicability

Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources.

cond-mat.mtrl-sci↗