A comprehensive study of the velocity, momentum and position matrix elements for Bloch states: Application to a local orbital basis

We present a comprehensive study of the velocity operator, v = ħhi [Ĥ, r], when used in crystalline solids calculations. The velocity operator is key to the evaluation of a number of physical properties and its computation, both from a practical and fundamental perspective, has been a long-standing debate for decades. Our work summarizes the different approaches found in the literature, but never connected before in a comprehensive manner. In particular we show how one can compute the velocity matrix elements following two different routes. One where the commutator is explicitly used and another one where the commutator is avoided by relying on the Berry connection. We work out an expression in the latter scheme to compute velocity matrix elements, generalizing previous results. In addition, we show how this procedure avoids ambiguous mathematical steps and how to properly deal with the two popular gauge choices that coexist in the literature. As an illustration of all this, we present several examples using tight-binding models and local density functional theory calculations, in particular using Gaussian-type localized orbitals as basis sets. We show how the the velocity operator cannot be approximated, in general, by the k-gradient of the Bloch Hamiltonian matrix when a non-orthonormal basis set is used. Finally, we also compare with its real-space evaluation through the identification with the canonical momentum operator when possible. This comparison offers us, in addition, a glimpse of the importance of non-local corrections, which may invalidate the naive momentum-velocity correspondencePID2019-109539GB-C43, CEX2018-000805-M, S2018/NMT-432

Ballistic spin-valves with Ni nanocontacts

Poster presented in TNT 2005 "Trends in Nanotechnology", Oviedo, Spain, 29 August-02 September, 2005

Nonequilibrium magneto-conductance as a manifestation of spin filtering in chiral nanojunctions

It is generally accepted that spin-dependent electron transmission may appear in chiral systems, even without magnetic components, as long as significant spin−orbit coupling is present in some of its elements. However, how this chirality-induced spin selectivity (CISS) manifests in experiments, where the system is taken out of equilibrium, is still debated. Aided by group theoretical considerations and nonequilibrium DFT-based quantum transport calculations, here we show that when spatial symmetries that forbid a finite spin polarization in equilibrium are broken, a net spin accumulation appears at finite bias in an arbitrary twoterminal nanojunction. Furthermore, when a suitably magnetized detector is introduced into the system, the net spin accumulation, in turn, translates into a finite magneto-conductance. The symmetry prerequisites are mostly analogous to those for the spin polarization at any bias with the vectorial nature given by the direction of magnetization, hence establishing an interconnection between these quantitiesJ.J.P. and M.A.G.-B. acknowledge financialsupport from Spanish MICINN (grant nos. PID2019-109539GB-C43 and TED2021- 131323B-I00), the María de Maeztu Program for Units of Excellence in R&D (grant no. CEX2018-000805-M), Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (grant no. S2018/NMT-4321), Generalitat Valenciana through Programa Prometeo (2021/017), Centro de Computación Científica of the Universidad Autónoma de Madrid, and Red Española de Supercomputació

Deep learning for disordered topological insulators through their entanglement spectrum

Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a technique based on the entanglement spectrum, which can be used to identify the hidden topology of systems without translational invariance. By training a neural network to distinguish between trivial and topological phases using the entanglement spectrum obtained from crystalline or weakly disordered phases, we can predict the topological phase diagram for generic disordered systems. This approach becomes particularly useful for gapless systems, while providing a computational speed-up compared to the commonly used Wilson loop technique for gapful situations. Our methodology is illustrated in two-dimensional models based on the Wilson-Dirac lattice Hamiltonia

Shift current with Gaussian basis sets and general prescription for maximally symmetric summations in the irreducible Brillouin zone

The bulk photovoltaic effect is an experimentally verified phenomenon by which a direct charge current is induced within a non-centrosymmetric material by light illumination. Calculations of its intrinsic contribution, the shift current, are nowadays amenable from first-principles employing plane-wave bases. In this work, we present a general method for evaluating the shift conductivity in the framework of localized Gaussian basis sets that can be employed in both the length and velocity gauges, carrying the idiosyncrasies of the quantum-chemistry approach. The (possibly magnetic) symmetry of the system is exploited in order to fold the reciprocal space summations to the representation domain, allowing us to reduce computation time and unveiling the complete symmetry properties of the conductivity tensor under general light polarizationPID2019-109539GB-C43, TED2021-131323B−I00, S2018/NMT-432

Charge-spin interconversion in graphene-based systems from density functional theory

We present a methodology to address, from first principles, charge-spin interconversion in two-dimensional materials with spin-orbit coupling. Our study relies on an implementation of density functional theory based quantum transport formalism adapted to such purpose. We show how an analysis of the k-resolved spin polarization gives the necessary insight to understand the different charge-spin interconversion mechanisms. We have tested it in the simplest scenario of isolated graphene in a perpendicular electric field where effective tight-binding models are available to compare with. Our results show that the flow of an unpolarized current across a single layer of graphene produces, as expected, a spin separation perpendicular to the current for two of the three spin components (out-of-plane and longitudinal), which is the signature of the spin Hall effect. Additionally, it also yields an overall spin accumulation for the third spin component (perpendicular to the current), which is the signature of the Rashba-Edelstein effect. Even in this simple example, our results reveal an unexpected competition between the Rashba and the intrinsic spin-orbit coupling. Remarkably, the sign of the accumulated spin density does not depend on the electron or hole nature of the injected current for realistic values of the Rashba couplin

Refined electron-spin transport model for single-element ferromagnetic systems: Application to nickel nanocontacts

Through a combination of atomistic spin-lattice dynamics simulations and relativistic ab initio calculations of electronic transport we shed light on unexplained electrical measurements in nickel nanocontacts created by break junction experiments under cryogenic conditions (4.2 K). We implement post-self-consistent-field corrections in the conductance calculations to account for spin-orbit coupling and the noncollinearity of the spins, resulting from the spin-lattice dynamics. We find that transverse magnetic domain walls are formed preferentially in (111)-oriented face-centered-cubic nickel atomic-sized contacts, which also form elongated constrictions, giving rise to enhanced individual domain wall magnetoresistance. Our calculations show that the ambiguity surrounding the conductance of a priori uniformly magnetized nickel nanocontacts can be traced back to the crystallographic orientation of the nanocontacts, rather than spontaneously formed magnetic domain walls “pinned” at their narrowest points.This work was supported by the Generalitat Valenciana through Grant No. PROMETEO2017/139. C.S. gratefully acknowledges financial support from the Dean Fellowship of the Weizmann Institute of Science and Generalitat Valenciana (Grant No. CDEIGENT2018/028). O.T. appreciates the support of the Harold Perlman family, and acknowledges funding by a research grant from Dana and Yossie Hollander, the Israel Science Foundation (Grant No. 1089/15), the Minerva Foundation (Grant No. 120865), and The Ministry of Science and Technology of Israel (Grant No. 3-16244). J.J.P. acknowledges financial support from Spanish MINECO through Grants No. FIS2016-80434-P and No. PID2019-109539GB-C43, the Fundación Ramón Areces, the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321), the European Union Seventh Framework Programme under Grant Agreement No. 604391 Graphene Flagship, the Centro de Computación Científica of the Universidad Autónoma de Madrid and the computer resources at MareNostrum and the technical support provided by the Barcelona Supercomputing Center (Grant No. FI-2019-2-0007). The SLD and DFT calculations in this paper were performed on the high-performance computing facilities of the University of Alicante and the University of South Africa

Dynamic bonding influenced by the proximity of adatoms to one atom high step edges

Low-temperature scanning tunneling microscopy is used here to study the dynamic bonding of gold atoms on surfaces under low coordination conditions. In the experiments, using an atomically sharp gold tip, a gold adatom is deposited onto a gold surface with atomic precision either on the first hollow site near a step edge or far away from it. Classical molecular dynamics simulations at 4.2 K and density-functional theory calculations serve to elucidate the difference in the bonding behavior between these two different placements, while also providing information on the crystalline classification of the STM tips based on their experimental performance.This work was supported by the Generalitat Valenciana through Grants No. CDEIGENT/2018/028, No. PROMETEO/2017/139, and No. PROMETEO/2021/017. The authors also acknowledge financial support from Spanish MICIN through Grant No. PID2019-109539 GB-C43, the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321). The theoretical modeling was performed on the high-performance computing facilities of the University of South Africa and the University of Alicante. Netherlands Organization for Scientific Research (NWO/OCW) supported the experiments

Theoretical approach for Electron Dynamics and Ultrafast Spectroscopy (EDUS)

In this manuscript, we present a theoretical framework and its numerical implementation to simulate the out-of-equilibrium electron dynamics induced by the interaction of ultrashort laser pulses in condensed-matter systems. Our approach is based on evolving in real time the density matrix of the system in reciprocal space. It considers excitonic and nonperturbative light−matter interactions. We show some relevant examples that illustrate the efficiency and flexibility of the approach to describe realistic ultrafast spectroscopy experiments. Our approach is suitable for modeling the promising and emerging ultrafast studies at the attosecond time scale that aim at capturing the electron dynamics and the dynamical electron−electron correlations via X-ray absorption spectroscopyG.C., M.M., and A.P. acknowledge Comunidad de Madrid through TALENTO Grant Ref 2017-T1/IND-5432 and 2021- 5A/IND-20959, Grants Ref RTI2018-097355-A-I00 and ref PID2021-126560NB-I00 (MCIU/AEI/FEDER, UE), and computer resources and assistance provided by Centro de Computación Científica de la Universidad Autónoma de Madrid (FI-2021-1-0032), Instituto de Biocomputación y Física de Sistemas Complejos de la Universidad de Zaragoza (FI-2020-3-0008), and Barcelona Supercomputing Center (FI2020-1-0005, FI-2021-2-0023, FI-2021-3-0019). J.J.P., J.J.E.-P., and A.J.U.-Á . acknowledge funding from Grant No. PID2019- 109539GB-C43 (MCIU/AEI/FEDER, UE), the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321), and the Generalitat Valenciana through Programa Prometeo/2021/01. F.M. acknowledges the MICIN project PID2019-105458RB-I00, the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2016-0686), and the “María de Maeztu” Programme for Units of Excellence in R&D (CEX2018-000805-M). R.E.F.S. acknowledges support from the fellowship LCF/BQ/PR21/11840008 from “La Caixa” Foundation (ID 100010434

Dynamic bonding influenced by the proximity of adatoms to one atom high step edges

Low-temperature scanning tunneling microscopy is used here to study the dynamic bonding of gold atoms on surfaces under low coordination conditions. In the experiments, using an atomically sharp gold tip, a gold adatom is deposited onto a gold surface with atomic precision either on the first hollow site near a step edge or far away from it. Classical molecular dynamics simulations at 4.2 K and density-functional theory calculations serve to elucidate the difference in the bonding behavior between these two different placements, while also providing information on the crystalline classification of the STM tips based on their experimental performanc