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Quantum Transport Simulations of Nano-systems
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Andrea Droghetti, Ivan Rungger
In the near future, most of the research efforts in quantum transport will be dedicated to account for many-body interactions from first-principles. We see two emerging complementary approaches. The first aims at developing a DFT theory for transport, which is based on solid theoretical foundations [47]. The drawback is the difficulty in designing appropriate xc functionals. The second aims at extending techniques, such as many-body perturbation theory (MBPT) (e.g., Ref. [49]) and dynamical mean-field theory (DMFT) (e.g. Refs. [7,10,12]) to transport. When applied to molecular junctions, MBPT is able to account very accurately for fundamental gap of molecules and electronic screening at the molecule-electrode interfaces. DMFT instead captures transport-related phenomena driven by the strong electron-electron interaction. In case of molecular devices, these phenomena include the Kondo effect, Coulomb blockade and inelastic spin excitations, which are not described even at the qualitative level by DFT+NEGF and related schemes. In case of solid state devices, DMFT correctly describes the narrowing of the 3d states in transition metals, the insulating nature of Mott and charge-transfer materials and the inelastic scattering by magnetic impurities in graphene nano-ribbons and related nano-structures. The drawback of DMFT is the computational complexity so that, in practice, strong correlation effects can only be accounted for in a small subspace of the scattering region comprising only few molecular or atomic orbitals.
Electron Transport across Oxide Interfaces on the Nanoscale
Published in Tamalika Banerjee, Oxide Spintronics, 2019
Kumari Gaurav Rana, Saurabh Roy, Tamalika Banerjee
where the lifetime is proportional to the inverse of the cumulative density of states from the Fermi level to the energy E [48]. We have only considered the z-component, as the BEEM transmissions across the M–S interface are measured along this direction. As seen in Fig. 3.14b, the attenuation length λLDA (E) is almost constant in the range between 1.6 eV and 2.2 eV (above EF) and is greater at 120 K than at RT. In recent works [49, 50], the importance of dynamical correlations in SRO has been discussed with the aid of dynamical mean field theory. Whereas the dynamical correlations and hence, the temperature dependent quasi-particle weight z is beyond the scope of LDA, we note that this weight is one in LDA and is a multiplicative factor of the spectrum and the velocity. Assuming the same quasi-particle weight for the eg manifold and neglecting its influence on τ, we get a reduction of the attenuation length, which is more pronounced at lower temperatures. In Fig. 3.14b, we plot the attenuation length multiplying λLDA by z and observe that under these assumptions, the attenuation length at RT is greater than at 120 K, in agreement with the experimental findings.
3He and Mott Organics
Published in Sergey Kravchenko, Strongly Correlated Electrons in Two Dimensions, 2017
V. Dobrosavljevič, D. Tanaskovič
We conclude that in the relevant temperature regime, transport should be dominated by inelastic electron–electron scattering, not the impurity-induced (Anderson) localization of quasiparticles, as described by disordered FL theories of Finkel’stein and followers (Finkel’stein, 1983, 1984; Punnoose and Finkel’stein, 2001). As illustrated schematically in Fig. 1.2, transport in this incoherent regime has a very different character than in the coherent “diffusive” regime found in good metals with disorder. Incoherent transport dominated by inelastic electron–electron scattering is typical of systems featuring strong electronic correlations, such as heavy-fermion compounds (Stewart, 1984) or transition metal oxides (TMOs) (Goodenough, 1963) close to the Mott (interaction-driven) MIT (Mott, 1990). Understanding this physical regime requires not only a different set theoretical tools but also an entirely different conceptual picture of electron dynamics. As we shall explain next, modern dynamical mean-field theory (DMFT) methods (Georges et al., 1996) make it possible to qualitatively and even quantitatively explain most universal features within this incoherent transport regime dominated by strong correlation effects.
Understanding and optimization of hard magnetic compounds from first principles
Published in Science and Technology of Advanced Materials, 2021
Takashi Miyake, Yosuke Harashima, Taro Fukazawa, Hisazumi Akai
A direct method to evaluate the magnetocrystalline anisotropy energy (MCA) is the total-energy-difference method. In this method, the total energy when the magnetization is along the easy axis is compared to that along the hard axis. The MCA can be also evaluated from the band energy using the force theorem [30–32] based on the perturbation theory when the spin–orbit interaction is weak or moderate. On the other hand, 4f electrons in rare-earth (RE) elements are hard to treat. There is no established approximation that is quantitatively accurate enough, and at the same time computationally cheap for practical use. Development of first-principles methods is an important issue. Trials using e.g. self interaction correction (SIC) [33,34] and dynamical mean-field theory (DMFT) [35,36] are underway. A conventional method for the MCA energy in rare-earth magnet compounds is based on the crystal field theory [37,38]. In this method, the crystal-field (CF) coefficients are computed by expanding the Kohn-Sham effective potential in eq.(3) by real spherical harmonics. The magnetocrystalline anisotropy constant is evaluated from the CF parameter as
Systematically improvable excitonic Hamiltonians for electronic structure theory
Published in Molecular Physics, 2019
Traditional electronic structure approaches are available to treat inter-fragment interactions in the excitonic picture. In principle, even the covalent bonding interaction can be represented by allowing correlated charge-state fluctuations, though excitonic renormalisation is probably most useful for weakly interacting fragments. System-wide induction can be captured at the mean-field level, but using polarisabilities from internally correlated fragments. The usual post-mean-field approaches (e.g. perturbation theory, coupled-cluster theory), can be used to handle inter-fragment electron correlation (i.e. Van der Waals forces). Excitonically renormalised Hamiltonians might also be used in dynamical mean-field theory calculations for the electronic structures of crystals [25]. The computational cost for a global calculation (after the effective Hamiltonian is obtained) will depend only on the numbers of fragments and states per fragment, not on the internal structure of those fragment states.
Excitonically renormalised coupled-cluster theory
Published in Molecular Physics, 2019
Starting a few decades ago, and continuing apace today, enormous progress is being made in performing useful chemical simulations by decomposing large quantum-mechanical systems into recoupled sub-systems. The state of the art generally consists of embedding fragments into the electrostatic environments of their neighbours (with various approaches to the exchange interaction) [1–9], or using a fragment-based decomposition of a reference wavefunction for subsequent electron-correlation calculations [10,11]; these approaches may be taken in combination with schemes for configurational sampling and techniques for handling redundancy in periodic systems [12–14]. Similarly, many local correlation methods [15–24] have been developed that use orbitals that are localised (not necessarily to a fragment) to separate strong and weak correlations, generally neglecting or treating perturbatively the long-range electron correlation. For modelling of generic physical phenomena in lattices, dynamical mean field theory [25] has been used with model Hamiltonians to represent the entanglement of different site states. The literature chronicling the evolution of fragment-based (and related) methods is vast, and has been reviewed several times [26–31].