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Register a new userThe self-consistent quantum-electrostatic problem in strongly non-linear regime
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The self-consistent quantum-electrostatic (also known as Poisson-Schrodinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.
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We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, The MZI interference visibility showed an unexplained lobe pattern behavior with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI paths difference. We argue that these effects may be a new many-body manifestation of particle-wave duality of quantum mechanics. When biasing the interferometer sources beyond the linear response regime, quantum shot-noise (a particle phenomena) must affect the interference pattern of the electrons that creates it, as a result from a simple invariance argument. An approximate solution of the interacting Hamiltonian indeed shows that the interference visibility has a lobe pattern with applied bias with a period proportional to the average path length and independent of the paths difference, together with a phase rigidity.
While offering unprecedented resolution of atomic and electronic structure, Scanning Probe Microscopy techniques have found greater challenges in providing reliable electrostatic characterization at the same scale. In this work, we introduce Electrostatic Discovery Atomic Force Microscopy, a machine learning based method which provides immediate quantitative maps of the electrostatic potential directly from Atomic Force Microscopy images with functionalized tips. We apply this to characterize the electrostatic properties of a variety of molecular systems and compare directly to reference simulations, demonstrating good agreement. This approach opens the door to reliable atomic scale electrostatic maps on any system with minimal computational overhead.
High level of dissipation in normal metals makes challenging development of active and passive plasmonic devices. One possible solution to this problem is to use alternative materials. Graphene is a good candidate for plasmonics in near infrared (IR) region. In this paper we develop quantum theory of a graphene plasmon generator. We account for the first time quantum correlations and dissipation effects that allows describing such regimes of quantum plasmonic amplifier as surface plasmon emitting diode and surface plasmon amplifier by stimulated emission of radiation. Switching between these generation types is possible in situ with variance of graphene Fermi-level or gain transition frequency. We provide explicit expressions for dissipation and interaction constants through material parameters and find the generation spectrum and correlation function of second order which predicts laser statistics.
Quantum embedding approaches involve the self-consistent optimization of a local fragment of a strongly correlated system, entangled with the wider environment. The `energy-weighted density matrix embedding theory (EwDMET) was established recently as a way to systematically control the resolution of the fragment-environment coupling, and allow for true quantum fluctuations over this boundary to be self-consistently optimized within a fully static framework. In this work, we reformulate the algorithm to ensure that EwDMET can be considered equivalent to an optimal and rigorous truncation of the self-consistent dynamics of dynamical mean-field theory (DMFT). A practical limitation of these quantum embedding approaches is often a numerical fitting of a self-consistent object defining the quantum effects. However, we show here that in this formulation, all numerical fitting steps can be entirely circumvented, via an effective Dyson equation in the space of truncated dynamics. This provides a robust and analytic self-consistency for the method, and an ability to systematically and rigorously converge to DMFT from a static, wave function perspective. We demonstrate that this improved approach can solve the correlated dynamics and phase transitions of the Bethe lattice Hubbard model in infinite dimensions, as well as one- and two-dimensional Hubbard models where we clearly show the benefits of this rapidly convergent basis for correlation-driven fluctuations. This systematically truncated description of the effective dynamics of the problem also allows access to quantities such as Fermi liquid parameters and renormalized dynamics, and demonstrates a numerically efficient, systematic convergence to the zero-temperature dynamical mean-field theory limit.
In a series of recent papers anomalous Hall and Nernst effects have been theoretically discussed in the non-linear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the non-linear regime. The formulae we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulae, an important byproduct of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.
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