ترغب بنشر مسار تعليمي؟ اضغط هنا

Pedagogical introduction to equilibrium Greens functions: condensed matter examples with numerical implementations

96   0   0.0 ( 0 )
 نشر من قبل Mariana Odashima
 تاريخ النشر 2016
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The Greens function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Greens functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Greens functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Greens function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Greens function method, which can be of interest when simulating simultaneously the properties of surface and bulk.



قيم البحث

اقرأ أيضاً

Teachers intentionally pick the most informative examples to show their students. However, if the teacher and student are neural networks, the examples that the teacher network learns to give, although effective at teaching the student, are typically uninterpretable. We show that training the student and teacher iteratively, rather than jointly, can produce interpretable teaching strategies. We evaluate interpretability by (1) measuring the similarity of the teachers emergent strategies to intuitive strategies in each domain and (2) conducting human experiments to evaluate how effective the teachers strategies are at teaching humans. We show that the teacher network learns to select or generate interpretable, pedagogical examples to teach rule-based, probabilistic, boolean, and hierarchical concepts.
In this work, an analytic model is proposed which provides in a continuous manner the current-voltage characteristic (I-V) of high performance tunneling field-effect transistors (TFETs) based on direct bandgap semiconductors. The model provides close d-form expressions for I-V based on: 1) a modified version of the well-known Fowler-Nordheim (FN) formula (in the ON-state), and 2) an equation which describes the OFF-state performance while providing continuity at the ON/OFF threshold by means of a term introduced as the continuity factor. It is shown that traditional approaches such as FN are accurate in TFETs only through correct evaluation of the total band bending distance and the tunneling effective mass. General expressions for these two key parameters are provided. Moreover, it is demonstrated that the tunneling effective mass captures both the ellipticity of evanescent states and the dual (electron/hole) behavior of the tunneling carriers, and it is further shown that such a concept is even applicable to semiconductors with nontrivial energy dispersion. Ultimately, it is found that the I-V characteristics obtained by using this model are in close agreement with state-of-the-art quantum transport simulations both in the ON- and OFF-state, thus providing validation of the analytic approach.
Circuit QED techniques have been instrumental to manipulate and probe with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices where the supe rconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of Mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the Circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments consists in using cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states.
We develop a theory of the quasi-static electrodynamic Greens function of deep subwavelength optical cavities containing an hyperbolic medium. We apply our theory to one-dimensional cavities realized using an hexagonal boron nitride and a patterned metallic substrate.
Since the breakthrough of twistronics a plethora of topological phenomena in two dimensions has appeared, specially relating topology and electronic correlations. These systems can be typically analyzed in terms of lattice models of increasing comple xity using Greens function techniques. In this work we introduce a general method to obtain the boundary Greens function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. As an illustration we apply our formalism to analyze the edge features of Chern insulators, topological superconductors as the Kitaev square lattice and the Checkerboard lattice in the flat band topological regime. The efficiency of the method is demonstrated by comparison to standard recursive Greens function calculations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا