اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEquivalence of Effective Medium and Random Resistor Network models for disorder-induced unsaturating linear magnetoresistance
56
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A linear unsaturating magnetoresistance at high perpendicular magnetic fields, together with a quadratic positive magnetoresistance at low fields, has been seen in many different experimental materials, ranging from silver chalcogenides and thin films of InSb to topological materials like graphene and Dirac semimetals. In the literature, two very different theoretical approaches have been used to explain this classical magnetoresistance as a consequence of sample disorder. The phenomenological Random Resistor Network model constructs a grid of four-terminal resistors, each with a varying random resistance. The Effective Medium Theory model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. Here, we demonstrate numerically that both models belong to the same universality class and that a restricted class of the Random Resistor Network is actually equivalent to the Effective Medium Theory. Both models are also in good agreement with experiments on a diverse range of materials. Moreover, we show that in both cases, a single parameter, i.e. the ratio of the fluctuations in the carrier density to the average carrier density, completely determines the magnetoresistance profile.
قيم البحث
اقرأ أيضاً
Recently it was shown (I.A.Gruzberg, A. Klumper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization length expo
nent $2.37 pm 0.011$ for plateau transitions in the integer quantum Hall effect. This is in striking agreement with the experimental value of $2.38 pm 0.06$. Randomness of the network was modeled by replacing standard scattering nodes of a regular network by pure tunneling resp.reflection with probability $p$ where the particular value $p=1/3$ was chosen. Here we investigate the role played by the strength of the geometric disorder, i.e. the value of $p$. We consider random networks with arbitrary probability $0 <p<1/2$ for extreme cases and show the presence of a line of critical points with varying localization length indices having a minimum located at $p=1/3$.
The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)simg^{mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a
function of size $L$ and distribution tail parameter $mu$. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit $mu$ --> 0. A {it disorder length} $xi_D$ is identified beyond which the system is effectively homogeneous. This length diverges as $xi_D sim |mu|^{- u}$ ($ u$ is the regular percolation correlation length exponent) as $mu$-->0. This suggest that exactly the same critical behavior can be induced by geometrical disorder and bu strong bond disorder with the bond occupation probability $p$<-->$mu$. Only lattices at the percolation threshold have renormalized probability distribution in a {it Levy-like} basin. At the threshold the disorder length diverges at a vritical tail strength $mu_c$ as $|mu-mu_c|^{-z}$, with $z=3.2pm 0.1$, a new exponent. Critical path analysis is used in a generalized form to give form to give the macroscopic conductance for lattice above $p_c$.
The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous media. Effect
ive conductance values are calculated for the networks using effective medium theory and pore-network models. The convergence between these values is analyzed as a function of network size. Effective medium theory results are calculated analytically and numerically. Pore-network results are calculated numerically using Monte Carlo sampling. The reduced standard deviations of the Monte Carlo sampled pore-network results are examined as a function of network size. Finally, a quasi-two-dimensional network is investigated to demonstrate the limitations of effective medium theory when applied to thin porous media. Power law fits are made to these data to develop simple models governing convergence. These can be used as a guide for future research that uses both effective medium theory and pore-network models.
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the systems units and inter-unit interactions. Understanding how physical rules shape the topological structure of those net
works can clarify a systems function and enhance our ability to design, guide, or control its behavior. In the emerging area of quantum network science, a key challenge lies in distinguishing between the topological properties that reflect a systems underlying physics and those that reflect the assumptions of the employed conceptual model. To elucidate and address this challenge, we study networks that represent non-equilibrium quantum-electronic transport through quantum antidot devices -- an example of an open, mesoscopic quantum system. The network representations correspond to two different models of internal antidot states: a single-particle, non-interacting model and an effective model for collective excitations including Coulomb interactions. In these networks, nodes represent accessible energy states and edges represent allowed transitions. We find that both models reflect spin conservation rules in the network topology through bipartiteness and the presence of only even-length cycles. The models diverge, however, in the minimum length of cycle basis elements, in a manner that depends on whether electrons are considered to be distinguishable. Furthermore, the two models reflect spin-conserving relaxation effects differently, as evident in both the degree distribution and the cycle-basis length distribution. Collectively, these observations serve to elucidate the relationship between network structure and physical constraints in quantum-mechanical models. More generally, our approach underscores the utility of network science in understanding the dynamics and control of quantum systems.
By using the self-consistent Born approximation, we investigate disorder effect induced by the short-range impurities on the band-gap in two-dimensional Dirac systems with the higher order terms in momentum. Starting from the Bernevig-Hughes-Zhang (B
HZ) model, we calculate the density-of-states as a function of the disorder strength. We show that due to quadratic corrections to the Dirac Hamiltonian, the band-gap is always affected by the disorder even if the system is gapless in the clean limit. Finally, we explore the disorder effects by using an advanced effective Hamiltonian describing the side maxima of the valence subband in HgTe~quantum wells. We show that the band-gap and disorder-induced topological phase transition in the real structures may differ significantly from those predicted within the BHZ model.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
