IntroductionĪccording to equivalence principal in general relativity, gravitational field is coupled to everything. We show how quantum gravity effects can play important role phenomenologically in many-body interactions of solids. Here we focus on the role of these natural cutoffs on Thomas-Fermi theory in condensed matter physics. These two natural cutoffs affects most of quantum field theoretic arguments in the spirit of condensed matter physics.
Also, in the context of newly proposed doubly special relativity theories, a test particle’s momentum cannot be arbitrarily imprecise leading nontrivially to a maximal momentum for a test particle.
This leads naturally to a minimal measurable length of the order of Planck length. The “Quantum Hall Effect” (QHE), discovered 1980 by K.It has been revealed, in the context of quantum gravity candidates, that measurement of position cannot be done with arbitrary precision and there is a finite resolution of space-time points. The theory, which leads, at high temperatures, to the well known Drude results for current density and resistance, shows that the IQHE is a consequence of the peculiar screening properties of a 2DES in a strong magnetic field at low temperatures, and that it can be understood without assumptions about special localization effects. The theory also explains, how the position and shape of these ISs depend on magnetic field and temperature, and why the confinement of the current density on these ISs leads to precisely quantized values of the macroscopic longitudinal and Hall resistance. The theory explains why, at low temperatures, at certain intervals of the applied perpendicular magnetic field, the current density is confined to “incompressible stripes” (ISs), in which a fixed number of Landau levels is occupied, and the longitudinal and Hall resistivity assume quantized values. We summarize and discuss a self-consistent screening and magneto-transport theory, developed to understand the results of scanning-force-microscope experiments on the current distribution in a two-dimensional electron system (2DES), located in a narrow Hall bar under the conditions of the integer quantum Hall effect (IQHE) and its breakdown. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited. Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect. Received: Novem| Accepted: Febru| Published: March 17, 2020 Special Issue: Quantum Confinement Effects in Nano Material Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Open Access Review Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect Macro-, micro- and nano structure of materialsĮnvironmental interactions, process modeling
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