Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime

We report new experimental data on the plateau-insulator transition in the quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By employing the fundamental symmetries of the quantum transport problem we are able to disentangle the universal quantum critical aspects of the magnetoresistance data (critical indices and scaling functions) and the sample dependent aspects due to macroscopic inhomogeneities. Our new results and methodology indicate that the previously established experimental value for the critical index (kappa = 0.42) resulted from an admixture of both universal and sample dependent behavior. A novel, non-Fermi liquid value is found (kappa = 0.57) along with the leading corrections to scaling. The statement of self-duality under the Chern Simons flux attachment transformation is verified.Comment: 4 pages, 2 figure

New Insights into the Plateau-Insulator Transition in the Quantum Hall Regime

We have measured the quantum critical behavior of the plateau-insulator (PI) transition in a low-mobility InGaAs/GaAs quantum well. The longitudinal resistivity measured for two different values of the electron density follows an exponential law, from which we extract critical exponents kappa = 0.54 and 0.58, in good agreement with the value (kappa = 0.57) previously obtained for an InGaAs/InP heterostructure. This provides evidence for a non-Fermi liquid critical exponent. By reversing the direction of the magnetic field we find that the averaged Hall resistance remains quantized at the plateau value h/e^2 through the PI transition. From the deviations of the Hall resistance from the quantized value, we obtain the corrections to scaling.Comment: accepted proceedings of EP2DS-15 (to be published in Physica E

The effect of carrier density gradients on magnetotransport data measured in Hall bar geometry

We have measured magnetotransport of the two-dimensional electron gas in a Hall bar geometry in the presence of small carrier density gradients. We find that the longitudinal resistances measured at both sides of the Hall bar interchange by reversing the polarity of the magnetic field. We offer a simple explanation for this effect and discuss implications for extracting conductivity flow diagrams of the integer quantum Hall effect.Comment: 7 pages, 8 figure

The effects of macroscopic inhomogeneities on the magneto transport properties of the electron gas in two dimensions

In experiments on electron transport the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magneto resistance data taken from low mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau-plateau transitions as well as the plateau-insulator transition that generally occurs at much stronger values of the external field only. It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau-plateau transitions, unlike the the plateau-insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magneto resistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et.al in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau-plateau transitions.Comment: 20 pages, 9 figure

Modeling electrolytically top gated graphene

We investigate doping of a single-layer graphene in the presence of electrolytic top gating. The interfacial phenomena is modeled using a modified Poisson-Boltzmann equation for an aqueous solution of simple salt. We demonstrate both the sensitivity of graphene's doping levels to the salt concentration and the importance of quantum capacitance that arises due to the smallness of the Debye screening length in the electrolyte.Comment: 7 pages, including 4 figures, submitted to Nanoscale Research Letters for a special issue related to the NGC 2009 conference (http://asdn.net/ngc2009/index.shtml

High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices

Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillations that do not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few T. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work points at unexplored physics in Hofstadter butterfly systems at high temperatures

Exact eigenstate analysis of finite-frequency conductivity in graphene

We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to the band centre are more extended and falls of nearly as $1/E_l^{2}$ as we move away from the band centre. Further studies of current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. We calculate conductivity using Kubo Greenwood formula and show that, for low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparison with square lattice and find that graphene is more easily localized when subject to disorder.Comment: 11 pages,15 figure

Физические методы реабилитации пациентов с остеоартрозом: наукометрический анализ доказательных исследований

Relevance. A rise in the life expectancy of the planet’s population, lack of exercise and growth in the number of people suffering from overweight lead to an increase in the number of patients suffering from diseases of the musculoskeletal system, including osteoarthritis. Given the absence of specific pharmacological treatment of osteoarthritis, as well as the increase in the number of patients with co-morbid pathology, it became necessary to search for the proven technologies of physical and rehabilitation medicine (PRM). The purpose of the study was to identify the most effective PRM technologies in the treatment of patients with osteoarthritis and to formulate recommendations on their use for practitioners, based on the proof obtained through the analysis of evidence-based high quality studies on the application of PRM technology. Materials and Methods. Over the past decade, there has been a significant increase in the number of studies on non-pharmacological methods of osteoarthritis treatment. The most studied of the PRM technologies with the proven effect were the following: physical exercises combined with traditional healthy gymnastics, acupuncture, peloid therapy, balneo therapy, as well as low-frequency electrotherapy, ultrasound therapy and infrared laser therapy. Conclusion. The use of PRM technologies in the treatment of patients with osteoarthritis should be based on the results of high-quality randomized controlled clinical trials which serve as the basis for the development of clinical recommendations. The process of the obtained data analysis should be conducted on the regular basis.Актуальность. Увеличение продолжительности жизни населения планеты, гиподинамия и рост числа людей с избыточной массой тела приводят к увеличению количества пациентов, страдающих заболеваниями опорно-двигательного аппарата, в том числе остеоартрозом. Учитывая отсутствие специфического фармакологического лечения остеоартроза, а также рост числа пациентов с коморбидной патологией, возникла необходимость поиска доказанных технологий физической и реабилитационной медицины (ФРМ). Цель исследования — выявить наиболее эффективные технологии ФРМ в лечении пациентов с остеоартрозом и сформулировать рекомендации по их применению для практических врачей, основанные на доказательствах, полученных в ходе анализа баз доказательных доброкачественных исследований по применению технологии ФРМ. Материал и методы. Статья основана на результатах наукометрического анализа 1183 исследований, проведенных с 2000 по 2019 г., посвященных использованию технологий ФРМ в лечении пациентов с остеоартрозом. В итоговый анализ технологий ФРМ преимущественно включены зарубежные клинические рекомендации/руководства (practice guidelines), систематические обзоры (СО), метаанализы РКИ, данные отдельных РКИ на английском или русском языках, оцененные на 6 баллов и выше по шкале PEDro. В результате наукометрического анализа были сформированы таблицы доказательств с присвоением каждой технологии ФРМ уровня убедительности доказательств и класса рекомендаций по GRADE в соответствии с ГОСТ Р 56034-2014. Результаты. За последнее десятилетие произошел ощутимый рост количества исследований, посвященных нефармакологическим методам лечения остеоартроза. Наиболее изученными из технологий ФРМ, которые имеют доказанный эффект, являются физические упражнения в сочетании с традиционной оздоровительной гимнастикой и акупунктурой, пелоидотерапия, бальнеотерапия, а также низкочастотная электротерапия, ультразвуковая терапия и инфракрасная лазеротерапия. Заключение. Использование технологий ФРМ в лечении пациентов с остеоартрозом должно быть основано на результатах качественных рандомизированных контролируемых клинических исследований, которые служат основой для разработки клинических рекомендаций. Анализ данных исследований должен носить регулярный характер

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201

Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem