Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum, consisting of highly degenerate Landau energy levels. When subject to both a magnetic field and a periodic electrostatic potential, two-dimensional systems of electrons exhibit a self-similar recursive energy spectrum. Known as Hofstadter's butterfly, this complex spectrum results from an interplay between the characteristic lengths associated with the two quantizing fields, and is one of the first quantum fractals discovered in physics. In the decades since its prediction, experimental attempts to study this effect have been limited by difficulties in reconciling the two length scales. Typical atomic lattices (with periodicities of less than one nanometre) require unfeasibly large magnetic fields to reach the commensurability condition, and in artificially engineered structures (with periodicities greater than about 100 nanometres) the corresponding fields are too small to overcome disorder completely. Here we demonstrate that moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic modulation with ideal length scales of the order of ten nanometres, enabling unprecedented experimental access to the fractal spectrum. We confirm that quantum Hall features associated with the fractal gaps are described by two integer topological quantum numbers, and report evidence of their recursive structure. Observation of a Hofstadter spectrum in bilayer graphene means that it is possible to investigate emergent behaviour within a fractal energy landscape in a system with tunable internal degrees of freedom.
The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states 1-3 . This novel edge state configuration has also been predicted to occur in graphene when spin-split electron-and hole-like Landau levels are forced to cross at the edge of the sample 4-7 . In particular, a quantum spin Hall analogue has been predicted at ν = 0 in bilayer graphene if the ground state is a spin ferromagnet 8,9 . Previous studies have demonstrated that the bilayer ν = 0 state is an insulator in a perpendicular magnetic field [10][11][12][13][14][15][16] , though the exact nature of this state has not been identified. Here we present measurements of the ν = 0 state in a dual-gated bilayer graphene device in tilted magnetic field. The application of an in-plane magnetic field and perpendicular electric field allows us to map out a full phase diagram of the ν = 0 state as a function of experimentally tunable parameters. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of order 4e 2 /h, consistent with predictions for the ferromagnet.Under a strong perpendicular magnetic field, bilayer graphene (BLG) develops a ν = 0 quantum Hall (QH) state at the charge neutrality point (CNP) which displays anomalous insulating behavior [10][11][12][13][14][15][16] . Transport studies in a dual-gated geometry 12-14 indicate that this gapped state results from an interaction-driven spontaneous symmetry breaking in the valley-spin space 17 . However, the exact order of the resulting ground state remains controversial. In high-mobility suspended BLG devices, a broken symmetry state at charge neutrality has also been observed at zero magnetic field whose nature has been under intense theoretical 9,18-22 and experimental 12,[14][15][16]23 investigation. Some experiments indicate there may be a connection between these two insulating states 14,16 .The ν = 0 state in BLG occurs at half filling of the lowest Landau level. Although the BLG zero-energy Landau level has an additional orbital degeneracy stemming from two accidentally degenerate magnetic oscillator wavefunctions 24 , minimization of exchange energy favors singlet pairs in the orbital space at all even filling factors 25 . This leaves an approximate SU(4) spin and pseudospin symmetry for the remaining ordering of the ground state. Comparable ground state competition has also been studied in double quantum wells in GaAs 2-dimensional electron systems (2DESs) 26 . Quantum phase transitions, in particular from canted antiferromagnetic to ferromagnetic ordering, can occur in those systems as an in-plane magnetic field is applied (Zeeman energy is increased) 27,28 .Our experiment is carried out in BLG samples with top and bottom gates in which thin single crystal hBN serves as a high quality dielectric on both sides (Fig. 1 bottom inset). By controlling top gate voltage (V T G ) and bottom gate voltage (V BG ) we can adjust carrier density n and perpendicular electric displacement fi...
Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse electric field. This result provides a model platform to study the role of symmetry 1 arXiv:1403.2112v1 [cond-mat.mes-hall]
This book is a major contribution to decision theory, focusing on the question of when it is rational to accept scientific theories. The author examines both Bayesian decision theory and confirmation theory, refining and elaborating the views of Ramsey and Savage. He argues that the most solid foundation for confirmation theory is to be found in decision theory, and he provides a decision-theoretic derivation of principles for how many probabilities should be revised over time. Professor Maher defines a notion of accepting a hypothesis, and then shows that it is not reducible to probability and that it is needed to deal with some important questions in the philosophy of science. A Bayesian decision-theoretic account of rational acceptance is provided together with a proof of the foundations for this theory. A final chapter shows how this account can be used to cast light on such vexed issues as verisimilitude and scientific realism.
HR and hiring managers in the current study were not overly enthusiastic about people with disabilities as reliable and productive employees. ADA and job accommodations training might improve these managers' attitudes toward people with disabilities. Intervention at the senior management level should focus on changing company policies to include disability as part of the company's diversity efforts.
Western health professionals often experience difficulties in service delivery to Aboriginal people because of the disparity between Aboriginal and Western health belief systems. This article reviews the literature which considers 'traditional' Aboriginal health beliefs and medical systems. The traditional Aboriginal model of illness causation emphasises social and spiritual dysfunction as a cause of illness. Supernatural intervention is regarded as the main cause of serious illness. There are gender divisions in Aboriginal society that impact on the delivery of Western healthcare. Management strategies such as preventative care, bush medicine, and the role of traditional healers are discussed. These belief systems are considered with particular reference to their interactions and implications with regard to the Western medical system. This information provides a framework to allow improved understanding by health professionals of the health-related decisions made by Aboriginal people.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.