To find out more, see our, Browse more than 100 science journal titles, Read the very best research published in IOP journals, Read open access proceedings from science conferences worldwide, The story of the most fascinating quantum fractal, Copyright © 2016 Morgan & Claypool Publishers. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction-a consequence of the exceptional topology of the graphene band structure. Hall effect (1879), a classical analysis ** ˆd a e t s t ;/ a 0 y state The spin Hall effect is investigated in a high mobility two-dimensional electron system with the spin-orbital coupling of both the Rashba and the Dresselhaus types. 23, 1 Sep 1998 | Physics Letters A, Vol. The chapter is subdivided as follows. The classical Hall effect, the integer quantum Hall effect and the fractional quantum Hall effect. 77, No. abstract = "There are two known distinct types of the integer quantum Hall effect. A common thread of the review is the semiclassical ... the spectacular quantum Hall phenomenon Thouless et al., 1982 . Institutional login Please login to gain access using the options above or find out how to purchase this book. If you have a user account, you will need to reset your password the next time you login. Berry curvature ∣ geometric tensor ∣ quantum dynamics ∣ quantum geometry ∣ quantum Hall effect In quantum mechanics the Berry phase is defined as a phase ac-cumulated by the wave function during the adiabatic evolution around a closed path in the parameter space denoted by s~. Our website is made possible by displaying certain online content using javascript. 4, © 2021 World Scientific Publishing Co Pte Ltd, Nonlinear Science, Chaos & Dynamical Systems, https://doi.org/10.1142/S0217984994001588, The angular-momentum aspect of Shift in FQHE, Topological aspects of phases in fractional quantum Hall effect, CONFORMAL FIELD THEORY, QUANTUM GROUP AND BERRY PHASE, TOPOLOGICAL TRANSPORT IN EDGE STATE OF HIERARCHIES, TOPOLOGICAL ASPECTS OF HIGH-Tc SUPERCONDUCTIVITY, FRACTIONAL QUANTUM HALL EFFECT AND BERRY PHASE, AREA PRESERVING DIFFEOMORPHISM, QUANTUM GROUP AND BERRY PHASE, Topological Aspects of Quantum Hall Fluid and Berry Phase, The Study of Wave Function and the Berry Phase of the Particles in Hall Fluid, The hierarchy of fractional quantum Hall states and the Zp spin system, Topological aspects of shift in hierarchies of the fractional quantum Hall effect, Symplectic structure and the fractional quantum Hall effect, The Hierarchy of Fractional Quantum Hall States and Berry Phase, Fractional quantum Hall fluid with even denominator filling factor and Berry phase, Topological aspects of a fermion and physics of the Hall fluid. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase. . Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. 01, 1 Dec 1997 | Physics Letters A, Vol. Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy; 2. This site uses cookies. . This phase can be obtained by … "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter Physics 7, 301-321 (2016) . A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. In monolayer graphene, the Berry’s phase contributes to the π - shift in the SdH oscillations and a half-integer shift in the Hall conductivity plateau as the Fermi energy ( E F ) crosses the n = 0 Landau level. 1-2, 15 August 1998 | Physical Review B, Vol. It looks like the computer you are using is not registered by an institution with an IOP ebooks licence. The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. If you have any questions about IOP ebooks e-mail us at ebooks@ioppublishing.org. 13, No. 6, 1 Oct 2005 | Physics Letters A, Vol. Enter your email address below and we will send you the reset instructions, If the address matches an existing account you will receive an email with instructions to reset your password, Enter your email address below and we will send you your username, If the address matches an existing account you will receive an email with instructions to retrieve your username, Indian Statistical Institute, Calcutta 700 035, India. You need an eReader or compatible software to experience the benefits of the ePub3 file format. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase π, which results in shifted positions of the Hall plateaus. In short, the quantum anomalous Hall effect (QAHE) is the quantized version of the regular anomalous Hall effect (AHE). 3, 25 January 2012 | International Journal of Modern Physics B, Vol. 12, No. 14, No. a first-order moment of the Berry curvature over the occupied states, and hence we call it the Berry curvature dipole. We use cookies on this site to enhance your user experience. You will only need to do this once. Subsequently, Berry has been honored with numerous scientific and mathematical awards, as well as being knighted by Queen Elizabeth in 1996. Download complete PDF book, the ePub book or the Kindle book, https://doi.org/10.1088/978-1-6817-4117-8ch9. Copyright © 2016 Morgan & Claypool Publishers The ambiguity of how to calculate this value properly is clarified. A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. 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