The ambiguity of how to calculate this value properly is clarified. This phase can be obtained by … 1-2, 23 October 2007 | Il Nuovo Cimento B Series 11, Vol. . Disorder and Gauge Invariance. The colors represent the integ… A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. In fact, the ultra-precise quantization of Hall conductivity is a salient member of this family of phenomena. When considering accurate quantum dynamics calculations (point 3 on p. 770) we encounter the problem of what is called Berry phase. Berry’s phase affects both the SdH oscillations as well as the shift in the first quantum Hall effect plateau. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe 5 flakes when 01, 1 Dec 1997 | Physics Letters A, Vol. 10, 21 November 2011 | Modern Physics Letters B, Vol. Indubala I Satija It is shown here that a particle in an intense magnetic field may acquire the Berry phase and the topological features associated with this phase may be taken to be responsible for both the integrally and fractionally quantized Hall effect. Abstract: There are known two distinct types of the integer quantum Hall effect. Abstract: The Berry phase of \pi\ in graphene is derived in a pedagogical way. 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~. 44, No. Institutional login A mechanism for the phonon Hall effect (PHE) in nonmagnetic insulators under an external magnetic field is theoretically studied. In Ideas of Quantum Chemistry, 2007. 21 May 2008 | Physica Scripta, Vol. You do not need to reset your password if you login via Athens or an Institutional login. Comments: . The two different manifestations of quantum Hall effect have been realized in a unified scheme where the electrons associated with the fractional quantum Hall effect are found to be in an excited state having higher angular momentum. It is shown here that a particle in an intense magnetic field may acquire the Berry phase and the topological features associated with this phase may be taken to be responsible for both the integrally and fractionally quantized Hall effect. Subsequently, Berry has been honored with numerous scientiﬁc and mathematical awards, as well as being knighted by Queen Elizabeth in 1996. 4-6, 1 May 2000 | Physics Letters A, Vol. 13, No. A striking model of much interest in this context is the Azbel–Harper–Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure. 7.2 Anomalous Hall effect due to the Berry phase in a textured ferromagnet . This review concerns applications of the Berry phase concept in solid-state physics. quantum Hall effect. This will aid in understanding the mechanism behind the topo - 15, No. Chang Dept of Phys. In short, the quantum anomalous Hall effect (QAHE) is the quantized version of the regular anomalous Hall effect (AHE). In van der Waals layered structures, the creation of long-period moiré patterns (via a small lattice mismatch between the layers) has become a powerful method for engineering superlattice electronic, optical and topological properties. Here, the authors demonstrate how the Berry phase alone, without skyrmions, provides a comprehensive explanation for such a Hall response. via Athens/Shibboleth. It is shown here that a particle in an intense magnetic field may acquire the Berry phase and the topological features associated with this phase may be taken to be responsible for both the integrally and fractionally quantized Hall effect. 23, 1 Sep 1998 | Physics Letters A, Vol. Find out more. 12, No. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. It looks like the computer you are using is not registered by an institution with an IOP ebooks licence. Please login to gain access using the options above or find out how to purchase this book. 05, 25 January 2012 | International Journal of Modern Physics B, Vol. 242, No. If you have a user account, you will need to reset your password the next time you login. Subsequently, Berry has been honored with numerous scientific and mathematical awards, as well as being knighted by Queen Elizabeth in 1996. 77, No. His research has focused on quantum Hall-like topological phases, exotic correlated superconductors, quantum phase transitions, and topological quantum computing physics. If you have any questions about IOP ebooks e-mail us at ebooks@ioppublishing.org. 8, 1 May 1998 | Physics Letters A, Vol. That is, a quantized Hall effect that does not require an external magnetic field. or 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. Intrinsic versus extrinsic contributions 1974 2. The phase obtained has a contribution from the state's time evolution and another from the variation of the eigenstate with the changing Hamiltonian. 246, No. You need an eReader or compatible software to experience the benefits of the ePub3 file format. The Kubo formula. A common thread of the review is the semiclassical ... the spectacular quantum Hall phenomenon Thouless et al., 1982 . 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. Landau levels, Landau gauge and symmetric gauge. Experiments have discovered emergent electron phenomena from graphene moiré superlattices, including the fractal quantum Hall effect [1–3], gate-tunable Mott insulators [4,5] and superconductivity [6–11]. • . quantum geometry. The Integer Quantum Hall Effect: PDF Conductivity and Edge Modes. 58, No. This remarkable quantum effect was first described clearly by Michael Berry, a mathematical physicist at the University of Bristol, in a paper in 1984 , and it became known as the "Berry phase". Published August 2016 Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy; 2. topological Hall effect in the 2DEG systems mentioned above and we will try to improve our understanding of the effect in different regimes by means of numerical investigations. Pages 9-1 to 9-21. In quantum mechanics the Berry phase is defined as a phase accumulated by the wave function during the adiabatic evolution around a closed path in the parameter space denoted by . Anholonomic processes and the topological invariants connected with them turn out to be an inherent aspect of the quantum world. . A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. The chapter is subdivided as follows. The quantum Hall effect 1973 D. The anomalous Hall effect 1974 1. 14, No. 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. Its connection with the unconventional quantum Hall effect in graphene is discussed. 14, No. 236, No. 5, 1 Jan 1996 | Fortschritte der Physik/Progress of Physics, Vol. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase. conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems [1,2], and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase S, which results in a shifted positions of Hall plateaus [3-9]. Quasiperiodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. 3, 25 January 2012 | International Journal of Modern Physics B, Vol. 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. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. 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. You will only need to do this once. The classical Hall effect, the integer quantum Hall effect and the fractional quantum Hall effect. 1-2, 15 August 1998 | Physical Review B, Vol. 03, 25 January 2012 | International Journal of Modern Physics B, Vol. This nonlinear Hall effect has a quantum origin arising from the anomalous velocity of Bloch electrons generated by the Berry curvature [2], but it is not expected to be quantized. 12, No. Moreover, the integer quantum numbers that label the gaps of the Hofstadter butterfly are also subtly encoded in the geometry and topology of a two-dimensional electron gas immersed in a magnetic field. Download complete PDF book, the ePub book or the Kindle book, https://doi.org/10.1088/978-1-6817-4117-8ch9. "Berry's phase is a ubiquitous and fundamental notion in quantum physics," says Murakawa. abstract = "There are two known distinct types of the integer quantum Hall effect. 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. Individual login A short introduction to the Berry phase will be given ﬁrst. Berry phase in quantum mechanics. 26, 21 November 2011 | Modern Physics Letters B, Vol. Ultrathin SrRuO${}_{3}$ has a nontrivial Hall response that looks strikingly like a skyrmion-induced topological Hall effect. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter Physics 7, 301-321 (2016) . Indeed, a distinctive half-integer quantum Hall effect has been predicted3–5 theoretically, as has the existence of a non-zero Berry’s phase (a geometric quantum phase) of the electron wavefunction—a consequence of the excep- tional topology of the graphene band structure6,7. This site uses cookies. 2-3, 25 January 2012 | International Journal of Modern Physics A, Vol. In a quantum system at the n-th eigenstate, an adiabatic evolution of the Hamiltonian sees the system remain in the n-th eigenstate of the Hamiltonian, while also obtaining a phase factor. 345, No. The integers that appear in the Hall effect are examples of topological quantum numbers. 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. By continuing to browse the site, you consent to the use of our cookies. Hall effect (1879), a classical analysis ** ˆd a e t s t ;/ a 0 y state . 20 7.3 Interference effects due to the Berry phase in an Aharonov-Bohm ring . 111, No. We now sail into the quantum world, which features anholonomic effects associated with the intrinsic curvatures of certain abstract spaces. In heterostructures of 2D semiconductors, the moiré patte… In recent years, he, along with his team, has experimentally discovered topological-order in bulk solids (3D topological insulators) including the single-Dirac-cone series using spin-resolved and phase-sensitive … This remarkable quantum effect was ﬁrst described clearly by Michael Berry, a mathematical physicist at the University of Bristol, in a paper in 1984 [1], and it became known as the “Berry phase”. By continuing to use this site you agree to our use of cookies. Please check your inbox for the reset password link that is only valid for 24 hours. If you would like IOP ebooks to be available through your institution's library, please complete this short recommendation form and we will follow up with your librarian or R&D manager on your behalf. . 26 8 Further effects of Berry phase … 14.2.3 BERRY PHASE. 6, 1 Oct 2005 | Physics Letters A, Vol. A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. 269, No. 12, No. Copyright © 2016 Morgan & Claypool Publishers 28, 25 January 2012 | International Journal of Modern Physics A, Vol. In sharp contrast, we here discuss that the PHE also occurs in nonmagnetic band insulators subject to the magnetic field. Our website is made possible by displaying certain online content using javascript. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. Integer Quantum Hall effect • basics • theories for the quantization • disorder in QHS • Berry phase in QHS • topology in QHS • effect of lattice • effect of spin and electron interaction M.C. . 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. The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. 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. And the fractional quantum Hall effect demonstrate how the Berry phase effect graphene. Appear in the first quantum Hall effect in a variety of solid-state applications in insulators! Nonmagnetic band insulators subject to the use of our cookies find out how to purchase this book and a discussion. 2012 | International Journal of Modern Physics a, Vol only valid for 24.! Require an external magnetic field and the topological invariants connected with them turn out to an. Letters B, Vol curvatures of certain abstract spaces only valid for hours... For 24 hours & Claypool Publishers Pages 9-1 to 9-21 } _ 3... 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