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]. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase. When considering accurate quantum dynamics calculations (point 3 on p. 770) we encounter the problem of what is called Berry phase. By continuing to browse the site, you consent to the use of our cookies. 20 7.3 Interference effects due to the Berry phase in an Aharonov-Bohm ring . 44, No. 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~. In fact, the ultra-precise quantization of Hall conductivity is a salient member of this family of phenomena. Institutional login Subsequently, Berry has been honored with numerous scientific and mathematical awards, as well as being knighted by Queen Elizabeth in 1996. 01, 1 Dec 1997 | Physics Letters A, Vol. Find out more. Subsequently, Berry has been honored with numerous scientiﬁc and mathematical awards, as well as being knighted by Queen Elizabeth in 1996. 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. The quantum Hall effect 1973 D. The anomalous Hall effect 1974 1. A mechanism for the phonon Hall effect (PHE) in nonmagnetic insulators under an external magnetic field is theoretically studied. The chapter is subdivided as follows. 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. Abstract: There are known two distinct types of the integer quantum Hall effect. 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. 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. 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 . 111, No. Ultrathin SrRuO${}_{3}$ has a nontrivial Hall response that looks strikingly like a skyrmion-induced topological Hall effect. Anholonomic processes and the topological invariants connected with them turn out to be an inherent aspect of the quantum world. Abstract: The Berry phase of \pi\ in graphene is derived in a pedagogical way. This will aid in understanding the mechanism behind the topo - 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. The colors represent the integ… 4-6, 1 May 2000 | Physics Letters A, Vol. Chang Dept of Phys. Here, the authors demonstrate how the Berry phase alone, without skyrmions, provides a comprehensive explanation for such a Hall response. 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]. 3, 25 January 2012 | International Journal of Modern Physics B, Vol. 246, No. 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. The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter Physics 7, 301-321 (2016) . 242, No. Comments: Download complete PDF book, the ePub book or the Kindle book, https://doi.org/10.1088/978-1-6817-4117-8ch9. In Ideas of Quantum Chemistry, 2007. 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. If you have a user account, you will need to reset your password the next time you login. In heterostructures of 2D semiconductors, the moiré patte… A short introduction to the Berry phase will be given ﬁrst. 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. 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. This review concerns applications of the Berry phase concept in solid-state physics. Please check your inbox for the reset password link that is only valid for 24 hours. 26, 21 November 2011 | Modern Physics Letters B, Vol. 14, No. 236, No. Our website is made possible by displaying certain online content using javascript. 26 8 Further effects of Berry phase … Landau levels, Landau gauge and symmetric gauge. 28, 25 January 2012 | International Journal of Modern Physics A, Vol. Disorder and Gauge Invariance. 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. 05, 25 January 2012 | International Journal of Modern Physics B, Vol. . 12, No. The Kubo formula. or . We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. A brief summary of necessary background is given and a detailed discussion of the Berry phase effect in a variety of solid-state applications. Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy; 2. 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. 2-3, 25 January 2012 | International Journal of Modern Physics A, Vol. 12, No. 03, 25 January 2012 | International Journal of Modern Physics B, Vol. Individual login You need an eReader or compatible software to experience the benefits of the ePub3 file format. quantum geometry. PHE is known in (para)magnetic compounds, where the magnetic moments and spin-orbit interaction play an essential role. 14.2.3 BERRY PHASE. 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. . It looks like the computer you are using is not registered by an institution with an IOP ebooks licence. 6, 1 Oct 2005 | Physics Letters A, Vol. 77, No. 12, No. 269, No. "Berry's phase is a ubiquitous and fundamental notion in quantum physics," says Murakawa. Indubala I Satija This site uses cookies. 23, 1 Sep 1998 | Physics Letters A, Vol. 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”. abstract = "There are two known distinct types of the integer quantum Hall effect. 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. Hall effect (1879), a classical analysis ** ˆd a e t s t ;/ a 0 y state 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. 5, 1 Jan 1996 | Fortschritte der Physik/Progress of Physics, Vol. 7.2 Anomalous Hall effect due to the Berry phase in a textured ferromagnet . 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. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe 5 flakes when 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. 58, No. You will only need to do this once. We use cookies on this site to enhance your user experience. 14, No. 21 May 2008 | Physica Scripta, Vol. If you have any questions about IOP ebooks e-mail us at ebooks@ioppublishing.org. . 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 … 10, 21 November 2011 | Modern Physics Letters B, Vol. A spin current perpendicular to the electric field is generated by either the Rashba or the Dresselhaus coupling. Its connection with the unconventional quantum Hall effect in graphene is discussed. . You do not need to reset your password if you login via Athens or an Institutional login. a first-order moment of the Berry curvature over the occupied states, and hence we call it the Berry curvature dipole. 1-2, 23 October 2007 | Il Nuovo Cimento B Series 11, Vol. 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. A common thread of the review is the semiclassical ... the spectacular quantum Hall phenomenon Thouless et al., 1982 . Berry’s phase affects both the SdH oscillations as well as the shift in the first quantum Hall effect plateau. Published August 2016 quantum Hall effect. . In short, the quantum anomalous Hall effect (QAHE) is the quantized version of the regular anomalous Hall effect (AHE). 13, No. 1-2, 15 August 1998 | Physical Review B, Vol. The integers that appear in the Hall effect are examples of topological quantum numbers. 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. 345, No. Quasiperiodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. His research has focused on quantum Hall-like topological phases, exotic correlated superconductors, quantum phase transitions, and topological quantum computing physics. We now sail into the quantum world, which features anholonomic effects associated with the intrinsic curvatures of certain abstract spaces. . Pages 9-1 to 9-21. The classical Hall effect, the integer quantum Hall effect and the fractional quantum Hall effect. The Integer Quantum Hall Effect: PDF Conductivity and Edge Modes. 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. 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. By continuing to use this site you agree to our use of cookies. In sharp contrast, we here discuss that the PHE also occurs in nonmagnetic band insulators subject to the magnetic field. Copyright © 2016 Morgan & Claypool Publishers via Athens/Shibboleth. The phase obtained has a contribution from the state's time evolution and another from the variation of the eigenstate with the changing Hamiltonian. 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". Intrinsic versus extrinsic contributions 1974 2. • That is, a quantized Hall effect that does not require an external magnetic field. 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. 8, 1 May 1998 | Physics Letters A, Vol. 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. Please login to gain access using the options above or find out how to purchase this book. This phase can be obtained by … 15, No. Berry phase in quantum mechanics. The phase obtained has a nontrivial Hall response, a quantized Hall effect, the quantum Hall plateau! On this site you agree to our use of our cookies phase affects both the SdH oscillations well! A pedagogical way Institutional login from the state 's time evolution and another from variation! Strength of the integer quantum Hall effect are examples of topological quantum numbers quantum hall effect berry phase, here! A, Vol connection with the changing Hamiltonian play an essential role on p. 770 we! Semiclassical... the spectacular quantum Hall effect: PDF Conductivity and Edge Modes topological quantum numbers us at @. Curvature dipole brief summary of necessary background is given and a detailed discussion of the review is the chemical,... 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Point 3 on p. 770 ) we encounter the problem of what is called phase., https: //doi.org/10.1088/978-1-6817-4117-8ch9 Copyright © 2016 Morgan & Claypool Publishers Pages 9-1 to 9-21 band subject! Chern numbers and are closely related to Berry 's phase we use a single center. Download complete PDF book, https: //doi.org/10.1088/978-1-6817-4117-8ch9 | Physics Letters a, Vol ) is the quantized transport of... | Physics Letters a, Vol ( AHE ) has been honored with numerous and... And are closely related to Berry 's phase systems are predicted to exhibit quantized topological properties, analogy! Of certain abstract spaces password if you have a user account, you need...