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UFN, 1998, Volume 168, Number 3, Pages 249–258 (Mi ufn1452)  

This article is cited in 40 scientific papers (total in 41 papers)

REVIEWS OF TOPICAL PROBLEMS

Topological phenomena in normal metals

S. P. Novikova, A. Ya. Mal'tsevb

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: Galvanomagnetic phenomena in metals in strong magnetic fields, associated with the Fermi surface geometry are considered. Using three-dimensional topology theorems, a full classification of all possibilities is made. For non-closed general-position electron orbits, special topological characteristics are introduced for the conductivity tensor at B → 0.

DOI: https://doi.org/10.3367/UFNr.0168.199803a.0249

Full text: PDF file (13 kB)
Full text: http://www.ufn.ru/.../a

English version:
Physics–Uspekhi, 1998, 41:3, 231–239

Bibliographic databases:

PACS: 02.40.Vh, 72.15.Gd
Received: February 1, 1998

Citation: S. P. Novikov, A. Ya. Mal'tsev, “Topological phenomena in normal metals”, UFN, 168:3 (1998), 249–258; Phys. Usp., 41:3 (1998), 231–239

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. “Sergei Petrovich Novikov (on his 60th birthday)”, Russian Math. Surveys, 54:1 (1999), 1–7  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. S. P. Novikov, “Levels of quasiperiodic functions on a plane, and Hamiltonian systems”, Russian Math. Surveys, 54:5 (1999), 1031–1032  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. R. De Leo, “The existence and measure of ergodic foliations in Novikov's problem of the semiclassical motion of an electron”, Russian Math. Surveys, 55:1 (2000), 166–168  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Novikov S., “1. Classical and Modern Topology 2. Topological Phenomena in Real World Physics”, Geom. Funct. Anal., 2000, no. Part 1, SI, 406–424  zmath  isi
    5. Peschansky V., Atalla R., “On the Magnetoresistance of the Organic Complexes (Bedt-Ttf)(2)Mhg(Scn)(4)”, Low Temp. Phys., 27:12 (2001), 1018–1020  crossref  adsnasa  isi  scopus
    6. Bruning J., Dobrokhotov S., “A Global Semiclassical Description of the Spectrum of the Two-Dimensional Magnetic Schrodinger Operator with a Periodic Potential”, Dokl. Math., 64:1 (2001), 131–136  zmath  isi
    7. J. Brüning, S. Yu. Dobrokhotov, K. V. Pankrashin, “The Asymptotic Form of the Lower Landau Bands in a Strong Magnetic Field”, Theoret. and Math. Phys., 131:2 (2002), 704–728  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Kaganov M., Peschansky V., “Galvano-Magnetic Phenomena Today and Forty Years Ago”, Phys. Rep.-Rev. Sec. Phys. Lett., 372:6 (2002), 445–487  crossref  isi
    9. Bruning J., Dobrokhotov S., Pankrashkin K., “The Spectral Asymptotics of the Two-Dimensional Schrodinger Operator with a Strong Magnetic Field. II”, Russ. J. Math. Phys., 9:4 (2002), 400–416  crossref  mathscinet  zmath  isi
    10. Peschanskii V., “Galvanomagnetic Phenomena in Organic Layered Conductors”, J. Exp. Theor. Phys., 94:5 (2002), 1035–1042  crossref  adsnasa  isi  scopus
    11. Bruning J., Dobrokhotov S., Pankrashkin K., “The Spectral Asymptotics of the Two-Dimensional Schrodinger Operator with a Strong Magnetic Field. I”, Russ. J. Math. Phys., 9:1 (2002), 14–49  mathscinet  zmath  isi
    12. Panati G., Spohn H., Teufel S., “Effective Dynamics for Bloch Electrons: Peierls Substitution and Beyond”, Commun. Math. Phys., 242:3 (2003), 547–578  crossref  mathscinet  adsnasa  isi  scopus
    13. Maltsev A., Novikov S., “Quasiperiodic Functions and Dynamical Systems in Quantum Solid State Physics”, Bull. Braz. Math. Soc., 34:1 (2003), 171–210  crossref  mathscinet  zmath  isi
    14. Teufel S., “Adiabatic Perturbation Theory in Quantum Dynamics - Introduction”, Adiabatic Perturbation Theory in Quantum Dynamics, Lect. Notes Math., 1821, Springer-Verlag Berlin, 2003, 1+  crossref  isi
    15. Bruening J., Demidov V.V., Geyler V.A., “Fermi Surfaces of Crystals in a High Magnetic Field”, International Journal of Nanoscience, Vol 2, No 6, International Journal of Nanoscience Series, 2, no. 6, ed. Suris R., World Scientific Publ Co Pte Ltd, 2003, 603–610  crossref  isi
    16. De Leo R., “Numerical Analysis of the Novikov Problem of a Normal Metal in a Strong Magnetic Field”, SIAM J. Appl. Dyn. Syst., 2:4 (2003), 517–545  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Maltsev A., Novikov S., “Dynamical Systems, Topology, and Conductivity in Normal Metals”, J. Stat. Phys., 115:1-2 (2004), 31–46  crossref  zmath  adsnasa  isi
    18. Maltsev A., “Quasiperiodic Functions Theory and the Superlattice Potentials for a Two-Dimensional Electron Gas”, J. Math. Phys., 45:3 (2004), 1128–1149  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Kosevich A., “Topology and Solid-State Physics (Review)”, Low Temp. Phys., 30:2 (2004), 97–117  crossref  adsnasa  isi  scopus
    20. Teufel S., Panati G., “Propagation of Wigner Functions for the Schrodinger Equation with a Perturbed Periodic Potential”, Multiscale Methods in Quantum Mechanics: Theory and Experiment, Trends in Mathematics, eds. Blanchard P., DellAntonio G., Birkhauser Boston, 2004, 207–220  zmath  isi
    21. I. A. Dynnikov, S. P. Novikov, “Topology of quasi-periodic functions on the plane”, Russian Math. Surveys, 60:1 (2005), 1–26  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. De Leo R., “First-Principles Generation of Stereographic Maps for High-Field Magneto Resistance in Normal Metals: an Application to Au and Ag”, Physica B, 362:1-4 (2005), 62–75  crossref  adsnasa  isi  elib  scopus
    23. Gelbukh I., “Presence of Minimal Components in a Morse Form Foliation”, Differ. Geom. Appl., 22:2 (2005), 189–198  crossref  mathscinet  zmath  isi  elib  scopus
    24. Kartsovnik M., Peschansky V., “Galvanomagnetic Phenomena in Layered Organic Conductors (Review)”, Low Temp. Phys., 31:3-4 (2005), 185–202  crossref  adsnasa  isi  elib  scopus
    25. Belov V.V. Dobrokhotov S.Yu. Tudorovskiy T.Ya., “Operator Separation of Variables for Adiabatic Problems in Quantum and Wave Mechanics”, J. Eng. Math., 55:1-4 (2006), 183–237  crossref  zmath  isi  scopus
    26. De Leo R., “Topology of Plane Sections of Periodic Polyhedra with an Application to the Truncated Octahedron”, Exp. Math., 15:1 (2006), 109–124  crossref  zmath  isi  elib  scopus
    27. Kosevich A., “Topology in the Electron Theory of Metals”, Topology in Condensed Matter, Springer Series in Solid-State Sciences, 150, ed. Monastyrsky M., Springer-Verlag Berlin, 2006, 3–29  crossref  mathscinet  zmath  adsnasa  isi
    28. Maltsev A., Novikov S., “Topology, Quasiperiodic Functions, and the Transport Phenomena”, Topology in Condensed Matter, Springer Series in Solid-State Sciences, 150, ed. Monastyrsky M., Springer-Verlag Berlin, 2006, 31–59  crossref  zmath  adsnasa  isi
    29. V. V. Grushin, S. Yu. Dobrokhotov, “Peierls Substitution and the Maslov Operator Method”, Math. Notes, 87:4 (2010), 521–536  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. Antonio Bianconi, Nicola Poccia, A.O. Sboychakov, A.L. Rakhmanov, K.I. Kugel, “Intrinsic arrested nanoscale phase separation near a topological Lifshitz transition in strongly correlated two-band metals”, Supercond. Sci. Technol, 28:2 (2015), 024005  crossref  isi  scopus
    31. Heikkila T.T., Volovik G.E., “Nexus and Dirac Lines in Topological Materials”, New J. Phys., 17 (2015), 093019  crossref  isi  scopus
    32. Maltsev A.Ya., “on the Analytical Properties of the Magneto-Conductivity in the Case of Presence of Stable Open Electron Trajectories on a Complex Fermi Surface”, J. Exp. Theor. Phys., 124:5 (2017), 805–831  crossref  isi  scopus
    33. Maltsev A.Ya., “Oscillation Phenomena and Experimental Determination of Exact Mathematical Stability Zones For Magneto-Conductivity in Metals Having Complicated Fermi Surfaces”, J. Exp. Theor. Phys., 125:5 (2017), 896–905  crossref  isi  scopus
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    40. De Leo R., “A Survey on Quasiperiodic Topology”, Advanced Mathematical Methods in Biosciences and Applications, Steam-H Science Technology Engineering Agriculture Mathematics & Health, eds. Berezovskaya F., Toni B., Springer International Publishing Ag, 2019, 53–88  crossref  isi
    41. Maltsev A.Ya., “Reconstructions of the Electron Dynamics in Magnetic Field and the Geometry of Complex Fermi Surfaces”, J. Exp. Theor. Phys., 131:6 (2020), 988–1020  crossref  isi
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