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024 7 _a10.1088/978-0-7503-3955-1
_2doi
035 _a(CaBNVSL)thg00082866
035 _a(OCoLC)1288247152
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQC20
_b.P573 2021eb
072 7 _aPHFC
_2bicssc
072 7 _aSCI077000
_2bisacsh
082 0 4 _a530.15
_223
100 1 _aPires, A.
_q(Antonio),
_eauthor.
_970647
245 1 2 _aA brief introduction to topology and differential geometry in condensed matter physics /
_cAntonio Sergio Teixeira Pires.
250 _aSecond edition.
264 1 _aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
_bIOP Publishing,
_c[2021]
300 _a1 online resource (various pagings) :
_billustrations (some color).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _a[IOP release $release]
490 1 _aIOP ebooks. [2021 collection]
500 _a"Version: 202111"--Title page verso.
504 _aIncludes bibliographical references.
505 0 _a1. Path integral approach -- 1.1. Path integral -- 1.2. Path integral in quantum field theory -- 1.3. Spin -- 1.4. Path integral and statistical mechanics -- 1.5. Fermion path integral
505 8 _a2. Topology and vector spaces -- 2.1. Topological spaces -- 2.2. Group theory -- 2.3. Cocycle -- 2.4. Vector spaces -- 2.5. Linear maps -- 2.6. Dual space -- 2.7. Scalar product -- 2.8. Metric space -- 2.9. Tensors -- 2.10. p-Vectors and p-forms -- 2.11. Edge product -- 2.12. Pfaffian
505 8 _a3. Manifolds and fiber bundle -- 3.1. Manifolds -- 3.2. Lie algebra and Lie groups -- 3.3. Homotopy -- 3.4. Particle in a ring -- 3.5. Functions on manifolds -- 3.6. Tangent space -- 3.7. Cotangent space -- 3.8. Push-forward -- 3.9. Fiber bundle -- 3.10. Magnetic monopole -- 3.11. Tangent bundle -- 3.12. Vector field
505 8 _a4. Metric and curvature -- 4.1. Metric in a vector space -- 4.2. Metric in manifolds -- 4.3. Symplectic manifold -- 4.4. Exterior derivative -- 4.5. The Hodge * operator -- 4.6. The pull-back of a one-form -- 4.7. Orientation of a manifold -- 4.8. Integration on manifolds -- 4.9. Stokes' theorem -- 4.10. Homology -- 4.11. Cohomology -- 4.12. Degree of a map -- 4.13. Hopf-Poincar�e theorem -- 4.14. Connection -- 4.15. Covariant derivative -- 4.16. Curvature -- 4.17. The Gauss-Bonnet theorem -- 4.18. Surfaces -- 4.19. Geodesics -- 4.20. Fundamental theorem of the Riemann geometry
505 8 _a5. Dirac equation and gauge fields -- 5.1. The Dirac equation -- 5.2. Two-dimensional Dirac equation -- 5.3. Electrodynamics -- 5.4. Time reversal -- 5.5. Gauge field as a connection -- 5.6. Chern classes -- 5.7. Abelian gauge fields -- 5.8. Non-Abelian gauge fields -- 5.9. Chern numbers for non-Abelian gauge fields -- 5.10. Maxwell equations using differential forms
505 8 _a6. Berry connection and particle moving in a magnetic field -- 6.1. Introduction -- 6.2. Berry phase -- 6.3. The Aharonov-Bohm effect -- 6.4. Non-Abelian Berry connections -- 6.5. The Aharonov-Casher effect
505 8 _a7. Quantum Hall effect -- 7.1. Integer quantum Hall effect -- 7.2. Currents at the edge -- 7.3. Kubo formula -- 7.4. The quantum Hall state on a lattice -- 7.5. Particle on a lattice -- 7.6. The TKNN invariant -- 7.7. Quantum spin Hall effect -- 7.8. Chern-Simons action -- 7.9. The fractional quantum Hall effect
505 8 _a8. Topological insulators -- 8.1. Two- and three-band insulators -- 8.2. Nielsen-Ninomiya theorem -- 8.3. Haldane model -- 8.4. Checkerboard lattice -- 8.5. States at the edge -- 8.6. The Z2 topological invariants -- 8.7. The Kane-Mele model -- 8.8. Three-dimensional topological insulators -- 8.9. Calculation of edge modes
505 8 _a9. Topological phases in one dimension -- 9.1. The Su-Schrieffer-Heeger model -- 9.2. Winding number and Zak phase -- 9.3. Finite chain -- 9.4. Alternative form of the SSH Hamiltonian -- 9.5. Localized states at a domain wall -- 9.6. The Ising chain in a transverse field -- 9.7. The Kitaev chain -- 9.8. Majorana fermion operators -- 9.9. Rashba spin-orbit superconductor in one dimension
505 8 _a10. Topological superconductors -- 10.1. Basics of superconductivity -- 10.2. Two-dimensional chiral p-wave superconductors -- 10.3. Two-dimensional chiral p-wave superconductor on a lattice -- 10.4. Continuum limit -- 10.5. Non-Abelian statistics -- 10.6. d-Wave pairing symmetry
505 8 _a11. Higher-order topological insulators -- 11.1. Crystalline symmetries -- 11.2. Second-order topological insulator in two dimensions -- 11.3. Gapless corner states -- 11.4. A three-dimensional chiral HOTI
505 8 _a12. Classification of topological states with symmetries -- 12.1. Symmetries -- 12.2. Time-reversal symmetry -- 12.3. Particle-hole symmetry -- 12.4. Chiral symmetry -- 12.5. Periodic table -- 12.6. Complex classes -- 12.7. Real classes -- 12.8. Classification for zero dimensions -- 12.9. Dirac Hamiltonians -- 12.10. Dimension reduction -- 12.11. Topological defects
505 8 _a13. Weyl semimetals -- 13.1. The Weyl equation -- 13.2. Linear Weyl modes -- 13.3. Chern numbers -- 13.4. An example -- 13.5. Fermi arcs -- 13.6. Weyl semimetal in an external magnetic field -- 13.7. Type II Weyl semimetals -- 13.8. Weyl semimetals with spins higher than 1/2 -- 13.9. Chiral anomaly -- 13.10. Dirac semimetals
505 8 _a14. Kubo theory and transport -- 14.1. Linear response theory -- 14.2. Electron transport -- 14.3. Anomalous Hall effect -- 14.4. Orbital magnetization -- 14.5. Spin transport -- 14.6. Interacting topological insulators
505 8 _a15. Magnetic models -- 15.1. One-dimensional antiferromagnetic model -- 15.2. Sine-Gordon soliton -- 15.3. Two-dimensional non-linear sigma model -- 15.4. XY model -- 15.5. Theta terms
505 8 _a16. Topological magnon insulators -- 16.1. Magnon Hall effect -- 16.2. The ferromagnetic honeycomb lattice -- 16.3. Generalized Bogoliubov transformation -- 16.4. Antiferromagnetic honeycomb lattice -- 16.5. Thermal Hall conductivity
505 8 _a17. K-theory -- 17.1. Rings -- 17.2. Equivalence relations -- 17.3. Grothendieck group -- 17.4. Sum of vector bundles -- 17.5. K-theory -- 17.6. K-theory and topological insulators -- 17.7. The 2Z invariant -- 17.8. The Atiyah-Singer index theorem.
520 3 _aThis book provides a self-consistent introduction to the mathematical ideas and methods from these fields that will enable the student of condensed matter physics to begin applying these concepts with confidence. This expanded second edition adds eight new chapters, including one on the classification of topological states of topological insulators and superconductors and another on Weyl semimetals, as well as elaborated discussions of the Aharonov-Casher effect, topological magnon insulators, topological superconductors and K-theory.
530 _aAlso available in print.
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
545 _aAntonio S.T. Pires graduated from the University of California in Santa Barbara in 1976. He is a Professor of Physics at the Universidade Federal de Minas Gerais, Brazil researching quantum field theory applied to condensed matter. He is a member of the Brazilian Academy of Science, was the Editor of the Brazilian Journal of Physics, and a member of the Advisory Board of the Journal of Physics: Condensed Matter. He has published the books ADS/CFT correspondence in condensed matter and theoretical tools for spin models in magnetic systems.
588 0 _aTitle from PDF title page (viewed on December 6, 2021).
650 0 _aMathematical physics.
_911013
650 0 _aCondensed matter
_xMathematics.
_921163
650 0 _aTopology.
_913470
650 0 _aGeometry, Differential.
_970648
650 7 _aCondensed matter physics (liquid state & solid state physics)
_2bicssc
_970144
650 7 _aCondensed matter.
_2bisacsh
_917064
710 2 _aInstitute of Physics (Great Britain),
_epublisher.
_911622
776 0 8 _iPrint version:
_z9780750339537
_z9780750339568
830 0 _aIOP (Series).
_pRelease 21.
_970649
830 0 _aIOP ebooks.
_p2021 collection.
_970650
856 4 0 _uhttps://iopscience.iop.org/book/978-0-7503-3955-1
942 _cEBK
999 _c82880
_d82880