Semiclassical Theory of Magnetic Energy Levels and Magnetic Susceptibility of Bloch Electrons
Abstract
In this paper the semiclassical condition for the quantization of magnetic energy levels of Bloch electrons is extended to one order higher in the magnetic field. The result enables us to make a calculation of the magnetic susceptibility of Bloch electrons which includes both the de Haas-van Alphen effect and the steady susceptibility. While the basic calculation is made for fairly simple closed orbits, the results have been extended to include spin splitting, self-intersecting orbits, and open orbits, but omitting consideration of banding of magnetic levels and magnetic breakdown. Possible new oscillations due to self-intersecting orbits are discussed.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
β can be shown to be equivalent to the Berry's phase experienced by an electron as it travels around a closed loop in momentum space.
“Mikitik and Sharlai, 1999 showed that the expressions of Roth, 1966 could be recast in a form such that β can be shown to be equivalent to the Berry's phase experienced by an electron as it travels around a closed loop in momentum space (Mikitik and Sharlai, 1999).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Roth, 1966
For arbitrary dispersions other values of β can occur, which can be calculated with knowledge of the Bloch functions.
“However, it was shown by Roth, 1966 that for arbitrary dispersions other values can occur, which can be calculated with knowledge of the Bloch functions.”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Roth, 1966
Cites
Methods of Theoretical Physics
Morse, P. M., Feshbach, H., & Hill, E. L. (1954) · American Journal of Physics · doi:10.1119/1.1933765 · Cited by 13,197 · see citing works
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283 · see citing works
Quantum mechanics as a statistical theory
Moyal, J. E. (1949) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100000487 · Cited by 3,116 · see citing works
Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
Harper, P. G. (1955) · Proceedings of the Physical Society. Section A · doi:10.1088/0370-1298/68/10/304 · Cited by 1,416 · see citing works
Burgess, R. E. (1973) · Journal of the Franklin Institute · doi:10.1016/0016-0032(73)90085-9 · Cited by 1,390 · see citing works
Zur Theorie des Diamagnetismus von Leitungselektronen
Peierls, R. F. (1933) · The European Physical Journal A · doi:10.1007/bf01342591 · Cited by 1,385 · see citing works
Landau, L. (1930) · The European Physical Journal A · doi:10.1007/bf01397213 · Cited by 1,383 · see citing works
Interpretation of the de Haas-van Alphen effect
Onsager, L. (1952) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440908521019 · Cited by 705 · see citing works
Bloch Electrons in a Magnetic Field
Blount, E. I. (1962) · Physical Review · doi:10.1103/physrev.126.1636 · Cited by 494 · see citing works
Motion in a Constant Magnetic Field
Johnson, M. H., & Lippmann, B. A. (1949) · Physical Review · doi:10.1103/physrev.76.828 · Cited by 450 · see citing works
Bloch Electrons in a Uniform Magnetic Field
Brown, E. (1964) · Physical Review · doi:10.1103/physrev.133.a1038 · Cited by 420 · see citing works
Dingle, R. (1952) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1952.0056 · Cited by 303 · see citing works
Theory of Bloch Electrons in a Magnetic Field: The Effective Hamiltonian
Kohn, W. (1959) · Physical Review · doi:10.1103/physrev.115.1460 · Cited by 248 · see citing works
Theg-factor and de haas-van alphen effect of electrons in bismuth
Cohen, M. H., & Blount, E. I. (1960) · Philosophical magazine · doi:10.1080/14786436008243294 · Cited by 248 · see citing works
Theory of bloch electrons in a magnetic field
Roth, L. M. (1962) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(62)90083-5 · Cited by 193 · see citing works
Self-citationQuantization of coupled orbits in metals
Pippard, A. B. (1962) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1962.0200 · Cited by 184 · see citing works
Pippard, A. B. (1964) · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · doi:10.1098/rsta.1964.0008 · Cited by 127 · see citing works
The diamagnetism of conduction electrons in metals
Hebborn, J. E., & Sondheimer, E. H. (1960) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(60)90131-1 · Cited by 113 · see citing works
Linear-Network Model for Magnetic Breakdown in Two Dimensions
Chambers, W. G. (1965) · Physical Review · doi:10.1103/physrev.140.a135 · Cited by 102 · see citing works
Effect of Magnetic Fields on Conduction—"Tube Integrals"
Shockley, W. (1950) · Physical Review · doi:10.1103/physrev.79.191.2 · Cited by 94 · see citing works
Effect of Spin-Orbit Splitting on the Fermi Surfaces of the Hexagonal-Close-Packed Metals
Cohen, M. H., & Falicov, L. M. (1960) · Physical Review Letters · doi:10.1103/physrevlett.5.544 · Cited by 78 · see citing works
Decoupling of Bloch Bands in the Presence of Homogeneous Fields
Wannier, G. H., & Fredkin, D. R. (1962) · Physical Review · doi:10.1103/physrev.125.1910 · Cited by 73 · see citing works
Lifshitz, I. M., & Kaganov, M. I. (1959) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0069.195911c.0419 · Cited by 71 · see citing works
Zero-Field Susceptibility of Bloch Electrons
Wannier, G. H., & Upadhyaya, U. N. (1964) · Physical Review · doi:10.1103/physrev.136.a803 · Cited by 62 · see citing works
The orbital diamagnetic susceptibility of Bloch electrons
Hebborn, J. E., Luttinger, J. M., Sondheimer, E. H., & Stiles, P. J. (1964) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(64)90186-6 · Cited by 60 · see citing works
Lifshitz, I. M., & Kaganov, M. I. (1962) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0078.196211b.0411 · Cited by 40 · see citing works
The Magnetic Energy Levels of Electrons in Metals
Brailsford, A. D. (1957) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/70/4/305 · Cited by 34 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528 · see citing works
“Mikitik and Sharlai, 1999 showed that the expressions of Roth, 1966 could be recast in a form such that β can be shown to be equivalent to the Berry’s phase experienced by an electron as it travels around a closed loop in momentum space (Mikitik and Sharlai, 1999).”
BackgroundStatistical Exchange-Correlation in the Self-Consistent Field
Slater, J. C. (1972) · Advances in quantum chemistry · doi:10.1016/s0065-3276(08)60541-9 · Cited by 1,017 · see citing works
Chang, M., & Niu, Q. (1996) · Physical review. B, Condensed matter · doi:10.1103/physrevb.53.7010 · Cited by 633 · see citing works
Manifestation of Berry's Phase in Metal Physics
Mikitik, G. P., & Sharlai, Y. V. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.2147 · Cited by 475 · see citing works
Gradhand, M., Fedorov, D. V., Pientka, F., Zahn, P. K., Mertig, I., & Gyorffy, B. L. (2012) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/24/21/213202 · Cited by 213 · see citing works
Fuchs, J.-N., Piéchon, F., Goerbig, M. O., & Montambaux, G. (2010) · The European Physical Journal B · doi:10.1140/epjb/e2010-00259-2 · Cited by 207 · see citing works
Quantum distance and anomalous Landau levels of flat bands
Rhim, J., Kim, K., & Yang, B. (2020) · Nature · doi:10.1038/s41586-020-2540-1 · Cited by 162 · see citing works
Quantum Hall effect of Weyl fermions in n-type semiconducting tellurene
Qiu, G., Niu, C., Wang, Y., Si, M., Zhang, Z., Wu, W., & Ye, P. D. (2020) · Nature Nanotechnology · doi:10.1038/s41565-020-0715-4 · Cited by 128 · see citing works
Wright, A. R., & McKenzie, R. H. (2013) · Physical Review B · doi:10.1103/physrevb.87.085411 · Cited by 101 · see citing works
Rhim, J., & Yang, B. (2021) · Advances in Physics X · doi:10.1080/23746149.2021.1901606 · Cited by 102 · see citing works
de Haas-van Alphen Effect and Fermi Surface of LaB 6
Ishizawa, Y., Tanaka, T., Bannai, E., & Kawai, S. (1977) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.42.112 · Cited by 99 · see citing works
The Kq-Representation in the Dynamics of Electrons in Solids
Žák, J. (1972) · Solid state physics · doi:10.1016/s0081-1947(08)60236-2 · Cited by 91 · see citing works
Quantum geometry in quantum materials
Yu, J., Bernevig, B. A., Queiroz, R., Rossi, E., Törmä, P., & Yang, B. (2025) · npj Quantum Materials · doi:10.1038/s41535-025-00801-3 · Cited by 91 · see citing works
Chapter 6 Magnetic Quantum Effects
Roth, L. M., & Argyres, P. N. (1966) · Semiconductors and semimetals · doi:10.1016/s0080-8784(08)62379-0 · Cited by 84 · see citing works
Self-citationAngular-Dependent Phase Factor of Shubnikov–de Haas Oscillations in the Dirac Semimetal Cd3As2
Xiang, Z., Zhao, D., Jin, Z., Shang, C., Ma, L. K., Ye, G. J., Lei, B., Wu, T., Xia, Z. C., & Chen, X. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.226401 · Cited by 80 · see citing works
Semiclassical theory of Landau levels and magnetic breakdown in topological metals
Alexandradinata, A., & Glazman, L. I. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.144422 · Cited by 75 · see citing works
Composite Fermi liquids in the lowest Landau level
Wang, C., & Senthil, T. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.245107 · Cited by 70 · see citing works
Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals
Samokhin, K. V. (2009) · Annals of Physics · doi:10.1016/j.aop.2009.08.008 · Cited by 65 · see citing works
An example of phase holonomy in WKB theory
Wilkinson, M. (1984) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/17/18/016 · Cited by 66 · see citing works
Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations
Alexandradinata, A., Wang, C., Duan, W., & Glazman, L. I. (2018) · Physical Review X · doi:10.1103/physrevx.8.011027 · Cited by 66 · see citing works
Semiclassical approximation for equations with periodic coefficients
Buslaev, V. S. (1987) · Russian Mathematical Surveys · doi:10.1070/rm1987v042n06abeh001502 · Cited by 63 · see citing works
Anisotropy of the Fermi Surface of p -Type PbTe
Burke, J. R., Houston, B., & Savage, H. T. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.2.1977 · Cited by 61 · see citing works
The g‐factor of the conduction electrons in Bi2Se3
Köhler, H., & Wöchner, E. (1975) · physica status solidi (b) · doi:10.1002/pssb.2220670229 · Cited by 58 · see citing works
Theory of impurity scattering in dilute metal alloys based on the muffin-tin model
Holzwarth, N. A. W. (1975) · Physical review. B, Solid state · doi:10.1103/physrevb.11.3718 · Cited by 57 · see citing works
Theory of Bloch Electrons in a Magnetic Field
Fischbeck, H. J. (1970) · physica status solidi (b) · doi:10.1002/pssb.19700380102 · Cited by 52 · see citing works
Model Calculations of Magnetic Band Structure
Butler, F. A., & Brown, E. (1968) · Physical Review · doi:10.1103/physrev.166.630 · Cited by 51 · see citing works
Aspects of Group Theory in Electron Dynamics
Brown, E. (1969) · Solid state physics · doi:10.1016/s0081-1947(08)60033-8 · Cited by 46 · see citing works
Geometric characterization of anomalous Landau levels of isolated flat bands
Hwang, Y., Rhim, J., & Yang, B. (2021) · Nature Communications · doi:10.1038/s41467-021-26765-z · Cited by 40 · see citing works
Zero-field magnetic response functions in Landau levels
Gao, Y., & Niu, Q. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1702595114 · Cited by 39 · see citing works
Measure of Diracness in two-dimensional semiconductors
Goerbig, M. O., Montambaux, G., & Piéchon, F. (2014) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/105/57005 · Cited by 37 · see citing works
Twisted Fermi surface of a thin-film Weyl semimetal
Bovenzi, N., Breitkreiz, M., O’Brien, T. E., Tworzydło, J., & Beenakker, C. W. J. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aaaa90 · Cited by 34 · see citing works
Semiclassical energy levels of electrons in metals with band degeneracy lines
Mikitik, G. P., & Sharlaı̆, Y. V. (1998) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.558717 · Cited by 33 · see citing works
High-Magnetic-Field Tunneling Spectra of ABC -Stacked Trilayer Graphene on Graphite
Yin, L., Shi, L., Li, S., Zhang, Y., Guo, Z., & He, L. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.146802 · Cited by 32 · see citing works
Temperature dependence of quantum oscillations from non-parabolic dispersions
Guo, C., Alexandradinata, A., Putzke, C. M., Estry, A., Tu, T., Kumar, N., Fan, F., Zhang, S., Wu, Q., Yazyev, O. V., et al. (2021) · Nature Communications · doi:10.1038/s41467-021-26450-1 · Cited by 33 · see citing works
Many-Body Effects on Diamagnetism of Free and Bloch Electrons
Philippas, M. A., & McClure, J. W. (1972) · Physical review. B, Solid state · doi:10.1103/physrevb.6.2051 · Cited by 30 · see citing works
Fermi-surface parameters of p -type PbTe as a function of carrier density
Jensen, J. D., Houston, B., & Burke, J. R. (1978) · Physical review. B, Condensed matter · doi:10.1103/physrevb.18.5567 · Cited by 29 · see citing works
Landau levels, response functions and magnetic oscillations from a generalized Onsager relation
Fuchs, J.-N., Piéchon, F., & Montambaux, G. (2018) · SciPost Physics · doi:10.21468/scipostphys.4.5.024 · Cited by 28 · see citing works
Manipulation of Dirac band curvature and momentum-dependent g factor in a kagome magnet
Li, H., Zhao, H., Jiang, K., Wang, Q., Yin, Q., Zhao, N., Liu, K., Wang, Z., Lei, H., & Zeljkovic, I. (2022) · Nature Physics · doi:10.1038/s41567-022-01558-3 · Cited by 28 · see citing works
Fermiology of Topological Metals
Alexandradinata, A., & Glazman, L. I. (2022) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-040721-021331 · Cited by 28 · see citing works
Thermodynamic signature of Dirac electrons across a possible topological transition in ZrTe5
Nair, N., Dumitrescu, P. T., Channa, S., Griffin, S. M., Neaton, J. B., Potter, A. C., & Analytis, J. G. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.041111 · Cited by 28 · see citing works
Quantum Hall conductances and localization in a magnetic field
Dana, I., & Žák, J. (1985) · Physical review. B, Condensed matter · doi:10.1103/physrevb.32.3612 · Cited by 28 · see citing works
The wave function of a Bloch electron in a magnetic field
Chambers, R. G. (1966) · Proceedings of the Physical Society · doi:10.1088/0370-1328/89/3/325 · Cited by 28 · see citing works
Theory of the Diamagnetic Interactions among the Conduction Electrons in Metals
Ying, S. C., McIntyre, B. J., & Quinn, J. J. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.2.1801 · Cited by 27 · see citing works
Experimental Manifestation of Berry Phase in Graphene
Young, A. F., Zhang, Y., & Kim, P. (2013) · Nanoscience and technology · doi:10.1007/978-3-319-02633-6_1 · Cited by 26 · see citing works
Massless multifold Hopf semimetals
Graf, A., & Piéchon, F. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.115105 · Cited by 23 · see citing works
Magnetophonon Resonance in Tellurium
Bresler, M. S., & Mashovets, D. V. (1970) · physica status solidi (b) · doi:10.1002/pssb.19700390208 · Cited by 22 · see citing works
Magnetic Breakdown: Effective Hamiltonian and de Haas-van Alphen Effect
Chambers, W. G. (1966) · Physical Review · doi:10.1103/physrev.149.493 · Cited by 21 · see citing works
Spintronics of Topological Insulators
Wang, K. L., Lang, M., & Kou, X. (2015) · Springer eBooks · doi:10.1007/978-94-007-6892-5_56 · Cited by 23 · see citing works
Magnetoresistance and growth of the coherent state in CeCu6
Coleridge, P. T. (1987) · Journal of Physics F Metal Physics · doi:10.1088/0305-4608/17/5/002 · Cited by 19 · see citing works
Fourier analysis applied to cyclotron resonance in metals having anisotropic Fermi surfaces
Olszewski, S., Roliński, T., & Kwiatkowski, T. (1999) · Physical review. B, Condensed matter · doi:10.1103/physrevb.59.3740 · Cited by 19 · see citing works
gfactor of conduction electrons in the de Haas–van Alphen effect
Mikitik, G. P., & Sharlaı̆, Y. V. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.65.184426 · Cited by 18 · see citing works
Arai, M., & Hatsugai, Y. (2009) · Physical Review B · doi:10.1103/physrevb.79.075429 · Cited by 18 · see citing works
Buot, F. A. (1986) · Physical Review A · doi:10.1103/physreva.33.2544 · Cited by 18 · see citing works
Magnetic Susceptibility of Topological Semimetals
Mikitik, G. P., & Sharlaı̆, Y. V. (2019) · Journal of Low Temperature Physics · doi:10.1007/s10909-019-02225-3 · Cited by 17 · see citing works
Semiclassical quantization of electrons in magnetic fields: The generalized Peierls substitution
Gosselin, P., Boumrar, H., & Mohrbach, H. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/84/50002 · Cited by 17 · see citing works
Wang, C., Duan, W., Glazman, L. I., & Alexandradinata, A. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.014442 · Cited by 18 · see citing works
Spinless fermions on frustrated lattices in a magnetic field
Barford, W., & Kim, J. H. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.559 · Cited by 17 · see citing works
Taut, M., Eschrig, H., & Richter, M. (2005) · Physical Review B · doi:10.1103/physrevb.72.165304 · Cited by 16 · see citing works
Landau Spectrum and Line Broadening in Real Metals
Davis, L. C., & Liu, S. H. (1967) · Physical Review · doi:10.1103/physrev.158.689 · Cited by 16 · see citing works
Topology and solid-state physics (Review)
Kosevich, A. M. (2004) · Low Temperature Physics · doi:10.1063/1.1645161 · Cited by 16 · see citing works
The Shubnikov–de Haas Effect in Semiconductors: A Comprehensive Review of Experimental Aspects
Seiler, D. G., & Stephens, A. E. (1991) · Modern problems in condensed matter sciences · doi:10.1016/b978-0-444-88873-0.50014-5 · Cited by 16 · see citing works
Field dependence of the Stoner factor in Pd-Ni alloys
Roeland, L. W., Wolfrat, J., Mak, D. K., & Springford, M. (1982) · Journal of Physics F Metal Physics · doi:10.1088/0305-4608/12/12/005 · Cited by 16 · see citing works
Formalism of distribution-function method in impurity screening
Buot, F. A. (1976) · Physical review. B, Solid state · doi:10.1103/physrevb.14.977 · Cited by 15 · see citing works
The Hall conductivity of a disordered alloy in the coherent-potential approximation
Niizeki, K., & Hoshino, K. (1976) · Journal of Physics C Solid State Physics · doi:10.1088/0022-3719/9/18/015 · Cited by 15 · see citing works
Pauly, C., Saunus, C., Liebmann, M., & Morgenstern, M. (2015) · Physical Review B · doi:10.1103/physrevb.92.085140 · Cited by 14 · see citing works
Fortin, J.-Y., Bellissard, J., Gusmão, M. A., & Ziman, T. A. L. (1998) · Physical review. B, Condensed matter · doi:10.1103/physrevb.57.1484 · Cited by 14 · see citing works
Breitkreiz, M., & Brouwer, P. W. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.196602 · Cited by 13 · see citing works
A formula for the orbital magnetic susceptibility of Bloch electrons in weak fields
Fukuyama, H. (1970) · Physics Letters A · doi:10.1016/0375-9601(70)90117-9 · Cited by 13 · see citing works
Quantum geometry and Landau levels of quadratic band crossings
Jung, J., Lim, H., & Yang, B. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.035134 · Cited by 12 · see citing works
Theory of Interacting Bloch Electrons in a Magnetic Field
Kita, T., & Arai, M. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.2813 · Cited by 12 · see citing works
Theory of the de Haas-van Alphen effect
Shoenberg, D. (1988) · Journal of Physics F Metal Physics · doi:10.1088/0305-4608/18/1/008 · Cited by 12 · see citing works
Revisiting the magnetic responses of bilayer graphene from the perspective of quantum distance
Oh, C., Rhim, J., & Yang, B. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.155412 · Cited by 11 · see citing works
Mikitik, G. P., & Sharlaı̆, Y. V. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.67.115114 · Cited by 11 · see citing works
Effective hamiltonians and magnetic energy bands?
Žák, J. (1986) · Physics Letters A · doi:10.1016/0375-9601(86)90683-3 · Cited by 11 · see citing works
A quantum ruler for orbital magnetism in moiré quantum matter
Slot, M. R., Maximenko, Y., Haney, P. M., Kim, S., Walkup, D., Strelcov, E., Le, S. T., Shih, E.-M., Yıldız, D., Blankenship, S. R., et al. (2023) · Science · doi:10.1126/science.adf2040 · Cited by 10 · see citing works
Phase shift of cyclotron orbits at type-I and type-II multi-Weyl nodes
Breitkreiz, M., Bovenzi, N., & Tworzydło, J. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.121403 · Cited by 9 · see citing works
Magnetic Properties of Metal Cluster Compounds
van Ruitenbeek, J. M., Leeuwen, D. A. V., & de Jongh, L. J. (1994) · Physics and chemistry of materials with low-dimensional structures · doi:10.1007/978-94-015-1294-7_10 · Cited by 8 · see citing works
Energy-Level Structure of Zinc in Magnetic Fields Using a Single-Band Effective Hamiltonian
Kapo, P. S., & Brown, E. (1973) · Physical review. B, Solid state · doi:10.1103/physrevb.7.3429 · Cited by 8 · see citing works
Perturbed crystals in the kq representation: III. The uniform magnetic field
Žák, J. (1977) · Physical review. B, Solid state · doi:10.1103/physrevb.16.4154 · Cited by 8 · see citing works
Spin susceptibility of superconductors with strong spin-orbit coupling
Samokhin, K. V. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.174505 · Cited by 7 · see citing works
Julian, S. R. (2023) · Canadian Journal of Physics · doi:10.1139/cjp-2022-0340 · Cited by 7 · see citing works
Fukuyama, H. (2006) · Annalen der Physik · doi:10.1002/andp.200510199 · Cited by 7 · see citing works
Dynamics of Bloch Electrons in a Magnetic Field
Misra, P. K. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.2.3906 · Cited by 7 · see citing works
Dilute indium alloys: Measurement and calculation of Fermi surface changes
Holtham, P. M., & Parsons, D. (1976) · Journal of Physics F Metal Physics · doi:10.1088/0305-4608/6/8/009 · Cited by 6 · see citing works
Falicov, L. M. (1980) · Springer eBooks · doi:10.1007/978-1-4899-0454-6_1 · Cited by 6 · see citing works
Ensembles of Electron States in Cubic Lattices Quantized in the Presence of a Magnetic Field
Olszewski, S., & Baszczak, M. (2002) · physica status solidi (b) · doi:10.1002/1521-3951(200208)232:2 · Cited by 6 · see citing works
Magnetic Properties of Nearly Free Electrons. II. Oscillatory Properties
Glasser, M. L. (1967) · Physical Review · doi:10.1103/physrev.162.558 · Cited by 6 · see citing works
Dynamics and Classical Transport of Carriers in Semiconductors
Roth, L. M. (1992) · Elsevier eBooks · doi:10.1016/b978-0-444-88855-6.50018-8 · Cited by 5 · see citing works
Self-citationSaddle point anomaly of Landau levels in graphenelike structures
Nikolaev, A. V. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.035419 · Cited by 5 · see citing works
Kang, J. S., Vu, D., & Heremans, J. P. (2021) · Journal of Applied Physics · doi:10.1063/5.0068312 · Cited by 5 · see citing works
Magnetic breakdown with spin flip
Proshin, Y. N., & Useinov, N. K. (1995) · Physics-Uspekhi · doi:10.1070/pu1995v038n01abeh000064 · Cited by 5 · see citing works
Landau diamagnetic response in metals as a Fermi surface effect
Nikolaev, A. V. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.224417 · Cited by 5 · see citing works
Topological Fermiology of gate-tunable Rashba electron gases
Hu, J., Fang, Z.-Z., Sheng, F., Hua, C., Xi, C., Kuang, G., Pi, L., Watanabe, K., Taniguchi, T., Xia, Q., et al. (2024) · Science Advances · doi:10.1126/sciadv.adp8208 · Cited by 4 · see citing works
Kasiab, M. Z., Tadele, K., Afrassa, M. A., & Akin‐Ojo, O. (2025) · AIP Advances · doi:10.1063/5.0269638 · Cited by 4 · see citing works
Pal, H. K. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.075419 · Cited by 4 · see citing works
Callaway, J. (1974) · Elsevier eBooks · doi:10.1016/b978-0-12-155202-2.50008-5 · Cited by 4 · see citing works
Transfer-matrix study of Bloch electrons in a magnetic field
Taylor, P. L. (1977) · Physical review. B, Solid state · doi:10.1103/physrevb.15.3558 · Cited by 4 · see citing works
Electron energy spectrum in a magnetic field for nonconvex bounded energy-constant surfaces
Giura, M., Marcon, R., & Marietti, P. (1975) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02732227 · Cited by 4 · see citing works
Orientation dependent resistivity scaling in mesoscopic NbP crystals
Mariani, G., Balduini, F., Drucker, N. C., Rocchino, L., Hasse, V., Felser, C., Schmid, H., Zota, C. B., & Gotsmann, B. (2025) · Communications Materials · doi:10.1038/s43246-025-00828-w · Cited by 3 · see citing works
Observation of the Magnetic Field Induced Fermi Surface Expansion in Aperiodic Quantum Oscillations
Kumari, A., Silotia, H., Das, S., Monga, S., Malik, V. K., Agarwal, A., & Chakraverty, S. (2025) · Advanced Functional Materials · doi:10.1002/adfm.202422986 · Cited by 3 · see citing works
- Authors
- Roth, L. M.
- Affiliations
- Tufts University (US)
- Corresponding author
- Roth, Laura M.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1966-05-13
- Volume
- 145
- Issue
- 2
- Pages
- 434-448
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2051341083
- Cited by
- 143
- References
- 27
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 3 · 2023: 5 · 2022: 6 · 2021: 8 · 2020: 5 · 2019: 4 · 2018: 10 · 2017: 2 · 2016: 1 · 2015: 5 · 2014: 1 · 2013: 2 · 2012: 1
- FWCI
- 2.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Engineering › Mechanical Engineering › Thermodynamic and Structural Properties of Metals and Alloys
- Keywords
- semiclassical quantization, Bloch electrons, magnetic susceptibility, de Haas-van Alphen effect, spin splitting, open orbits, periodic orbits, magnetic breakdown
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
