Abstract
The topology of energy surfaces in reciprocal space is studied in detail for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in the tight-binding approximation, taking into account hopping integrals t and t′ between the nearest and next-nearest neighbor sites, respectively. It is shown that lines and surfaces formed by van Hove k points can arise at values τ = t′/t = τ* corresponding to a change in the surface topology. At a small deviation of τ from these special values, the spectrum near the van Hove line (surface) only slightly depends on k. This corresponds to a giant effective mass proportional to |τ - τ*|−1 near several van Hove points. Singular contributions to the density of states near these special t values are analyzed and explicit expressions are obtained for the density of states in terms of elliptic integrals. It is shown that, in some cases, the maximum density of states is achieved at energies corresponding to k points in high-symmetry directions inside the Brillouin zone rather than at its edges. The corresponding contributions to electronic and magnetic characteristics are discussed, in particular, in application to itinerant weak magnets.
Similar content being viewed by others
References
S. V. Vonsovskii, M. I. Katsnel’son, and A. V. Trefilov, Fiz. Met. Metalloved. 76 (3), 3 (1993).
M. I. Katsnel’son, G. V. Peschanskikh, and A. V. Trefilov, Sov. Phys. Solid State 32, 272 (1990).
V. L. Moruzzy, J. P. Janak, and A. R. Williams, Calculated Electronic Properties of Metals (Plenum, New York, 1978).
D. A. Papacostantopoulos, Handbook of Band Structure of Elemental Solids (Plenum, New York, 1986).
A. Hausoel, M. Karolak, E. Sasioglu, A. Lichtenstein, K. Held, A. Katanin, A. Toschi, and G. Sangiovann, Nat. Commun. 8, 16062 (2017).
M. I. Katsnel’son and A. V. Trefilov, JETP Lett. 40, 1092 (1984).
M. I. Katsnel’son and A. V. Trefilov, JETP Lett. 42, 485 (1985).
L. van Hove, Phys. Rev. 89, 1189 (1953).
R. J. Jelitto, J. Phys. Chem. Solids 30, 609 (1969).
S. Katsura and T. Horiguchi, J. Math. Phys. 12, 230 (1971).
P. A. Igoshev and V. Yu. Irkhin, J. Exp. Theor. Phys. 128, 909 (2019).
R. H. Swendsen and H. Callen, Phys. Rev. B 6, 2860 (1972).
M. Ulmke, Eur. Phys. J. B 1, 301 (1998).
S. V. Vonsovsky, Yu. P. Irkhin, V. Yu. Irkhin, and M. I. Katsnelson, J. Phys. Coll. 49 (C8), 253 (1988).
G. Santi, S. B. Dugdale, and T. Jarlborg, Phys. Rev. Lett. 87, 247004 (2001).
A. S. Hamid, A. Uedono, Zs. Major, T. D. Haynes, J. Laverock, M. A. Alam, S. B. Dugdale, and D. Fort, Phys. Rev. B 84, 235107 (2011).
J. Inoue, Phys. B (Amsterdam, Neth.) 149, 376 (1988).
Y. Nishihara and S. Ogawa, J. Phys. Soc. Jpn. 60, 300 (1991).
D. J. Singh, Phys. Rev. B 92, 174403 (2015).
P. E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16223 (1994).
A. A. Stepanenko, D. O. Volkova, P. A. Igoshev, and A. A. Katanin, J. Exp. Theor. Phys. 125, 879 (2017).
Acknowledgments
We are grateful to M.I. Katsnelson, A.O. Anokhin, and A.A. Katanin for valuable discussions.
Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment no. AAAA-A18-118020190095-4, project Quantum) and by the Government of the Russian Federation (program 211, state contract no. 02.A03.21.0006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2019, Vol. 110, No. 11, pp. 741–747.
Electronic Supplementary Material
Rights and permissions
About this article
Cite this article
Igoshev, P.A., Irkhin, V.Y. Electron Spectrum Topology and Giant Singularities of the Electron Density of States in Cubic Lattices. Jetp Lett. 110, 727–733 (2019). https://doi.org/10.1134/S0021364019230085
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364019230085