Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field
Tóm tắt
The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.
Tài liệu tham khảo
B. A. Boyko, A. I. Bykov, M. I. Dolotenko, et al., in Book of Abstracts of the VIII International Conference on Megagauss Magnetic Field Generation and Related Topics, Tallahassee, USA, p. 149.
P. G. Harper, Proc. Phys. Soc. London, Sect. A 68, 874 (1955).
G. E. Zil’berman, Zh. Éksp. Teor. Fiz. 32, 296 (1957) [Sov. Phys. JETP 5, 208 (1957)]; Zh. Éksp. Teor. Fiz. 34, 515 (1958) [Sov. Phys. JETP 7, 355 (1958)].
M. Ya. Azbel’, Zh. Éksp. Teor. Fiz. 46, 929 (1964) [Sov. Phys. JETP 19, 634 (1964)].
D. R. Hofstadter, Phys. Rev. B 14, 2239 (1976).
V. Ya. Demikhovskii and A. A. Perov, Zh. Éksp. Teor. Fiz. 114, 1795 (1998) [JETP 87, 973 (1998)].
V. Ya. Demikhovskii and A. A. Perov, Phys. Low-Dimens. Struct. 7/8, 135 (1998).
H. Silberbauer, J. Phys.: Condens. Matter 4, 7355 (1992).
P. S. Sandhu, Ju. H. Kim, and J. S. Brooks, Phys. Rev. B 56, 11566 (1997).
S. Y. Han, J. S. Brooks, and Ju. H. Kim, Phys. Rev. Lett. 85, 1500 (2000).
D. Weiss, M. L. Roukes, A. Mensching, et al., Phys. Rev. Lett. 66, 2790 (1991).
T. Schlösser, K. Ensslin, J. P. Kotthaus, et al., Semicond. Sci. Technol. 11, 1582 (1996).
D. Peter, D. Mayou, and M. Cyrot, Phys. Rev. Lett. 65, 386 (1990).
G. Montambaux and M. Kohmoto, Phys. Rev. B 41, 11417 (1990).
H. Hasegawa, J. Phys. Soc. Jpn. 59, 4384 (1990).
Z. Kunszt and A. Zee, Phys. Rev. B 44, 6842 (1991).
V. Ya. Demikhovskii, A. A. Perov, and D. V. Khomitsky, Phys. Lett. A 267, 408 (2000).
I. M. Lifshits, M. Ya. Azbel’, and M. I. Kaganov, Electron Theory of Metals (Nauka, Moscow, 1971; Consultants Bureau, New York, 1973).
R. E. Peierls, Z. Phys. 80, 763 (1933).
J. Zak, Phys. Rev. A 134, 1602 (1964); 134, 1607 (1964).
E. M. Lifshitz and L. P. Pitaevskii, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1978; Pergamon, New York, 1980), Part 2.
A. P. Cracknell and K. C. Wong, Fermi Surface: Its Concept, Determination and Use in Physics of Metals (Clarendon, Oxford, 1973; Atomizdat, Moscow, 1978).
D. Shoenberg, Magnetic Oscillations in Metals (Cambridge Univ. Press, Cambridge, 1984; Mir, Moscow, 1986).
C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963; Nauka, Moscow, 1967).
Y. Hasegawa et al., Phys. Rev. B 41, 9174 (1990).