140
L. Didukh et al.
4 Conclusions
In a new variant of Hartree–Fock approximation for the calculation of electrical and
magnetic properties of strongly correlated electron systems in nanoscale material,
the quasiparticle energy spectrum is obtained. The spectrum is temperature- and
concentration-dependent, exact in atomic and band limits. The electron–hole asymmetry in the model reflects a peculiar behavior of specific nanomaterials, generalizing
the Hubbard model and t–J model. Hopping integrals are renormalized by electron
correlations and appear to be concentration-dependent. As a consequence, at a change
of conductance type, the bandwidth, activation energy, and conductivity are found
to undergo sharp changes, kinetic energy increases, and Fermi surface symmetry
broke down. At the external pressure and decreasing temperature, the transition from
insulator to metallic phase occurs due to the reduction of electron correlation. The
proposed approach will be developed further for studies of conductance and effective
masses of carriers in ferromagnetic phase within the ideology of works [18, 20].
The above-described mechanisms, revealed by the approach we used in the present
work, will be even more pronounced in the degenerated case, for which similar studies
have been done in papers [21–23].
References
1. Fesenko O, Yatsenko L (2019) Nanocomposites, nanostructures, and their applications. NANO
2018. Springer Proceedings in Physics, vol 221. Springer, Cham
2. Wei J, Wang Z, Chen W, Cobden DH (2009) New aspects of the metal–insulator transition in
single-domain vanadium dioxide nanobeams. Nat Nanotechnol 4:420–424
3. Jager M, Ott C, Kraus P et al (2017) Tracking the insulator-to-metal phase transition in VO2
with few-femtosecond extreme UV transient absorption spectroscopy. PNAS 114:9558–9563
4. Lantz G, Mansart B, Grieger D et al (2017) Ultrafast evolution and transient phases of a
prototype out-of-equilibrium Mott-Hubbard material. Nat Commun 8:13917–13924
5. Majid S, Gautam K, Ahad A et al (2019) Mott-Hubbard insulator-metal transition in the VO2
thin film: a combined XAS and resonant PES study. arXiv:1907.12746
6. Pang S, Kim Y, Shin YJ et al (2017) Electronic characteristics of ultrathin SrRuO3 films and
their relationship with the metal−insulator transition. arXiv:1712.05137
7. Lee J, Kwon SG, Park J-G et al (2015) Size dependence of metal-insulator transition in
stoichiometric Fe3O4 Nanocrystals. Nano Lett 7:4337–4342
8. Aleshin AN (2007) Quasi-one-dimensional transport in conducting polymer nanowires. Phys
Solid State 49:2015–2033
9. Didukh L (1997) Model of narrow-band material with electron-hole asymmetry. J Phys Stud
1:241–250 [In Ukrainian]
10. Didukh L (1998) Energy spectrum of electrons in the Hubbard model: a new mean-field
approximation. Physica Status Solidi (B) 206:R5–R6
11. Didukh L (1998) A modified form of the polar model of crystals. Condens Matter Phys 1:125–
144
12. Didukh L (2000) A modified form of the polar model of crystals. Acta Phys Pol B 31:3097–3133
13. Didukh LD, Stasyuk IV (1968) Effective Hamiltonian in the Anderson model. Fiz Met Metalov
26:582–588 [In Russian]
L. Didukh et al.
4 Conclusions
In a new variant of Hartree–Fock approximation for the calculation of electrical and
magnetic properties of strongly correlated electron systems in nanoscale material,
the quasiparticle energy spectrum is obtained. The spectrum is temperature- and
concentration-dependent, exact in atomic and band limits. The electron–hole asymmetry in the model reflects a peculiar behavior of specific nanomaterials, generalizing
the Hubbard model and t–J model. Hopping integrals are renormalized by electron
correlations and appear to be concentration-dependent. As a consequence, at a change
of conductance type, the bandwidth, activation energy, and conductivity are found
to undergo sharp changes, kinetic energy increases, and Fermi surface symmetry
broke down. At the external pressure and decreasing temperature, the transition from
insulator to metallic phase occurs due to the reduction of electron correlation. The
proposed approach will be developed further for studies of conductance and effective
masses of carriers in ferromagnetic phase within the ideology of works [18, 20].
The above-described mechanisms, revealed by the approach we used in the present
work, will be even more pronounced in the degenerated case, for which similar studies
have been done in papers [21–23].
References
1. Fesenko O, Yatsenko L (2019) Nanocomposites, nanostructures, and their applications. NANO
2018. Springer Proceedings in Physics, vol 221. Springer, Cham
2. Wei J, Wang Z, Chen W, Cobden DH (2009) New aspects of the metal–insulator transition in
single-domain vanadium dioxide nanobeams. Nat Nanotechnol 4:420–424
3. Jager M, Ott C, Kraus P et al (2017) Tracking the insulator-to-metal phase transition in VO2
with few-femtosecond extreme UV transient absorption spectroscopy. PNAS 114:9558–9563
4. Lantz G, Mansart B, Grieger D et al (2017) Ultrafast evolution and transient phases of a
prototype out-of-equilibrium Mott-Hubbard material. Nat Commun 8:13917–13924
5. Majid S, Gautam K, Ahad A et al (2019) Mott-Hubbard insulator-metal transition in the VO2
thin film: a combined XAS and resonant PES study. arXiv:1907.12746
6. Pang S, Kim Y, Shin YJ et al (2017) Electronic characteristics of ultrathin SrRuO3 films and
their relationship with the metal−insulator transition. arXiv:1712.05137
7. Lee J, Kwon SG, Park J-G et al (2015) Size dependence of metal-insulator transition in
stoichiometric Fe3O4 Nanocrystals. Nano Lett 7:4337–4342
8. Aleshin AN (2007) Quasi-one-dimensional transport in conducting polymer nanowires. Phys
Solid State 49:2015–2033
9. Didukh L (1997) Model of narrow-band material with electron-hole asymmetry. J Phys Stud
1:241–250 [In Ukrainian]
10. Didukh L (1998) Energy spectrum of electrons in the Hubbard model: a new mean-field
approximation. Physica Status Solidi (B) 206:R5–R6
11. Didukh L (1998) A modified form of the polar model of crystals. Condens Matter Phys 1:125–
144
12. Didukh L (2000) A modified form of the polar model of crystals. Acta Phys Pol B 31:3097–3133
13. Didukh LD, Stasyuk IV (1968) Effective Hamiltonian in the Anderson model. Fiz Met Metalov
26:582–588 [In Russian]