<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2017-8-1-48-58</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-733</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Metal-insulator (fermion-boson)-crossover origin of pseudogap phase of cuprates I:  anomalous heat conductivity, insulator resistivity boundary, nonlinear entropy</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Abdullaev</surname><given-names>B.</given-names></name></name-alternatives><bio xml:lang="en"><p>Tashkent 100174</p></bio><email xlink:type="simple">bakhodir.abdullaeff@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Park</surname><given-names>C.-H.</given-names></name></name-alternatives><bio xml:lang="en"><p>30 Jangjeon-dong, Geumjeong-gu, Busan 609-735</p></bio><email xlink:type="simple">cpark@pusan.ac.kr</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Park</surname><given-names>K.-S.</given-names></name></name-alternatives><bio xml:lang="en"><p>2066, Seoburo, Jangangu, Suwon, Gyeonggido</p></bio><email xlink:type="simple">pmpark@skku.edu</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Kang</surname><given-names>I.-J.</given-names></name></name-alternatives><bio xml:lang="en"><p>Suwon, Kyunggido</p></bio><email xlink:type="simple">hacret@hanmail.net</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Institute of Applied Physics, National University of Uzbekistan</institution><country>Uzbekistan</country></aff><aff xml:lang="en" id="aff-2"><institution>Research Center for Dielectric and Advanced Matter Physics, Department of Physics, Pusan National University</institution><country>Korea, Republic of</country></aff><aff xml:lang="en" id="aff-3"><institution>Department of Physics, Sungkyunkwan University</institution><country>Korea, Republic of</country></aff><aff xml:lang="en" id="aff-4"><institution>Samsung Mobile Display</institution><country>Korea, Republic of</country></aff><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>13</day><month>08</month><year>2025</year></pub-date><volume>8</volume><issue>1</issue><fpage>48</fpage><lpage>58</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Abdullaev B., Park C., Park K., Kang I., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Abdullaev B., Park C., Park K., Kang I.</copyright-holder><copyright-holder xml:lang="en">Abdullaev B., Park C., Park K., Kang I.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/733">https://nanojournal.ifmo.ru/jour/article/view/733</self-uri><abstract><p>Among all the experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator– bosonic metal– fermionic metal transitions.</p></abstract><kwd-group xml:lang="en"><kwd>high critical temperature superconductivity</kwd><kwd>cuprate</kwd><kwd>metal-insulator-crossover</kwd><kwd>temperature-doping phase diagram</kwd><kwd>anomalous heat conductivity</kwd><kwd>insulator resistivity boundary</kwd><kwd>nonlinear entropy</kwd></kwd-group><funding-group><funding-statement xml:lang="en">Authors B. Abdullaev and C.-H. Park acknowledge the support of the research by the National Research  Foundation (NRF) Grant (NRF-2013R1A1A2065742) of the Basic Science Research Program of Korea.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Takagi H. et al. Systematic evolution of temperature-dependent resistivity in La2 xSrxCuO4. Phys. Rev. Lett., 1992, 69, P. 2975–2979.</mixed-citation><mixed-citation xml:lang="en">Takagi H. et al. Systematic evolution of temperature-dependent resistivity in La2 xSrxCuO4. Phys. Rev. Lett., 1992, 69, P. 2975–2979.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Keimer B. et al. Magnetic excitations in pure, lightly doped, and weakly metallic La2CuO4. Phys. Rev. B, 1992, 46, P. 14034.</mixed-citation><mixed-citation xml:lang="en">Keimer B. et al. Magnetic excitations in pure, lightly doped, and weakly metallic La2CuO4. Phys. Rev. B, 1992, 46, P. 14034.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Wuyts B., Moshchalkov V.V., Bruynseraede Y. Resistivity and Hall effect of metallic oxygen-deficient YBa2Cu3Ox films in the normal state. Phys. Rev. B, 1996, 53, P. 9418.</mixed-citation><mixed-citation xml:lang="en">Wuyts B., Moshchalkov V.V., Bruynseraede Y. Resistivity and Hall effect of metallic oxygen-deficient YBa2Cu3Ox films in the normal state. Phys. Rev. B, 1996, 53, P. 9418.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Abe Y. et al.Normal-state magnetotransport in La1905Ba0095CuO4 single crystals. Phys. Rev. B, 1999, 59, P. 14753.</mixed-citation><mixed-citation xml:lang="en">Abe Y. et al.Normal-state magnetotransport in La1905Ba0095CuO4 single crystals. Phys. Rev. B, 1999, 59, P. 14753.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Ando Y. et al. Logarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting La2 xSrxCuO4 in the Zero-Temperature Limit. Phys. Rev. Lett., 1995, 75, P. 4662–4665.</mixed-citation><mixed-citation xml:lang="en">Ando Y. et al. Logarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting La2 xSrxCuO4 in the Zero-Temperature Limit. Phys. Rev. Lett., 1995, 75, P. 4662–4665.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Boebinger G.S. et al. Insulator-to-Metal Crossover in the Normal State of La2 xSrxCuO4 Near Optimum Doping. Phys. Rev. Lett., 1996, 77, P. 5417–5420.</mixed-citation><mixed-citation xml:lang="en">Boebinger G.S. et al. Insulator-to-Metal Crossover in the Normal State of La2 xSrxCuO4 Near Optimum Doping. Phys. Rev. Lett., 1996, 77, P. 5417–5420.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Fournier P. et al. Insulator-Metal Crossover near Optimal Doping in Pr2 xCexCuO4: Anomalous Normal-State Low Temperature Resistivity. Phys. Rev. Lett., 1998, 81, P. 4720–4723.</mixed-citation><mixed-citation xml:lang="en">Fournier P. et al. Insulator-Metal Crossover near Optimal Doping in Pr2 xCexCuO4: Anomalous Normal-State Low Temperature Resistivity. Phys. Rev. Lett., 1998, 81, P. 4720–4723.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Ono S. et al. Metal-to-Insulator Crossover in the Low-Temperature Normal State of Bi2Sr2 xLaxCuO6+ . Phys. Rev. Lett., 2000, 85, P. 638–641.</mixed-citation><mixed-citation xml:lang="en">Ono S. et al. Metal-to-Insulator Crossover in the Low-Temperature Normal State of Bi2Sr2 xLaxCuO6+ . Phys. Rev. Lett., 2000, 85, P. 638–641.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ando Y. et al. Supporting evidence of the unusual insulating behavior in the low-temperature normal-state resistivity of underdoped La2 xSrxCuO4. J. Low Temp. Phys., 1996, 105, P. 867–875.</mixed-citation><mixed-citation xml:lang="en">Ando Y. et al. Supporting evidence of the unusual insulating behavior in the low-temperature normal-state resistivity of underdoped La2 xSrxCuO4. J. Low Temp. Phys., 1996, 105, P. 867–875.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Hill R.W. et al. Breakdown of Fermi-liquid theory in a copper-oxide superconductor. Nature, 2001, 414, P. 711–715.</mixed-citation><mixed-citation xml:lang="en">Hill R.W. et al. Breakdown of Fermi-liquid theory in a copper-oxide superconductor. Nature, 2001, 414, P. 711–715.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Proust C. et al. Heat transport in Bi2+xSr2 xCuO6+ : Departure from the Wiedemann-Franz law in the vicinity of the metal-insulator transition. Phys. Rev. B, 2005, 72, P. 214511.</mixed-citation><mixed-citation xml:lang="en">Proust C. et al. Heat transport in Bi2+xSr2 xCuO6+ : Departure from the Wiedemann-Franz law in the vicinity of the metal-insulator transition. Phys. Rev. B, 2005, 72, P. 214511.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Loram J.W. et al. Electronic specific heat of YBa2Cu3O6+x from 1.8 to 300 K. Phys. Rev. Lett., 1993, 71, P. 1740–1743.</mixed-citation><mixed-citation xml:lang="en">Loram J.W. et al. Electronic specific heat of YBa2Cu3O6+x from 1.8 to 300 K. Phys. Rev. Lett., 1993, 71, P. 1740–1743.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Loram J.W. et al. Evidence on the pseudogap and condensate from the electronic specific heat. J. Phys. Chem. Solids, 2001, 62, P. 59–64.</mixed-citation><mixed-citation xml:lang="en">Loram J.W. et al. Evidence on the pseudogap and condensate from the electronic specific heat. J. Phys. Chem. Solids, 2001, 62, P. 59–64.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Fujita K. et al. Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking. Science, 2014, 344, P. 612–616.</mixed-citation><mixed-citation xml:lang="en">Fujita K. et al. Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking. Science, 2014, 344, P. 612–616.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Vojta M. Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity. Adv. Phys., 2009, 58, P. 699–820.</mixed-citation><mixed-citation xml:lang="en">Vojta M. Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity. Adv. Phys., 2009, 58, P. 699–820.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Vojta M. Stripes and electronic quasiparticles in the pseudogap state of cuprate superconductors. Physica C, 2012, 481, P. 178.</mixed-citation><mixed-citation xml:lang="en">Vojta M. Stripes and electronic quasiparticles in the pseudogap state of cuprate superconductors. Physica C, 2012, 481, P. 178.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Sebastian S.E., Harrison N., Lonzarich G.G. Towards resolution of the Fermi surface in underdoped high-Tc superconductors. Rep. Prog. Phys., 2012, 75, P. 102501.</mixed-citation><mixed-citation xml:lang="en">Sebastian S.E., Harrison N., Lonzarich G.G. Towards resolution of the Fermi surface in underdoped high-Tc superconductors. Rep. Prog. Phys., 2012, 75, P. 102501.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev B., Park C.-H., Musakhanov M.M. Anyon bosonization of 2D fermions and single boson phase diagram implied from experiment on visualizing pair formation in superconductor Bi2Sr2CaCu2O8+ . Physica C, 2011, 471, P. 486–491.</mixed-citation><mixed-citation xml:lang="en">Abdullaev B., Park C.-H., Musakhanov M.M. Anyon bosonization of 2D fermions and single boson phase diagram implied from experiment on visualizing pair formation in superconductor Bi2Sr2CaCu2O8+ . Physica C, 2011, 471, P. 486–491.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Gomes K.K. et al. Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+ . Nature, 2007, 447, P. 569–572.</mixed-citation><mixed-citation xml:lang="en">Gomes K.K. et al. Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+ . Nature, 2007, 447, P. 569–572.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Pan S.H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x. Nature, 2001, 413, P. 282–285.</mixed-citation><mixed-citation xml:lang="en">Pan S.H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x. Nature, 2001, 413, P. 282–285.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev B., Abdullaev D.B. Park C.-H., Musakhanov M.M. Intra pseudogap- and superconductivy-pair spin and charge fluctuations and underdome metal-insulator (fermion-boson)-crossover phenomena as keystones of cuprate physics. Nanosystems: Phys. Chem. Math., 2015, 6, P. 803–824.</mixed-citation><mixed-citation xml:lang="en">Abdullaev B., Abdullaev D.B. Park C.-H., Musakhanov M.M. Intra pseudogap- and superconductivy-pair spin and charge fluctuations and underdome metal-insulator (fermion-boson)-crossover phenomena as keystones of cuprate physics. Nanosystems: Phys. Chem. Math., 2015, 6, P. 803–824.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev B., Roessler U., Musakhanov M. An analytic approach to the ground state energy of charged anyon gases. Phys. Rev. B, 2007, 76, P. 075403(1-7).</mixed-citation><mixed-citation xml:lang="en">Abdullaev B., Roessler U., Musakhanov M. An analytic approach to the ground state energy of charged anyon gases. Phys. Rev. B, 2007, 76, P. 075403(1-7).</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">March N.M., Young W.H., Sampanthar S. The Many Body Problems in Quantum Mechanics. Cambridge, University Press, 1967.</mixed-citation><mixed-citation xml:lang="en">March N.M., Young W.H., Sampanthar S. The Many Body Problems in Quantum Mechanics. Cambridge, University Press, 1967.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Nakamae S. et al. Electronic ground state of heavily overdoped nonsuperconducting La2 xSrxCuO4. Phys. Rev. B, 2003, 68, P. 100502(R).</mixed-citation><mixed-citation xml:lang="en">Nakamae S. et al. Electronic ground state of heavily overdoped nonsuperconducting La2 xSrxCuO4. Phys. Rev. B, 2003, 68, P. 100502(R).</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Smith M.F., et al. Origin of anomalous low-temperature downturns in the thermal conductivity of cuprates. Phys. Rev. B, 2005, 71, P. 014506.</mixed-citation><mixed-citation xml:lang="en">Smith M.F., et al. Origin of anomalous low-temperature downturns in the thermal conductivity of cuprates. Phys. Rev. B, 2005, 71, P. 014506.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Luo J.L., et al. The magnetic field dependence of the electronic specific heat of Y08Ca02Ba2Cu3O6+x. ArXiv: cond-mat/0112065, 2001, 7 p.</mixed-citation><mixed-citation xml:lang="en">Luo J.L., et al. The magnetic field dependence of the electronic specific heat of Y08Ca02Ba2Cu3O6+x. ArXiv: cond-mat/0112065, 2001, 7 p.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Vedeneev S.I., Maude D.K. Metal-to-insulator crossover and pseudogap in single-layer Bi2+xSr2 xCu1+yO6+ single crystals in high magnetic fields. Phys. Rev. B, 2004, 70, P. 184524.</mixed-citation><mixed-citation xml:lang="en">Vedeneev S.I., Maude D.K. Metal-to-insulator crossover and pseudogap in single-layer Bi2+xSr2 xCu1+yO6+ single crystals in high magnetic fields. Phys. Rev. B, 2004, 70, P. 184524.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Landau L.D., Lifshitz E.M. Statistical Physics, Part 1. Oxford, Pergamon Press, 1980. [29] Lifshitz E.M., Pitaevskii L.P. Statistical Physics, Part 2. Oxford, Pergamon Press, 1980.</mixed-citation><mixed-citation xml:lang="en">Landau L.D., Lifshitz E.M. Statistical Physics, Part 1. Oxford, Pergamon Press, 1980. [29] Lifshitz E.M., Pitaevskii L.P. Statistical Physics, Part 2. Oxford, Pergamon Press, 1980.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev B. Implicit Anyon or Single Particle Boson Mechanism of HTCS and Pseudogap Regime. In Trends in Boson Research, edit. by A.V. Ling. N.Y.: Nova Science Publisher Inc., 2006, P. 139–161.</mixed-citation><mixed-citation xml:lang="en">Abdullaev B. Implicit Anyon or Single Particle Boson Mechanism of HTCS and Pseudogap Regime. In Trends in Boson Research, edit. by A.V. Ling. N.Y.: Nova Science Publisher Inc., 2006, P. 139–161.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullaev B., Park C.-H. Bosonization of 2D Fermions due to Spin and Statistical Magnetic Field Coupling and Possible Nature of Superconductivity and Pseudogap Phases Below Eg. J. Korean Phys. Soc., 2006, 49, P. S642–S646.</mixed-citation><mixed-citation xml:lang="en">Abdullaev B., Park C.-H. Bosonization of 2D Fermions due to Spin and Statistical Magnetic Field Coupling and Possible Nature of Superconductivity and Pseudogap Phases Below Eg. J. Korean Phys. Soc., 2006, 49, P. S642–S646.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Ichimaru S. Plasma Physics: An Introduction to Statistical Physics of Charged Particles. New York, Benjamin/Cummings, 1986, Chap. 7.</mixed-citation><mixed-citation xml:lang="en">Ichimaru S. Plasma Physics: An Introduction to Statistical Physics of Charged Particles. New York, Benjamin/Cummings, 1986, Chap. 7.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Tallon J.L., Loram J.W. The doping dependence of T– what is the real high-Tc phase diagram? Physica C, 2001, 349, P. 53.</mixed-citation><mixed-citation xml:lang="en">Tallon J.L., Loram J.W. The doping dependence of T– what is the real high-Tc phase diagram? Physica C, 2001, 349, P. 53.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Abrikosov A.A. Fundamentals of the Theory of Metals. Amsterdam, Elsevier Science, 1988.</mixed-citation><mixed-citation xml:lang="en">Abrikosov A.A. Fundamentals of the Theory of Metals. Amsterdam, Elsevier Science, 1988.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Daou R., et al. Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor. Nature Phys., 2009, 5, P. 31.</mixed-citation><mixed-citation xml:lang="en">Daou R., et al. Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor. Nature Phys., 2009, 5, P. 31.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Kim D.H., Lee P.A., Wen X.-G. Massless Dirac Fermions, Gauge Fields, and Underdoped Cuprates. Phys. Rev. Lett., 1997, 79, P. 2109.</mixed-citation><mixed-citation xml:lang="en">Kim D.H., Lee P.A., Wen X.-G. Massless Dirac Fermions, Gauge Fields, and Underdoped Cuprates. Phys. Rev. Lett., 1997, 79, P. 2109.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Varma C.M. Theory of the pseudogap state of the cuprates. Phys. Rev. B, 2006, 73, P. 155113</mixed-citation><mixed-citation xml:lang="en">Varma C.M. Theory of the pseudogap state of the cuprates. Phys. Rev. B, 2006, 73, P. 155113</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
