: Int. J. Modern Phys. B 32, 1840031 (2018) [요약]
금속의 자유전자들 사이에서 쿨롱 반발에너지가 매우 큰 금속을 강상관 금속이라고 하고 어떤 임계값을 넘으면 면 부도체 즉 절연체가 된다. 이 절연체를 모트 절연체라고 하며 이 현상을 설명하는 것이 응집물질 물리학의 오랜 물리문제이다. 그런데 30 년이상 물리문제인 고온 초전도 현상을 보이는 물질의 모체 물질은 모트 절연체로 알려져 왔고, 그 모트 절연체에 도핑, 압력, 온도를 가하면 모트 절연체에서 금속으로 전이(Metal-Insulator Transition: MIT)가 일어난다. 그 금속이 저온에서 고온 초전 도 현상을 보인다. 이 메카니즘을 설명하는 것이 30년 이상 미해결 문제이다.
작성자(김현탁)는 이 문제에 대해서 모트 MIT를 BR(Brinkman-Rice picture)픽쳐를 확장하여 Impurity-induced (Hole-driven) MIT를 발견하고 그것을 기반으로 30년 이상의 물리문제를 설명한다. 그것에 대한 Impurity-driven MIT를 간략하게 설명한다.
<그림 1> Drawing of Eq. (1) in the extended BR picture [1,2].
impurity doped insulator. The metal-insulator transition (MIT) is shown at red dot line between doped insulator and metal specifying excitation. nc º NcµDris the doping concentration for the MIT. The quantum critical point is given at the transition point.(c) The antiferromagnetic Mott insulator with the Mott gap of Ucis assumed at U/Uc=1 in the BR picture (Fig. 2c), as denoted by black dot in Fig. 2b. Fig. 2dshows a band structure of an impurity-doped Mott insulator (red dot in Fig.2b) with both the main Hubbard bands for direct transition and an impurity (or extrinsic semiconductor) band for indirect transition. UB – upper Hubbard band, LB – lower Hubbard band[40], EF–Fermilevel,Δdirect– energy gap for direct transition, Δact– activation energy for indirect transition, Ω – thermal phonon. Impurity concentration Ntot=Ncis proportional to Dr=Ntot/ntotintheEBRpicture,wherentotis the carrier density in the main Hubbard band. The IMT (or MIT) is indirect between Fig. 2dand Fig. 2e, which names the indirect Mott MIT [5]. For a strongly correlated insulator of VO2, the IMT criterion, Ntot=Nc,is 0.018% [4].
[1] H T Kim, Physica C 341-348 (2000) 259.
[2] H. T. Kim, http://arxiv.org/abs/cond-mat/0110112.
[3] H. T. Kim, B. G. Chae, D. H. Youn, S. L. Maeng, G. Kim, K. Y. Kang, Y. S. Lim, New J. Phys. 6 (2004) 52.
[4 M. Kang and S. W. Kim, J W Ryu, J. Appl. Phys. 118 (2015) 035105.
[5] H. T. Kim, M. Kim, A. Sohn, T. Slusar, G. Seo, H. Cheong, D W Kim, J. Phys.: Condens. Matter 28 (2016) 085602 (2016).
Impurity-driven Insulator-to-Metal Transition in VO2
How is a relation between impurities and the insulator-to-metal transition (IMT) explained in strongly correlated systems ? A representative strongly correlated Mott insulator VO2(3d1) has the direct gap (DdirectµVdirect) of 0.6 eV and the indirect gap (activation energy) of Dact/2µVindirect»0.15 eV coming from impurity indirect band (see Fig. 4c in [1]). At Tc, Ddirect=Dact=0 is satisfied and the IMT occurs. The metal carriers near core region can be trapped when the critical onsite Coulomb repulsion Ucbetween carriers exists; the metal become a Mott insulator. Then, a potential energy for the Mott insulator can be defined as
Vg=(Vdirect+Uc)+Vindirect,= -(2/3)EF(1 + e(Ntem(T)/ntot)) +Uc,
= -(2/3)EF(1 + e(Ntot/ntot) (1-exp(-Dact/kBT))) +Uc, --- (1)
where Vdirect= -(2/3)EFcomes from the screened Coulomb pseudopotential at K=0. Dr=Ntot/ntot»0.018% is defined as the critical impurity doping quantity [2], where ntotis the bound charge density in the direct d-band and Ntotis the bound charge density in the impurity indirect band (see Fig. 4c in [1]). Vindirect=-(2/3)EFe(Ntem(T)/ntot)is calculated by the Tayler-series expansion of the chemical potential μ when impurity carriers in metal exist, where Ntem(T)=Ntot(1-exp(-Dact/kBT)) is defined.
When Vg=0 at Eq. (1), Uc=-(Vdirect+Vindirect)is given.
Then, Uc= (2/3)EF(1 + e(Ntot/ntot) (1-exp(-Dact/kBT))),
= (2/3)C(ntot+Ntot)2/3(1 + e(Ntot/ntot) (1-exp(-Dact/kBT))) is expressed in terms of Ntot, where EF=C(ntot+Ntot)2/3isdefinedandCis a proportional constant.
At the IMT, since Dact=0is givenand Ntotis excited,
Uc=(2/3)C(ntot+Ntot)2/3is reduced as U=(2/3)C(ntot)2/3<Uc.
Then, the correlated Mott insulator becomes metal by the breakdown of Uc-->Uinduced by excitation of Ntotfrom bound state to conduction band. The IMT can be switched by the doping (excitation; Dact»0, Ntotgoes to conduction band, so Ntot=0) and the de-doping (de-excitation;Dact»0.15, Ntotis bound from conduction band to indirect band) of Dr=Ntot/ntotto the bound state, by applying external parameters such as heat, pressure, doping etc. The Mott insulator with the metallic electronic structure is formed by bounding the carriers of ntotin the metal state trapped by the impurity carrier density Ntot; this is an impurity-driven IMT and can be applied to all strongly correlated systems.
[1] Hyun-Tak Kim, Minjung Kim, Ahrum Sohn, Tetiana Slusar, Giwan Seo, Hyeonsik Cheongand Dong-Wook Kim, J.
Phys.:Condens. Matter 28 (2016) 085602.
[2] Hyun-Tak Kim, Byung-Gyu Chae, Doo-Hyeb Youn, Sung-Lyul Maeng, Gyungock Kim, Kwang-Yong Kang, Yong-Sik Lim,New J. Phys. 6 (2004) 52.
Diagram explaining the high-Tc mechanism for the formation of the node gap
The dx2-y2 electronic structure can be formed when the metal-insulator transition(MIT) occurs at the node in an isotropic pseudogap structure (bluedashedring). The small pink circles in the large pink circle are regarded as the nodal Fermi points made by the d-wave MIT near doping xc. The pink circle is the Fermi surface formed by increased doping. The red-dashed arrow indicates that bound charges in the pseudogap potential at the node are excited to the Fermi energy, due to the d-wave MIT (conceptual indication). The small green circles in the large green circle are superconducting intrinsic gaps at the node when the nodal Fermi points become a superconductor (pink circle -> green circle) [1,2]. The green ring is the isotropic superconducting s-wave-like gap resulting from the Fermi arc at optimal doping. If the superconducting energy gap has dx2-y2-wave-pairing symmetry, the d-wave-MIT should occur at the anti-node. However, this research does not support the d-wave pairing symmetry. The constant maximum carrier density at the nodal Fermi point (or velocity) was first disclosed [1].
<그림 2> A mechanism of the node gap formation
metal-insulator transition from the pseudogap insulator to metal at node.) [2] H. T. Kim, B. J. Kim, K. Y. Kang, Physica C460-462 (2007) 943.