Japanese　

Homepage of Hiroshi Kontani

Name：　Hiroshi Kontani

Main interest：　Strongly Correlated Electron Systems (cuprate superconductors, Fe-based superconductors, heavy fermions systems)

Address：　Sc-Lab, Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, 464-8602 Nagoya, Japan

Office：　Room 610, Science Hall　
Email: kon(at)slab.phys.nagoya-u.ac.jp

Lectures in 2020

　　　Quantum Mechanics IV　　（4th grade, Spring）

　　　Statistical Mechanics II　（3rd grade, Autumn）

　　　Exercise in Physics II−１　 （2nd grade, Autumn）

Curriculum Vitae
Publication List
Last Update： March 25, 2020

My Reserch

Strongly correlated electron systems exhibit novel physical phenomena such as high-temperature superconductivity and exotic quantum phase transitions, but conventional theoretical analyses have been prevented by strong Coulomb interaction. To elucidated novel phenomena in many strongly correlated metals, we have developed new theoretical methods such as large-scale Feynman diagram calculations and the renormalization group (RG) theory originally developed by K. G. Wilson. More detailed explanations are listed below.

　●Fe-based Superconductors： Mechanisms of Superconductivity and Electronic Nematic State
Fe-based superconductors, which was discovered in 2008, exhibit high-Tc next to the cuprate superconductors. After thediscovery, lots of researched have been performed for these hogh-Tc superconductors all over the world. To solve important unsolved issues, we have focused on the many-body effect beyond the mean-field-type approximations, called the vertex corrections.

In Fe-based superconductors, the conduction electrons acquire d-orbital degrees of freedom, and interesting “orbital physics” emergenear the superconducting phase. We discovered that the electronic nematic transition in Fe-based superconductors, which is the spontaneous rotational symmetry breaking of correlated electrons, originates from the orbital order driven by vertex corrections [1,2]. The strong orbital fluctuations mediate the s-wave SC gap without sign reversal, called the s++ wave state [3,4]. The s++ wave state is supported by the tiny impurity effect on Tc [5] and the resonance-like hump structure in neutron inelastic scattering measurements [6].

Recently, novel electronicproperties in FeSe attract increasing attention. We revealed that the “nonmagnetic nematic state” in FeSe is naturally explained as the orbital order due to the vertex correction [7,8]. The increment of Tc under the pressure (Tc~40K) and heavily electron-doping (~65K) is understood as the orbital fluctuation pairing mechanism.

[1] S. Onari and H. Kontani, Phys. Rev. Lett. 109, 137001 (2012).
[2] H. Kontani and Y. Yamakawa, Phys. Rev. Lett. 113, 047001 (2014).
[3] H. Kontani and S. Onari, Phys. Rev. Lett. 104, 157001 (2010).
[4] S. Onari, Y. Yamakawa, and H. Kontani, Phys. Rev. Lett. 112, 187001 (2014).
[5] S. Onari and H. Kontani, Phys. Rev. Lett. 103, 177001 (2009).
[6] S. Onari, H. Kontani, and M Sato, Phys. Rev. B 81, 060504(R) (2010).
[7] Y. Yamakawa, S. Onari, and H. Kontani, Phys. Rev. X 6, 021032 (2016).
[8] S. Onari, Y. Yamakawa, and H. Kontani, Phys. Rev. Lett. 116, 227001 (2016).
[9] Y. Yamakawa and H. Kontani, Phys. Rev. B 96, 144509 (2017).
[10] Y. Yamakawa and H. Kontani, Phys. Rev. B 96, 045130 (2017)


　●Quantum Liquid Crystal States in Cuprate Superconductors
Cuprate high-Tc superconductors have been studied actively for over 30 years, after the discovery in 1986. In the last 10 years, both theoretical and experimental studies have been developed and attracted renewed interest. Especially, novel self-organization phenomena of correlated electrons, called the quantum liquid crystal states, have been studied intensively.

We attack this problem by focusing on the quantum interference between spin and change fluctuations, described by the Aslamazov-Larkin vertex corrections. Based on the functional RG theory and the density-wave equation theory, we reveal that the strong bond-order is driven by strong spin fluctuations in the single-orbital Hubbard models [1-4]. (The bond order is the spontaneous modulation of hopping integrals due to electron correlations.) Experimentally observed axial charge-density-wave with wavevector q=(p,0) at T_CDW (~200K) and the electronic nametic transition at the pseudogap temperature T^* (~300K) are naturally explained as the double stage bond-order transition scenario proposed by the present theory [1-4]. In addition, resent theoretical study revealed that some exotic loop current orders can be realized by the Aslamazov-Larkin vertex corrections. The fluctuations of these rich quantum liquid crystal orders will mediate significant pairing interaction for high-Tc state at optimally doping, in collaboration with the magnetic fluctuations [1-4].

[1] Y. Yamakawa and H. Kontani, Phys. Rev. Lett. 114, 257001 (2015).
[2] M. Tsuchiizu, Y. Yamakawa, and H. Kontani, Phys. Rev. B 93, 155148 (2016).
[3] K. Kawaguchi, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, J. Phys. Soc. Jpn. 86, 063707 (2017).
[4] M. Tsuchiizu, K. Kawaguchi, Y. Yamakawa, and H. Kontani, Phys. Rev. B 97, 165131 (2018).


　●Anomalous Hall Effect, Spin Hall Effect
We also studied novel quantum transport phenomena, such as spin Hall effect and anomalous Hall effect, by focusing on the impact of orbital degrees of freedom. We revealed that the giant spin Hall effects in 4d and 5d transition metals originates from the orbital Berry phase due to the orbital degrees of freedom and the spin-orbit interaction [1-4]. The theoretical prediction has been confirmed experimentally by Otani group (ISSP). The present mechanism also explains the large topological anomalous Hall effect in pyrochlore compounds Nd₂Mo2O₇ (tilting angle θ~2°) and coplanar antiferromagnetic metal Mn₃Si (θ=90°) [5,6].

[1] H. Kontani et al., Phys. Rev. Lett. 100, 096601 (2008).
[2] H. Kontani et al., Phys. Rev. Lett. 102, 016601 (2009).
[3] H. Kontani, J. Goryo, and D. S. Hirashima, Phys. Rev. Lett. 102, 086602 (2009).
[4] M. Morita et al., Phys. Rev. B 83, 174405 (2011).
[5] T Tomizawa, and H. Kontani, Phys. Rev. B 80, 100401(R) (2009).
[6] T. Tomizawa and H. Kontani, Phys. Rev. B 82, 104412 (2010).

　●Transport Phenomena in Strongly Correlated Electrons
The superconducting transition temperature Tc in cuprate superconductors reaches ~160K. To understand the pairing mechanism, remarkable deviations from the Fermi liquid properties in conventional metals, called the non-Fermi liquid like states, have attracted great attention. The reason is that the high-Tc state originates from the non-Fermi liquid like normal states through the second-order phase transition.

For example, the Hall coefficient R_H exhibits the Curie-Weiss temperature dependence for wide temperature and doping range, in highly contrast to the T-independent R_H in conventional metals. Especially, R_H in electron-doped cuprates exhibits negative values, irrespective of the fact that the topology of the Fermi surface is hole-like. Such strong deviation from conventional Fermi-liquid behavior in R_H has been discussed very actively, as a possible strong evidence for the violation of Fermi liquid ground state.

To attach this problem, we developed the transport theory in strongly correlated metals, by focusing on the impact of the current vertex correction [1-4]. We revealed that the current vertex corrections give remarkable anomalous behaviors not only in R_H, but also in magnetoresistance, thermoelectric power, and Nernst coefficient. Thus, anomalous transport phenomena in cuprates are satisfactorily understood as universal properties of the nearly antiferromagnetic metals in a unified way. In fact, theories in Refs. [1-4] are applicable for other nearly antiferromagnetic metals, such as heavy fermion CeMIn₅ (M=Co, Rh, Ir) and organic superconductors κ-(BEDT-TTF). Recently, anomalous transport phenomena in Fe-based superconductors are satisfactorily explained [5].

[1] H. Kontani, K. Kanki, and K. Ueda, Phys. Rev. B 59, 14723 (1999).
[2] H. Kontani, Phys. Rev. Lett 89, 237003 (2002).
[3] H. Kontani, Rep. Prog. Phys. 71, 026501 (2008).
[4] H. Kontani, "Transport Phenomena in Strongly Correlated Fermi Liquids" (Springer Berlin Heidelberg, Berlin, Heidelberg, 2013).
[5] S. Onari and H. Kontani, Phys. Rev. B 96, 094527 (2017).

　　●Universal Relation in Heavy Fermion Systems:
Strongly correlated metals composed of 4f and 5f elements are called the heavy fermions systems, because the effective electron mass is drastically enlarged (m^*/m_e=100~1000) due to the strong Coulomb interaction of f-electrons. In these systems, the specific heat and the resistivity follows the Fermi liquid relations C = γT and ρ = AT². In addition, in may Ce-based compounds, empirical universal relation A/γ² ~ a₀ = 1×10^-5μΩcm(K mol/mJ)² holds, known as Kadowaki-Woods relation. However, strong violation of this “universal relation” has been reported recently in various heavy fermions, especially Yb-based compounds. This finding casted a serious and fundamental question on the ground state of heavy fermion systems.

In many heavy fermion systems, the Kondo temperature T_K can be larger than the crystalline electric field (CEF). In this case, the degeneracy N becomes as large as 6 (J=5/2 in Ce) and 8 (J=7/2 in Yb). Based on the microscopic Fermi liquid theory, we derived the “ground Kadowaki-Woods relation A/γ² ~ 2a₀/N(N+1)” [1,2]. Original Kadowaki-Woods relation is satisdied when N=2 (Kramers douoblet case). Figure shows the KW ratio of various heavy-fermion compounds with N=2~8. Since various compounds with N>2 has been discovered now, the ground Kadowaki-Woods relation is the universal relation of heavy fermion systems.

[1] H. Kontani, J. Phys. Soc. Jpn. 73, 515 (2004). (Editor’s choice)
[2] N. Tsujii, H. Kontani and K. Yoshimura, Phys. Rev. Lett. 94, 057201 (2005).　

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