Possibility of a strongly correlated Dirac metal in kagome latticeHiroi Lab. M1 Ryutaro Okuma1010/2014OutlineDirac fermionInteresting phenomena caused by massless fermion Dirac cone in strongly correlated systemA theoretical candidate for a Dirac metal: Ga-Herbertsmithite Structural stabilities, ferromagnetism, and f-wave superconductivityPromising compounds to be kagome Dirac metalDirac equationClassical equation describes relativistic motion of a free fermion If m = 0 dispersion becomes linear like photon

m=0m>0Dirac fermion in solid state physics: graphenedispersion relation in tight binding model

At Femi level energy bands crosses near K and K point(Dirac cone protected by chiral symmetry )Zero gap semiconductor ( D(EF)=0 )

Half integer quantum Hall effect and SdH oscillation at room temperatureIn 2D systems, Hall conductivity xy takes on the quantized values Ne2/h at LOW T & in STRONG BThe Hall conductivity of graphene: xy = (N+1/2)e2/h

B = 14T, T = 4KNature 438, 197-200(2005)Shubnikov de Haas Oscillation is observed at room temperature

related to Berry PhaseApplication: Transistor and Transparent Electrode

Solid State Commun. 146, 351355 (2008)

ACS Nano, 4 (1), pp 4348(2010)Dirac fermion: m = 0 High mobility ~200,000cm2/V-1s-1(Si~1400)Strong and FlexibleTransparent ElectrodeLED, solar battery, touch panel

Graphene families: silicene, germanene, staneneHoneycomb lattice consisting of only Si, and Ge was synthesized recentlyLarger LS coupling leads to topological insulatorStanene(Sn graphene) would be zero on the edge.

STM image of silicene on Ag(111) layer PRL 108, 155501 (2012)77 structure of germanene New J. Phys. 16 095002 (2014)PRL 111, 136804 (2013)Dirac cone in strongly correlated system: Ba(FeAs)2Antiferromagnetic metal (Tw = 132K)By e- doping superconducting (max Tc = 56K)Dirac point due to the node of SDW gapBa(FeAs)2I4/mmm

PRL 106, 217004 (2011)

Magnetoresistance linear to B(usually B2)Dirac cone+strongly correlated e-Novel Physics?A necessary condition for existence of Dirac pointGeneralized von Neumann Wigner Theoremnd=nu-m2+1-nc nd:dimension of the Dirac point (usually 0 point)nu: unknown parameters of Hamiltonian m: degeneracy at Dirac point (usually 2)nc: number of constraints by symmetry operationPhys. Rev. B 83, 245125 (2011).If theres a band crossing and nc=m2-1thats symmetry protected Dirac cone.

Flat band and symmetry protected Dirac point on a kagome lattice

Flat band from n=0 to n=1/3Due to the properties of line graphSymmetry protected Dirac cone zero gap semiconductorEnergy band of nearest neighbor Hubbard model on kagome lattice

Organic Kagome Dirac Metal: (EDT-TTF-CONH2)6[Re6Se8(CN)6]dimer TTF molecules form S=1/2 kagome latticeelectron per site: 4/6*2=4/3 Dirac metalMI transition at 150~200KR-3 P1

[Re6Se8(CN)6]4-EDT-TTF-CONH2SG:R-3

J. Am. Chem. Soc., 127 (33), 1178511797(2005)A structurally perfect kagome mineral Herbertsmithite (ZnCu3(OH)6Cl2)S=1/2 antiferromagnetic Mott insulatorCu2+ forms uniform kagome networkA candidate for a spin liquidSynthesized by hydrothermal method

ZnCu3(OH)6Cl2SG: R-3m

Photo Copyright Steve RustGa substituted Herbertsmithite: GaCu3(OH)6Cl2A theoretically proposed compound isostructural to Herbertsmithite (Nature Comm. 5 54261 (2014))Valence of Cu is +1.67 (n=4/3)Dirac cone shifts between K and X (symmetry protected)Ion radius for Zn2+(4-fold): 0.47; Ga3+: 0.60

BZ and Femi surface of Ga-HebertsmithiteStructural stability of Ga-HerbertsmithiteStability was checked by Extended Hubbard modelU = 5-7eV, t = 0.3 eV, V = 0.11 eVKagome structure is stable against weak distortion

Strucual data for Ga-HebertsmithiteelementxyzGa(Zn)000Cu1/31/61/6O0.1244(0.1265)0.24882(0.2529)0.09852(0.1050)H0.198(0.192)0.397(0.384)0.066(0.084)Cl000.31342(0.30521)R-3m: ==90, =120a=6.9779(6.8342), c=13.4589(14.0320)Weak ferromagnetismNagaokas theorem asserts that t/U