Application of interface to Wannier90 : anomalous Nernst effect Fumiyuki Ishii Kanazawa Univ. Collaborator: Y. P. Mizuta, H.

Transcription

1 Application of interface to Wannier90 : anomalous Nernst effect Fumiyuki Ishii Kanazawa Univ. Collaborator: Y. P. Mizuta, H. Sawahata, 스키루미온

2 Outline 1. Interface to Wannier90 2. Anomalous Nernst effect

3 Wannier90

4 Capabilities of Wannier90 Boltzmann transport (Seebeck etc.) Quantum transport Anomalous Hall effect Optical conductivity Orbital magnetization

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6 Seebeck coefficient of silicon An approach with OpenMX + Wannier Wannier bands constructed from OpenMX solutions via Wannier90 Energy [ev] inside the gap -15 W L Γ X U/K Γ Seebeck coefficient at T=300K estimated from the 8 Wannier bands Seebeck coeff. [µv/k] S>0 : hole conduction S<0 : electron conduction Chemical potential [ev]

7 Optical conductivity of SrVO Energy(eV) Optical Conductivity (S/cm) Photon energy (ev) Γ M R Γ X M Experiment: Makino et al., PRB (1998)

8 Thermoelectric coefficients KANAZAWA UNIVERSITY Seebeck coeff. Nernst coeff. σ xx = e 2 τ ( dk vx n (k) 2 f ), ε n nk σ xy = e2 dk Ω n z (k)f(ε nk )= σ yx, h n α ij = 1 ( ε µ dεσ ij (ε) T =0 f ) e T ε for i = x or y, j = x or y, Y. P. Mizuta, & F. I, JPS Conf. Proc. 3, (2014), ibid. 5, (2015). Sci. Rep. 6, 2876(2016) S = S 0 + H N H N = N 0 H S H pure (conventional) Seebeck coeff. Hall angle pure Nernst coeff. S 0 xx H xx xy xx N 0 xy xx T + S N T T T generated E-field T linear response conductivities in j = E + ( rt )

9 Mechanism for Large Seebeck Coefficient KANAZAWA UNIVERSITY S = 0 k B e τ constant approximaion Asymmetry in σ xx (ε) : D(ε), v x (ε), is origin of large S R d" " µ xx(") =e 2 D(")v 2 x(") k B T R d" xx (") df (") d" xx(") df (") d" Narrow gap semiconductor, Semimetals

10 Mechanism for Large Nernst Coefficient KANAZAWA UNIVERSITY Asymmetry in σ xy (ε) : Ω(ε), D(ε), is origin of large N 0 Candidate Material?

11 Anomalous Nernst Effect (ANE) in Skyrmion Crystal T V x V y non-trivial spin texture (SkX etc.) emergent magnetic field For any insulator or isolated band, A xy = C e2 h C : Chern number Berry curvature in k-space: Ω z (k) anomalous Hall conductivity (AHC) anomalous Nernst conductivity (ANC) A xy = A xy = 1 e e2 X ~ Z n d"[ Z dk [ n (k)] z f(" nk ) A " xy(")] T =0

12 - s-orbital SkX model (Hydrogen Atom with OpenMX) Y. P. Mizuta and F. Ishii, Scientific Reports 6, (2016) ~ 2nm Large ANE -1.6 T=300K Chemical potential (ev) 0.0

13 Large anomalous Nernst effect in a Skyrmion crystal Y. P. Mizuta and F. Ishii, Scientific Reports 6, (2016) Figure 2. (a) Band structure and Fermi energy dependence of (b) longitudinal and (c) anomalous Hall conductivity of 6 6 SkX. The blue dashed line indicates the µ 0 mentioned in the main text.

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15 Variation with size n=6, 8, 10, 12 KANAZAWA UNIVERSITY Variation of the maximum N in the space of µ as the skyrmion size (n 2 ) grows. Larger SkX gives stronger TE voltage