Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of periodic systems

Based on infinite one-dimensional periodic chain models (Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki) of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, albeit preserved in the molecular systems with only bound states, no longer generally held for the periodic systems. Hence it breaks the Kleinman symmetry in the off-resonant regions. Our theory qualitatively explain the widely observed deviations of Kleinman symmetry in experiments. New nonlinear optical experiments are proposed to verify the overall symmetry break. PACS: 78.66.Qn, 42.65.An, 72.20.Dp, 78.20.Bh Typeset using REVTEX Author to whom correspondence should be addressed. Email: [email protected] 1 The nth-order optical susceptibility is generally defined as a rank n tensor χ (n) μα1α2···αn(−ωσ;ω1, ω2, · · · , ωn), where ωσ ≡ n