Chiral melting of the Si(113) (3 × 1) reconstruction

Abstract

We report the results of synchrotron X-ray scattering studies of the disordering of the Si(113) (3 × 1) reconstruction. A continuous commensurate—solid to incommensurate—fluid transformation at T c = 950 ± 40 K is observed. At the transformation, the reconstructed layer becomes uniaxially incommensurate along the cubic (11¯0) ( x-direction). It remains commensurate along the (332¯) ( y-direction). Critical scattering shows power-law behavior over nearly two decades of reduced temperature with exponents β¯ for the incommensurability ( ɛ), t x = 0.65 ± 0.07 for the inverse correlation length in the incommensurate direction ( ϰ x ), v y = 1.06 ± 0.07 for the inverse correlation length in the commensurate direction ( ϰ y ), and γ = 1.56 ± 0.13 for the susceptibility ( χ). Below T c the variation of the square of the order parameter, proportional to the peak intensity at the commensurate position ( I 0), varies with an exponent 2 β = 0.22 ± 0.04. It is noteworthy that the correlation lengths in the disordered phase scale anisotropically, i.e. v x ≠ v y , and that the collected exponents do not conform to those of any previously measured universality class. Two universal constants of the transformation have also been measured. The ratio of the incommensurability and the inverse correlation length along the incommensurate direction in the disordered phase is found to be independent of temperature, i.e. β¯, consistent with predictions for a new two-dimensional chiral melting universality class, and to have the value w 0 = 1.6 ± 0.2. Also, the hyperscaling ratio R s = χϰ xϰ y / I 0 V r, where V r is the two-dimensional resolution volume, is independent of the reduced temperature, consistent with the derived hyperscaling relationship v x + v y = γ + 2 β. According to the hypothesis of two-scale-factor universality, R s is a universal constant, which we find takes the value R s = 0.07 ± 0.03. These results are discussed in the context of proposed phase diagrams of two-dimensional threefold-degenerate uniaxial overlayers where the chirality, or difference in free energy of light and heavy domain walls, is varied. A comparison is made to recent LEED measurements of the (3 × 1)-to-disordered transformations of Si and Ge.