Phase Transitions in Two-Dimensional Incommensurate Systems

New Calculations of ICDW Eigenmode Frequencies of 2H-TaSe2

“…Figs. 2 to 4 give the pictures when we consider the caseã 06 1 and temperatures T of 112.7, 117.9 and 121.5 K. We have used the same values introduced by other authors [10,11] for the phenomenological parameters, that is, we have takenã 03 In this numerical illustration we have used the Landau parameter [9]ã 020 2X35 Â 10 À4 (SI). We can observe that the acoustic phasons are similar to those obtained by other authors [6,10] indicating that the inclusion of the sixth-order term in the homogeneous part of the free-energy potential changes only the expressions of the optical amplitudons.…”

“…The real order parameter ar Re 3 j1 w j r is obtained from the electronic charge density rr, and w j r are complex order parameters linked to the three components of the triple charge-density-waves occurring in this material [9]. Normally, we define the following vectors: Q j j 1Y 2Y 3 are the three incommensurate vectors, which lie in directions 120 o apart; G j j 1Y F F F Y 6 are the six shortest reciprocal lattice vectors in the hexagonal symmetry; q j j 1Y 2Y 3 are the charge-density-wave vectors and q are the excitation wave vectors.…”

“…Normally, we define the following vectors: Q j j 1Y 2Y 3 are the three incommensurate vectors, which lie in directions 120 o apart; G j j 1Y F F F Y 6 are the six shortest reciprocal lattice vectors in the hexagonal symmetry; q j j 1Y 2Y 3 are the charge-density-wave vectors and q are the excitation wave vectors. We must remember from [6,9] that…”

“…In this work we report some calculations of amplitudons and phasons using an extended expression for the Landau-Lifshitz free energy density keeping terms up to sixth order [9]. In Section 2 we present calculations involving the ICDW phase, maintaining the same notation of Rocha et al [9].…”

“…In Section 2 we present calculations involving the ICDW phase, maintaining the same notation of Rocha et al [9]. In Section 3 we will perform calculations involving eigenmodes frequencies and providing new analytical results, for two distinct directions of the excitation wave vector (q), for the case of phasons and amplitudons, respectively.…”