79 PHONON SYMMETRIES AND PHASE TRANSITION IN TlSe AND TlInSe 2 NAZIM MAMEDOV 1* , GUSEYN ORUDZHEV 1 , KOJIRO MIMURA 2 , KAZUKI WAKITA 3 , YONG GU SHIM 4 , SUSAN SCHORR 5 , MUNIRA NIZAMETDINOVA 6 , VUSALA JAFAROVA 1 , SADIG HAMIDOV 1 AND FIRUDIN HASHIMZADE 1 1 Institute of Physics, Azerbaijan National Academy of Sciences, H. Javid ave. 33, Baku AZ-1143, Azerbaijan 2 Osaka Prefecture University, Department of Mathematical Sciences, Graduate School of Engineering, Sakai 599-8531, Japan 3 Chiba Institute of Technology, Department of Electrical, Electronics and Computer Engineering, Narashino, Chiba 275-0016, Japan 4 Osaka Prefecture University, Department of Physics and Electronics, Graduate School of Engineering, Sakai 599-8531, Japan 5 Free University, Department of GeoSciences, Malteser str., 74-100, D-12259 Berlin, Germany 6 University of Architecture and Construction, Department of Physics, A. Sultanova str. 5, Baku AZ1143, Azerbaijan The symmetry and atomic displacements corresponding to each phonon have been derived from the calculations of the phonon band structure of TlSe and TlInSe 2 chain compounds, which belong to the same family of materials. It is shown that at least acoustic branches along Δ-symmetry line are, for the most part, Einstein-like and their frequency is a weak function of the wave-vector. Anti-crossing between acoustic and low-frequency optic modes along Г- T direction of the Brillouin zone is found to be similar to that observed in thermoelectric Ba-Ni-Ge clathrates. The found symmetry-forbidden crossing on A-symmetry line between the two-fold degenerated low-frequency phonon modes with A 5 symmetry is vanishing in TlInSe 2 in the point with the wave vector of 0.67Å -1 along the Г-H-T direction of the Brillouin zone. On the other hand, a kink transforming into a gap-like structure with decreasing temperature has been observed at the same wave- vector for the uppermost valence band of TlInSe 2 , accessed by angle-resolved photo-emission spectroscopy at SPRING-8 facility (Japan). Both theoretical and experimental data obtained are evident of an incommensurate phase transition due to pseudo-Jahn-Teller effect in TlInSe 2 . 1. INTRODUCTION The ternary Tl-contained compounds, TlMeX 2 , crystallize either into a tetragonal chain structure (MeX = TlSe, InSe, InTe, GaTe) with space group D 4h 18 [1] or into a monoclinic layered structure (MeX= GaSe, GaS, InS) with space group C 2h 6 [2]. In either case the main building blocks are the MeX 4 tetrahedrons arranged into the chains or layers and the Tl- atoms positioned between these chains or layers. Both structures are low-dimensional and can transform into one another under the proper conditions such as, for example, 2Gpa and 873K for TlGaSe 2 [2]. The most interesting properties, which promise novel applications in MEMS (micro-electro- mechanical systems) and other devices are giant thermoelectric power [3] and giant thermoelastic effect [4], both are believed to be an attribute of a wide-range incommensurate (modulated) phase emerging in TlMeX 2 in the course of the subsequent phase transitions. Our attention has been attracted to TlInSe 2 whose superior thermoelectric and thermoelastic properties have already been verified in an experimental way [3,4]. Concerning the nature of phase transitions, which eventually lead to these properties, the situation is not completely clear. According to the angle-resolved electron photoemission spectroscopy (ARPES) of TlInSe 2 [5,6], in a certain arbitrary point on the A-line of the Brillouin zone (BZ) the uppermost valence band exhibits a kink structure that transforms into a gap-like structure upon farther temperature decrease. On the other hand, the available experimental data on heat capacity of TlInSe 2 [7-10] are rather ambiguous regarding the clear manifestations of phase transition. The heat effects (if any), accompanying the transition, are small and indicative of the dependence of the obtained results on the thermal history of the measured samples [8, 10]. In connection with this, we consider it important to mention that memory effects are inherent in incommensurate phases and that our very recent studies of the negative differential resistance, reported earlier for all chain TlMeX 2 [11-13], have disclosed its strong history dependence that was not mentioned before. According to the works [11-13], non-linear electric properties of all chain TlMeX 2 (including TlInSe 2 ) have thermal nature. In this work we report the symmetry and dispersion of the phonons, as well as atomic displacements leading to the low- frequency phonons near 0.67Å -1 wave vector along the BZ direction parallel to the chains of TlSe and TlInSe 2 . We also discuss the possible nature of incommensurate phase transition in TlInSe 2 . All details concerning the calculations of the phonon band structure of TlSe and TlInSe 2 can be found in our recent work [14]. 2. PHONON SPECTRA AND SYMMETRIES In TlSe or TlInSe 2 the full vibration representation consists of 24 modes and is given, depending on the position (Г-point, T-point, Δ-line, A-line etc.) of the wave-vector in the BZ, as Г vib =Г 1 +2Г 2 +Г 3 +2Г 4 +3Г 5 +Г 6 +3Г 9 +4Г 10 T vib =T 1 +T 2 +T 3 +3T 4 +3T 5 +T 6 +T 7 +2T 9 +4T 10 Δ vib =6Δ 1 +8Δ 2 +4Δ 3 +6Δ 4 A vib =4A 1 +2A 2 +A 3 +3A 4 +7A 5 Here the irreducible representations Г 5 , Г 10 , T 5 , T 10 , and A 5 are two-dimensional, while the others are one-dimensional. Since phonon symmetries in the obtained phonon band structures of TlSe and TlInSe 2 [15] were not specified, here we give these symmetries for each phonon branch shown in