Endotaxial Polytype Engineering: Enhancement of Incommensurate Charge Density Waves in TaS₂

Charge density waves (CDWs) are an emergent periodic modulation of the electron density that spans a crystal with strong electron-lattice coupling. CDW phases spontaneously break crystal symmetry, facilitate metal–insulator transitions, and compete with superconductivity [1–4]. At elevated temperatures, many materials exhibit a CDW incommensurate (IC-) with the high symmetry parent phase [5–8]. Unfortunately, the IC-CDWs are inherently weak and disordered. In TaS₂, a popular layered CDW material, long-range order has not been demonstrated for the IC-CDW [9–11]. Using new methods of endotaxial polytype engineering [12] we show it is possible to restore long-range order of the IC-CDW phase. Through this process, 2D CDW layers are encapsulated within metallic polytypes to enhance charge order. Furthermore, with restored IC-CDWs we can better understand the nature of disorder in these systems. We show that the IC-CDWs in 1T-TaS₂ are hexatically disordered and undergo a continuous melting as temperature is increased. The hexatic CDW phase retains six-fold orientational order while translation order quickly decays from proliferation of defects with temperature.<br/><br/>Here we use endotaxial engineering to enhance CDWs—even at elevated temperatures. The polytype heterostructures consist of monolayers of octahedrally coordinated charge ordered TaS₂ embedded within matrices of metallic prismatic TaS₂. These endotaxial heterostructures have been shown to raise the critical temperature of the long-range ordered commensurate (C-) CDW phase by 150 K [12].<br/><br/>Surprisingly, long-range order of the IC-CDW phase is significantly enhanced in the polytype heterostructures [13]; in-situ selected area electron diffraction (SAED) of the heterostructures shows sharper and brighter superlattice peaks than the IC-CDW phase in pristine 1T-TaS₂. This enhancement of long-range CDW order is accompanied by a marked increase in the in-plane resistivity of the IC phase. The increased intensity is surprising given the number of charge ordered TaS₂ layers is decreasing.<br/><br/>The signature of IC-CDWs in TaS₂ is the presence of azimuthally diffused superlattice peaks decorating bright Bragg peaks in SAEDs. These azimuthally blurred superlattice peaks strongly resemble the structure factor of hexatic phases found in two-dimensional (2D) systems. 2D crystals can melt continuously through intermediate orientationally ordered hexatic phase [14–17]. Similarly, in pristine 1T-TaS₂, the IC-CDW phase is in a hexatic glassy state due to intrinsic disorder. By restoring crystallinity of the IC-CDW, we observe the full hexatic melting process: heating further melts the ordered IC-CDW phase with continuous azimuthal broadening and weakening of superlattice peaks as expected for hexatic phases.<br/><br/>In summary, we demonstrate that polytype engineering can stabilize fragile long-range order in IC-CDW even at high temperatures. The ordered IC-CDW phase melts continuously with hexatic characteristics.<br/> <br/> <br/>References:<br/> <br/>[1] JA Wilson, FJ Di Salvo, S Mahajan <i>Adv. Phys.</i> <b>24</b> (1975) p.117.<br/>[2] R Ang et al., <i>Nat. Commun.</i> <b>6</b> (2015) 60981.<br/>[3] E Navarro-Moratalla et al., <i>Nat. Commun.</i> <b>7</b> (2016) 11043.<br/>[4] L Li et al., <i>npj Quantum Mater.</i> <b>2</b> (2017) 11.<br/>[5] J Chang et al., <i>Nat. Phys.</i> <b>8</b> (2012) p.871.<br/>[6] L Nie, G Tarjus, and SA Kivelson, <i>Proc. Natl. Acad. Sci.</i> <b>111</b> (2014) p.7980.<br/>[7] I El Baggari et al., <i>Proc. Natl. Acad. Sci.</i> <b>115</b> (2018) p.1445.<br/>[8] M Frachet et al., <i>npj Quant. Mater.</i> <b>7</b> (2022) p.115.<br/>[9] ND Mermin and H Wagner, <i>Phys. Rev. Lett.</i> <b>17 </b>(1966) p.1133.<br/>[10] PC Hohenberg, <i>Phys. Rev.</i> <b>158</b> (1967) p. 383.<br/>[11] Y Imry and S-K Ma, <i>Phys. Rev. Lett.</i> <b>35 </b>(1975) p.1399.<br/>[12] SH. Sung et al., <i>Nat. Commun.</i> <b>13</b> (2022) p.413.<br/>[13] SH. Sung et al., <i>Arxiv</i> 2307.04587 (2023)<br/>[14] JM Kosterlitz and DJ Thouless, <i>J. Phys. C: Solid State Phys.</i> <b>5</b> (1972) p.L124<br/>[15] BI Halperin and DR Nelson, <i>Phys. Rev. Lett.</i> <b>2</b> (1978) p.121<br/>[16] DR Nelson and BI Halperin, <i>Phys. Rev. B</i> <b>19</b> (1979) p.2457<br/>[17] AP Young, <i>Phys. Rev.</i> <b>19</b> (1979) p. 1855