Suk Hyun Sung1,2,Pat Kezer2,Nishkarsh Agarwal2,Yin Min Goh1,Noah Schnitzer3,Ismail El Baggari1,Kai Sun2,Lena Kourkoutis3,John Heron2,Robert Hovden2
Harvard University1,University of Michigan2,Cornell University3
Suk Hyun Sung1,2,Pat Kezer2,Nishkarsh Agarwal2,Yin Min Goh1,Noah Schnitzer3,Ismail El Baggari1,Kai Sun2,Lena Kourkoutis3,John Heron2,Robert Hovden2
Harvard University1,University of Michigan2,Cornell University3
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 TaS<sub>2</sub>, 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-TaS<sub>2</sub> 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 TaS<sub>2</sub> embedded within matrices of metallic prismatic TaS<sub>2</sub>. 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-TaS<sub>2</sub>. 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 TaS<sub>2</sub> layers is decreasing.<br/><br/>The signature of IC-CDWs in TaS<sub>2</sub> 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-TaS<sub>2</sub>, 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