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1T-Tas2 As a Quantum Spin Liquid K 1T-TaS2 as a quantum spin liquid K. T. Lawa and Patrick A. Leeb,1 aDepartment of Physics, Hong Kong University of Science and Technology, Hong Kong, China; and bDepartment of Physics, Massachusetts Institute of Technology, Cambridge MA 02139 Contributed by Patrick A. Lee, May 26, 2017 (sent for review April 24, 2017; reviewed by Steven A. Kivelson and N. Phuan Ong) 1T-TaS2 is unique among transition metal dichalcogenides in that Mott insulator. This fact was pointed out by Fazekas and Tosatti it is understood to be a correlation-driven insulator, where the (8) in 1976. Band calculations show that band folding creates a unpaired electron in a 13-site cluster experiences enough correla- cluster of bands near the Fermi surface. Rossnagel and Smith tion to form a Mott insulator. We argue, based on existing data, (9) found that, due to spin–orbit interaction, a very narrow band that this well-known material should be considered as a quantum is split off, which crosses the Fermi level with a 0.1- to 0.2-eV spin liquid, either a fully gapped Z2 spin liquid or a Dirac spin liq- gap to the other subbands. The narrow bandwidth means that uid. We discuss the exotic states that emerge upon doping and a weak residual repulsion is sufficient to form a Mott insulator, propose further experimental probes. thus supporting the proposal of Fazekas and Tosatti, and dis- tinguishes 1T-TaS2 from other TMD. Apparently, the formation spin liquid j Mott insulator j transition metal dichalcogenide of the commensurate clusters is essential for the strong correla- tion behavior in these 4d and 5d systems. Currently, the assign- ment of cluster Mott insulator to the undoped 1T-TaS2 ground he transition metal dichalcogenide (TMD) is an old subject state is widely accepted. A band about 0.2 eV below the Fermi Tthat has enjoyed a revival recently due to the interests in its energy has been interpreted as the lower Hubbard band in angle- topological properties and unusual superconductivity. The layer resolved photo-emission spectroscopy (ARPES) (10, 11), and the structure is easy to cleave or intercalate and can exist in single- electronic-driven nature of the 200 K transition has been con- layer form (1, 2). This material was studied intensively in the firmed by time-dependent ARPES on the basis of the fast relax- 1970s and 1980s and was considered the prototypical example ation time of the spectra (12). of a charge density wave (CDW) system (3). Due to imperfect Surprisingly, with a few exceptions, the issue of magnetism nesting in two dimensions, in most of these materials, the onset associated with the Mott insulator has not been discussed in the of CDW gaps out only part of the Fermi surface, leaving behind a literature. In the standard picture of a Mott insulator, the spins metallic state that often becomes superconducting. Conventional form local moments, which then form an antiferromagnetic (AF) band theory and electron–phonon coupling appear to account ground state due to exchange coupling. No such AF ordering has for the qualitative behavior (3). There is, however, one notable been reported in 1T-TaS2. There is not even any sign of the local exception, namely 1T-TaS2. The Ta forms a triangular lattice, moment formation, which usually appears as a rise in the spin sandwiched between two triangular layers of S, forming an ABC- susceptibility with decreasing temperature, following a Curie type stacking. As a result, the Ta is surrounded by S, forming Weiss law. As seen in Fig. 2, the magnetic susceptibility drops an approximate octahedron. In contrast, the 2H-TaS2 forms an at the CDW transitions, but remains almost flat below 200 K (3). ABA-type stacking, and the Ta is surrounded by S, forming a (The small rise below 50 K can be attributed to 5 × 10−4 impu- trigonal prism. In a single layer, inversion symmetry is broken in rity spin per Ta.) This serious discrepancy from the Mott pic- 2H structure. The system is a good metal below the CDW onset ture did not escape the attention of Fazekas and Tosatti (8); they around 90 K, and, eventually, the spin–orbit coupling gives rise attempted to explain this by arguing that the g factor is very small to a special kind of superconductivity called Ising superconduc- due to spin–orbit coupling. However, their argument depends tivity (4–6). In 1T-TaS2, inversion symmetry is preserved. The sensitively on the assumption of a cubic environment for the Ta system undergoes a CDW transition at about 350 K with a jump atoms, which is now known not to be true. In fact, Rossnagel and in the resistivity. It is known that this transition is driven by an Smith (9) claim that a single band crosses the Fermi level that is incommensurate triple-Q CDW (ICDW). A similar transition mainly made up of xy and x 2 − y 2 orbitals. This picture suggests is seen in 1T-TaSe2 at 470 K. However, whereas TaSe2 stays metallic below this transition, 1T-TaS2 exhibits a further resis- tivity jump around 200 K that is hysteretic, indicative of the first- Significance order nature of this transition. These transitions are also visible in the spin susceptibility data shown in Fig. 2. In early samples, In solids with an odd number of electrons per unit cell, band the resistivity rises only by about a factor of 10 as the temperature theory requires that they are metals, but strong interaction is lowered from 200 K to 2 K and, below that, obeys Mott hop- can turn them into insulators, called Mott insulators. In this ping law (log resistivity goes as T −1=3) (7). More recent samples case, the electrons form local moments that, in turn, form an show better insulating behavior, and it is generally agreed that antiferromagnetic ground state. In 1973, P. W. Anderson pro- the ground state is insulating. The 200 K transition is accom- posed that, in certain cases, quantum fluctuations may pre- vent magnetic order and result in a paramagnetic ground state paniedp by a lock-inp to a commensurate CDW (CCDW), form- ing a 13 × 13 structure. As shown in Fig. 1, this structure called a quantum spin liquid. After many years of searching, a is described as clusters of stars of David where the sites of the few examples have been discovered in the past several years. stars move inward toward the site in the middle. The stars of We point out that a well-studied material, TaS2, may be a spin David are packed in such a way that they form a triangular lat- liquid candidate. We propose further experiments that probe tice. Thus, the unit cell is enlarged to have 13 Ta sites. The for- the exotic properties of this new state of matter. mal valence of Ta is 4+, and each Ta site has a single 5d elec- Author contributions: K.T.L. and P.A.L. performed research; and P.A.L. wrote the paper. tron. We have an odd number of electrons per unit cell. (We first restrict ourselves to a single layer. Interlayer effects will be Reviewers: S.A.K., Stanford University; and N.P.O., Princeton University. discussed later in this section.) According to band theory, the The authors declare no conflict of interest. ground state must be metallic. The only option for an insulat- Freely available online through the PNAS open access option. ing ground state in the pure material is a correlation driven 1To whom correspondence should be addressed. Email: [email protected]. 6996–7000 j PNAS j July 3, 2017 j vol. 114 j no. 27 www.pnas.org/cgi/doi/10.1073/pnas.1706769114 Downloaded by guest on September 29, 2021 SDW at wave vector Q will induce a charge density wave order at 2Q, but these new diffraction spots have not been seen. Fur- thermore, the ARPES should show clearly the back-folded band instead of a broad smear (10, 11). Finally, since the initial submis- sion of this paper, we have learned that NMR and µSR (spin res- onance) data indeed rule out static magnetic moments (17, 18). We therefore believe long-range AF or SDW is unlikely. Instead, 1T-TaS2 may be an example of the elusive quantum spin liquid. There is, however, one remaining caveat. Up to now, we have not discussed the issue of interlayer coupling, which can intro- duce complications for our interpretations. Above 200 K, the ICDW are stacked in an ABC pattern, leading to a tripling of the unit cell in the c direction. However, below 200 K, the stars of David are stacked directly on top of each other to form bilayers. These bilayers are stacked randomly or in an incommensurate fashion (18, 19). The doubling of the unit in the bilayer means that we now have an even number of electrons per unit cell, and a spin liquid ground state may or may not survive, depend- ing on which of the following two options are realized. The first option is for the spins to form singlets between the unit cells. Fig. 1. In the cluster Mott phase of 1T-TaS2, Ta atoms (red dots) belonging This state no longer fits the definition of a spin liquid, because it to a star of David move toward the Ta atom at the center. Thirteen Ta atoms is topologically trivial and is smoothly connected to an ordinary form a unit cell, and these unit cells form a triangular lattice. The directions band insulator. It is more analogous to ladder compounds, which and lengths of the arrows are schematic.
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