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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">586182</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2020.586182</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Review</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Electronic and Superconducting Properties of Some FeSe-Based Single Crystals and Films Grown Hydrothermally</article-title>
<alt-title alt-title-type="left-running-head">Dong et al.</alt-title>
<alt-title alt-title-type="right-running-head">Properties of Some FeSe-based Crystals and Films</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Dong</surname>
<given-names>Xiaoli</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">
<sup>&#x2a;</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1038058/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhou</surname>
<given-names>Fang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhao</surname>
<given-names>Zhongxian</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<label>
<sup>1</sup>
</label>Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<label>
<sup>2</sup>
</label>University of Chinese Academy of Sciences, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<label>
<sup>3</sup>
</label>Songshan Lake Materials Laboratory, <addr-line>Dongguan</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/289254/overview">Jun Zhao</ext-link>, Fudan University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1041862/overview">Hechang Lei</ext-link>, Renmin University of China, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/96428/overview">Masahiro Ishigami</ext-link>, University of Central Florida, United States</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Xiaoli Dong, <email>dong@iphy.ac.cn</email>
</corresp>
<fn fn-type="other" id="fn001">
<p>This article was submitted to Condensed Matter Physics, a section of the journal Frontiers in Physics</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>11</day>
<month>11</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="collection">
<year>2020</year>
</pub-date>
<volume>8</volume>
<elocation-id>586182</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>07</month>
<year>2020</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>09</month>
<year>2020</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2020 Dong, Zhou and Zhao</copyright-statement>
<copyright-holder>Dong, Zhou and Zhao</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Our recent year&#x2019;s studies of the prototypal FeSe and molecule-intercalated (Li,Fe)OHFeSe superconductor systems are briefly reviewed here, with emphasis on the link between the superconducting and normal-state properties observed in the single crystals and films. These samples were successfully synthesized by our recently developed soft-chemical hydrothermal methods, which are also briefly described. Particularly in the Mn-doped high-<italic>T</italic>
<sub>c</sub> (Li,Fe)OHFeSe film, a strong enhancement of the superconducting critical current density was achieved, which is promising for practical application of the superconductivity.</p>
</abstract>
<kwd-group>
<kwd>superconductivity of iron selenides</kwd>
<kwd>normal state properties</kwd>
<kwd>electronic phase separation</kwd>
<kwd>spin nematicity</kwd>
<kwd>high critical current density</kwd>
<kwd>hydrothermal growth</kwd>
</kwd-group>
<counts>
<page-count count="0"/>
</counts>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Iron-based superconductors [<xref ref-type="bibr" rid="B1">1</xref>] have received extensive attention because of their rich physics, including magnetic and nematic instabilities, electronic correlations, and quantum phenomena [<xref ref-type="bibr" rid="B2">2</xref>&#x2013;<xref ref-type="bibr" rid="B9">9</xref>]. As the second class of high-<italic>T</italic>
<sub>c</sub> materials after the discovery of cuprate superconductors, the iron-based superconductors are also promising for practical application owing to their large critical current density, high upper critical field, and small anisotropy [<xref ref-type="bibr" rid="B10">10</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. The recent observation of Majorana zero modes in iron-based superconductors implies a potentiality for future application in topological quantum calculating [<xref ref-type="bibr" rid="B18">18</xref>&#x2013;<xref ref-type="bibr" rid="B21">21</xref>]. Unlike an electronic configuration of Cu-3d<sup>9</sup> in the cuprates, the iron-based compounds have an electronic configuration of Fe-3d<sup>6</sup> and a small crystal-field splitting [<xref ref-type="bibr" rid="B2">2</xref>, <xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B22">22</xref>&#x2013;<xref ref-type="bibr" rid="B24">24</xref>]. An immediate consequence of this is that all the five Fe-3d orbitals could be involved in the low-energy interactions [<xref ref-type="bibr" rid="B25">25</xref>], giving rise to the multiband nature of the iron-based superconductivity, and the complexity and multiplicity of the normal-state properties. The iron-based family has two major subclasses, the iron chalcogenide and pnictide superconductors. Among them, the iron selenide superconductors have been shown to display a highly tunable superconducting critical <italic>T</italic>
<sub>c</sub> and unique electronic properties in the normal state, thus providing a superior platform to investigate the underlying physics for iron-based superconductivity.</p>
<p>Superconductivity of FeSe-based compounds emerges from the edge&#x2010;sharing FeSe&#x2010;tetrahedra blocks, each formed by one iron-plane sandwiched between two selenium-planes. An important feature is that the superconducting <italic>T</italic>
<sub>c</sub> can be tuned in a wide range. The simplest binary FeSe shows bulk superconductivity at a lower <italic>T</italic>
<sub>c</sub> &#x223c; 9&#xa0;K under ambient pressure [<xref ref-type="bibr" rid="B26">26</xref>]. It is notable that <italic>T</italic>
<sub>c</sub> can be boosted to tens of kelvin (30-50&#xa0;K), by the applications of high pressure [<xref ref-type="bibr" rid="B27">27</xref>&#x2013;<xref ref-type="bibr" rid="B33">33</xref>], charge-carrier injection [<xref ref-type="bibr" rid="B34">34</xref>], electrochemical etching [<xref ref-type="bibr" rid="B35">35</xref>], and chemical intercalation. The weak van der Waals bonding between the neighboring FeSe-blocks allows a variety of FeSe-based intercalates to be obtained, such as the atom-intercalated A<sub>y</sub>Fe<sub>2-x</sub>Se<sub>2</sub> (A &#x3d; alkali metal) [<xref ref-type="bibr" rid="B36">36</xref>&#x2013;<xref ref-type="bibr" rid="B40">40</xref>], molecule-intercalated (Li<sub>0.8</sub>Fe<sub>0.2</sub>)OHFeSe [<xref ref-type="bibr" rid="B41">41</xref>], and atom/molecule-co-intercalated Li<sub>x</sub>(C<sub>5</sub>H<sub>5</sub>N)<sub>y</sub>Fe<sub>2-z</sub>Se<sub>2</sub> [<xref ref-type="bibr" rid="B42">42</xref>], A<sub>x</sub>(NH<sub>2</sub>)<sub>y</sub>(NH<sub>3</sub>)<sub>1-y</sub>Fe<sub>2</sub>Se<sub>2</sub> [<xref ref-type="bibr" rid="B43 B44">43, 44</xref>], A<sub>x</sub>(NH<sub>3</sub>)<sub>y</sub>Fe<sub>2</sub>Se<sub>2</sub> [<xref ref-type="bibr" rid="B45">45</xref>&#x2013;<xref ref-type="bibr" rid="B47">47</xref>] and A<sub>x</sub>(C<sub>2</sub>H<sub>8</sub>N<sub>2</sub>)<sub>y</sub>Fe<sub>2</sub>Se<sub>2</sub> [<xref ref-type="bibr" rid="B48">48</xref>]. Moreover, the highest superconducting gap opening temperature (&#x223c;65&#xa0;K) among all the iron-based superconductors has been observed in a monolayer FeSe grown on a SrTiO<sub>3</sub> substrate [<xref ref-type="bibr" rid="B49 B50">49, 50</xref>]. On the other hand, distinct from most iron-based superconductor systems, FeSe does not order magnetically at ambient pressure, whereas a unique electronic nematic ordering has been observed to develop with a rotational-symmetry-breaking transition from a tetragonal to an orthorhombic phase at <italic>T</italic>
<sub>s</sub> &#x223c; 90&#xa0;K [<xref ref-type="bibr" rid="B51 B52">51, 52</xref>]. The electronic nematicity is directly related to a degeneracy lifting of the bands with Fe 3d<sub>xz</sub> and 3d<sub>yz</sub> orbital characters [<xref ref-type="bibr" rid="B53">53</xref>&#x2013;<xref ref-type="bibr" rid="B55">55</xref>]. Compared to the Fermi-surface topology of the prototypal FeSe, in the molecule-intercalated (Li,Fe)OHFeSe single crystals, only the electron pockets near the Brillouin zone corners are observed, in absence of the hole pocket near the zone center [<xref ref-type="bibr" rid="B56 B57">56, 57</xref>]. This raises question about a proposed pairing scenario of the electronic scatterings between the hole-like and electron-like pockets. Study of the FeSe-based superconductors is essential for a better understanding of the unconventional superconductivity.</p>
<p>To investigate the link between the unconventional superconductivity and unusual normal-state electronic properties, and the potential for the superconductivity application, high-quality single crystal and film samples are highly demanded. Recent years, we have been exploring soft-chemical methods suitable for synthesizing the FeSe-based superconductor single crystals and single-crystalline films hard to obtain by conventional high-temperature growth. By developing hydrothermal ion-exchange [<xref ref-type="bibr" rid="B58">58</xref>&#x2013;<xref ref-type="bibr" rid="B60">60</xref>] and ion-deintercalation [<xref ref-type="bibr" rid="B61 B62">61, 62</xref>] approaches, we have succeeded in synthesizing series of high-quality sizable single crystals of the intercalated (Li,Fe)OHFeSe and binary FeSe systems, respectively. Our further study [<xref ref-type="bibr" rid="B9">9</xref>] has shown a strong electronic two-dimensionality and a nearly linear extracted magnetic susceptibility in the hydrothermal high-<italic>T</italic>
<sub>c</sub> (42&#xa0;K) (Li,Fe)OHFeSe single crystal, suggesting the presence of two-dimensional magnetic fluctuations in the normal state. In a series of the (Li, Fe)OHFeSe single crystals, a coexistence of antiferromagnetism with superconductivity has been detected [<xref ref-type="bibr" rid="B60">60</xref>]. We explain such coexistence by electronic phase separation, similar to the previously observed in high-<italic>T</italic>
<sub>c</sub> cuprates and iron arsenides. An electronic phase diagram is further established for (Li, Fe)OHFeSe system [<xref ref-type="bibr" rid="B60 B63">60, 63</xref>]. In hydrothermal binary Fe<sub>1&#x2212;<italic>x</italic>
</sub>Se single crystals, we have observed a field-induced two-fold rotational symmetry emerging below <italic>T</italic>
<sub>sn</sub> in angular-dependent magnetoresistance measurements, and a linear relationship between <italic>T</italic>
<sub>c</sub> and <italic>T</italic>
<sub>sn</sub> [<xref ref-type="bibr" rid="B61 B64">61, 64</xref>]. Importantly, we find in our recent study [<xref ref-type="bibr" rid="B9">9</xref>] that the superconductivity of FeSe system emerges from the strongly correlated, hole-dominated Fe<sub>1&#x2212;<italic>x</italic>
</sub>Se as the non-stoichiometry is reduced to <italic>x</italic> &#x223c; 5.3%. Interestingly, such an <italic>x</italic> threshold for superconductivity of the prototypal FeSe is similar to that (<italic>x</italic> &#x223c; 5% [<xref ref-type="bibr" rid="B65">65</xref>]) for high-<italic>T</italic>
<sub>c</sub> superconductivity of the intercalated (Li, Fe)OHFeSe sharing the common superconducting FeSe-blocks.</p>
<p>We have also successfully synthesized a series of high-quality single-crystalline films of (Li, Fe)OHFeSe system, by inventing a hydrothermal epitaxial film technique [<xref ref-type="bibr" rid="B16 B17 B66">16, 17, 66</xref>]. We find that doping Mn into high-<italic>T</italic>
<sub>c</sub> (Li, Fe)OHFeSe films can raise the superconducting critical current density <italic>J</italic>
<sub>c</sub> by one order of magnitude to 0.32&#xa0;MA/cm<sup>2</sup> at a high field of 33&#xa0;T [<xref ref-type="bibr" rid="B17">17</xref>]. Such a high <italic>J</italic>
<sub>c</sub> value is the record so far among the iron-based superconductors, and is thus promising for high-field application of the superconductivity. Besides, our breakthrough in the crystal growth has greatly promoted other related studies and progresses have been made [<xref ref-type="bibr" rid="B57">57</xref>, <xref ref-type="bibr" rid="B59">59</xref>, <xref ref-type="bibr" rid="B60">60</xref>, <xref ref-type="bibr" rid="B67">67</xref>&#x2013;<xref ref-type="bibr" rid="B71">71</xref>], including the ARPES study of Fermi-surface topology [<xref ref-type="bibr" rid="B57">57</xref>] and the observation of pressure-induced second high-<italic>T</italic>
<sub>c</sub> (&#x3e;50&#xa0;K) phase [<xref ref-type="bibr" rid="B70">70</xref>] in the (Li,Fe)OHFeSe system. Our developed growth method has also been adopted in the studies of other research groups [<xref ref-type="bibr" rid="B56">56</xref>, <xref ref-type="bibr" rid="B72">72</xref>&#x2013;<xref ref-type="bibr" rid="B83">83</xref>].</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>Soft-Chemical Hydrothermal Growth Methods Developed for FeSe-Based Single Crystals and Films</title>
<p>The discovery of Li<sub>0.8</sub>Fe<sub>0.2</sub>OHFeSe (FeSe-11111) superconductor [<xref ref-type="bibr" rid="B41">41</xref>] brings new opportunity for the study of iron-based superconductivity. (Li, Fe)OHFeSe is free from the complications of the structural transition, associated with the electronic nematicity, and the chemical phase separation, related to the intergrown insulating K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub> (KFS&#x2010;245 phase) [<xref ref-type="bibr" rid="B63">63</xref>], as compared to the prototypal FeSe-11 and K<sub>1&#x2010;y</sub>Fe<sub>2&#x2010;x</sub>Se<sub>2</sub>&#x2010;122 superconductors, respectively. Moreover, it shows an ambient-pressure high <italic>T</italic>
<sub>c</sub> &#x3d; 42&#xa0;K and a pressure-induced higher <italic>T</italic>
<sub>c</sub> &#x3e; 50&#xa0;K under 12.5&#xa0;GPa [<xref ref-type="bibr" rid="B70">70</xref>]. Having a Fermi-surface topology [<xref ref-type="bibr" rid="B56 B57">56, 57</xref>] similar to the high-<italic>T</italic>
<sub>c</sub> (&#x3e;65&#xa0;K) FeSe monolayer, (Li, Fe)OHFeSe system turns out to be an ideal platform for studying the superconducting and normal-state properties of high-<italic>T</italic>
<sub>c</sub> iron-based superconductors. Initially, only the powder samples of (Li, Fe)OHFeSe can be prepared hydrothermally [<xref ref-type="bibr" rid="B41 B63 B65 B84 B85">41, 63, 65, 84, 85</xref>]. For in-depth investigations on the intrinsic and anisotropic physical properties, the high-quality single crystal and film samples are indispensable.</p>
<p>The crystal structure of (Li, Fe)OHFeSe consists of a stacking of one superconducting (SC) FeSe-block alternating with one insulating (Li, Fe)OH-block along the <italic>c</italic>-axis. The (Li, Fe)OHFeSe compound suffers an easy decomposition because of the inherent weak hydrogen bonding. Therefore, none of the conventional high-temperature methods is applicable to grow the single crystals. To overcome this problem, we have developed a soft-chemical hydrothermal ion-exchange method capable of producing high-quality sizable single crystals of (Li, Fe)OHFeSe [<xref ref-type="bibr" rid="B58">58</xref>]. <xref ref-type="fig" rid="F1">Figure 1</xref> schematically illustrates the hydrothermal ion-exchange process. For the hydrothermal ion-exchange reaction, large and high-quality K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub> crystal is used as a kind of matrix. The structure of K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub> is formed by an alternative stacking of K-layer and FeSe-tetrahedron-block similar to the target compound. The K ions in K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub> are completely de-intercalated during the hydrothermal process. Simultaneously, the (Li, Fe)OH-blocks constructed by ions from the hydrothermal solution are intercalated into the matrix, and the ordered vacant Fe-sites (20% in amount) originally in the matrix Fe<sub>0.8</sub>Se-blocks are almost occupied. A series of large and high-quality (Li, Fe)OHFeSe single crystals [<xref ref-type="bibr" rid="B60">60</xref>] are thus derived. The derived (Li, Fe)OHFeSe single crystal almost inherits the original shape of the matrix (insets of <xref ref-type="fig" rid="F1">Figures 1B,C</xref>). Inspired by the successful hydrothermal ion-exchange method for the single crystals, we have further invented a hydrothermal epitaxial film technique to fabricate a series of high-quality single-crystalline films of un-doped [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B66">66</xref>] and Mn-doped [<xref ref-type="bibr" rid="B17">17</xref>] (Li, Fe)OHFeSe, showing an optimal zero-resistivity <italic>T</italic>
<sub>c</sub> &#x3d; 42.4&#xa0;K. The high-quality (Li, Fe)OHFeSe films has enabled a systematic study of the superconducting and normal-state properties [<xref ref-type="bibr" rid="B66">66</xref>].</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Illustration of hydrothermal ion-exchange growth of (Li,Fe)OHFeSe crystals [<xref ref-type="bibr" rid="B58">58</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g001.tif"/>
</fig>
<p>By modifying the hydrothermal reaction conditions, we have also developed a hydrothermal ion-deintercalation (HID) method, as illustrated in <xref ref-type="fig" rid="F2">Figure 2</xref>. The atomic ratio of the FeSe-blocks can be continuously tuned by the HID process, yielding a series of non-stoichiometric Fe<sub>1-<italic>x</italic>
</sub>Se single crystals at various charge-doping levels [<xref ref-type="bibr" rid="B9 B61 B62">9, 61, 62</xref>]. FeSe crystals used to be grown by chemical-vapor-transport [<xref ref-type="bibr" rid="B86 B87">86, 87</xref>], flux-free floating-zone [<xref ref-type="bibr" rid="B88">88</xref>], and flux solution methods. These methods are hard to tune the chemical stoichiometry.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Scematic llutration of the hydrothermal ion-deintercalation method. During the HID process, Fe<sub>1-<italic>x</italic>
</sub>Se single crystals are derived from the readily obtainable phase-pure matrix single crystals of K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub>. The original interlayer K ions and Fe vacancies (20% in amount) in K<sub>0.8</sub>Fe<sub>1.6</sub>Se<sub>2</sub> were completely de-intercalated and substantially reduced, respectively, yielding the target single crystals of phase-pure Fe<sub>1-<italic>x</italic>
</sub>Se [<xref ref-type="bibr" rid="B9 B61 B62">9, 61, 62</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g002.tif"/>
</fig>
</sec>
<sec id="s3">
<title>Electronic and Superconducting Properties Studied in the Hydrothermal Single Crystals and Films</title>
<p>Now we briefly review our recent year&#x2019;s studies of the series of FeSe-based single crystals and films grown by the hydrothermal methods.</p>
<sec id="s3-1">
<title>Strong Electronic Two-Dimensionality in High<italic>-T</italic>
<sub>c</sub> (Li,Fe)OHFeSe Single Crystal</title>
<p>
<xref ref-type="fig" rid="F3">Figure 3A</xref> shows the temperature dependence of the in-plane resistivity, <italic>&#x3c1;</italic>
<sub>ab</sub>, for the high-<italic>T</italic>
<sub>c</sub> (42&#xa0;K) (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OHFe<sub>0.98</sub>Se single crystal [<xref ref-type="bibr" rid="B58">58</xref>], which displays a metallic behavior over the whole measuring temperature range in the normal state. As a measure of the charge transport anisotropy, the ratio of the out-of-plane to in-plane resistivity, <italic>&#x3c1;</italic>
<sub>c</sub>/<italic>&#x3c1;</italic>
<sub>ab</sub>, was found to increase with lowering temperature and reach a high value of 2,500 at 50&#xa0;K. It is obvious that the normal-state electronic property turns out to be highly two dimensional just above <italic>T</italic>
<sub>c</sub>. Shown in <xref ref-type="fig" rid="F3">Figure 3C</xref> is the temperature dependence of static magnetic susceptibility, which is slightly dependent on the magnitude of the applied field. In the higher temperature range, all the data can be fitted to a modified Curie-Weiss law <italic>&#x3c7;</italic>
<sub>m</sub> &#x3d; <italic>&#x3c7;</italic>
<sub>0</sub> &#x2b; <italic>&#x3c7;</italic>
<sub>CW</sub> (the solid lines), where <italic>&#x3c7;</italic>
<sub>0</sub> is the Pauli paramagnetic contribution from itinerant charge carriers. A deviation from the Curie&#x2010;Weiss law is clearly visible below a characteristic <italic>T</italic>
<sup>&#x2a;</sup> (&#x223c; 120&#xa0;K ) for a dip-like <italic>T</italic>&#x2010;dependence of the Hall coefficient (<xref ref-type="fig" rid="F3">Figure 3B</xref>), coinciding with the upturn in Hall coefficient and the change in resistivity behavior. From the Hall&#x2010;dip <italic>T</italic>
<sup>&#x2a;</sup> down to the superconducting <italic>T</italic>
<sub>c</sub>, both the extracted iron-plane magnetic susceptibility (with the Curie-Weiss term subtracted; inset of <xref ref-type="fig" rid="F3">Figure 3C</xref>) and the in&#x2010;plane resistivity (inset of <xref ref-type="fig" rid="F3">Figure 3A</xref>) exhibit a linear temperature dependence, suggesting the presence of two-dimensional antiferromagnetic spin fluctuations in the iron planes.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The electrical transport and magnetic properties of (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OHFe<sub>0.98</sub>Se single crystal [<xref ref-type="bibr" rid="B58">58</xref>]. <bold>(A)</bold> The in-plane electric resistivity and the ratio of out-of-plane to in&#x2010;plane resistivity as functions of temperature. The inset shows the linear resistivity below the Hall-dip temperature <italic>T&#x002A;</italic> down to <italic>T</italic>
<sub>c</sub>. <bold>(B)</bold> The temperature dependence of in-plane Hall coefficient shows a dip&#x2010;like feature around <italic>T&#x002A;</italic> &#x223c;120 K. <bold>(C)</bold> The temperature dependencies of static magnetic susceptibility under magnetic fields along <italic>c</italic>-axis. A deviation from the Curie&#x2010;Weiss law is clearly visible below the Hall&#x2010;dip temperature <italic>T&#x002A;</italic>. After subtracting the Curie-Weiss term (the solid fitted curves) from the (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OH-blocks, a nearly linear magnetic susceptibility from the FeSe-blocks is obvious (the inset).</p>
</caption>
<graphic xlink:href="fphy-08-586182-g003.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>Phase Diagram and Electronic Phase Separation of (Li,Fe)OHFeSe System</title>
<p>The first phase diagram of (Li, Fe)OHFeSe system [<xref ref-type="bibr" rid="B63">63</xref>] was based on the powder samples. In a subsequent work [<xref ref-type="bibr" rid="B60">60</xref>], we established a more complete phase diagram for the system (<xref ref-type="fig" rid="F4">Figure 4</xref>), based on a series of the hydrothermal single crystals in the superconducting (SC) and non-superconducting regimes. In some of the SC samples (<italic>T</italic>
<sub>c</sub> &#x3c; &#x223c;38&#xa0;K, cell parameter <italic>c</italic> &#x3c; &#x223c;9.27&#xa0;&#xc5;), we observed a strong drop in the magnetization at an almost constant temperature scale <italic>T</italic>
<sub>afm</sub> &#x223c; 125&#xa0;K (<xref ref-type="fig" rid="F5">Figure 5C</xref>), indicating the occurrence of antiferromagnetism well above <italic>T</italic>
<sub>c</sub>. Our analysis of electron energy-loss spectroscopy combined with selected-area electron diffraction confirmed the absence of magnetic impurity phases such as Fe<sub>3</sub>O<sub>4</sub> [60]. Therefore, the antiferromagnetic signal is intrinsic to (Li, Fe)OHFeSe system. Moreover, a positive correlation between the sizes of the antiferromagnetic signal and the Meissner signal was observed (<xref ref-type="fig" rid="F5">Figures 5D</xref>). These experimental results demonstrate the coexistence of an antiferromagnetic state with the superconducting state in (Li, Fe)OHFeSe at <italic>T</italic>
<sub>c</sub> &#x3c; &#x223c;38&#xa0;K and <italic>c</italic> &#x3c; &#x223c;9.27&#xa0;&#xc5;. Such coexistence can be explained by electronic phase separation [<xref ref-type="bibr" rid="B60">60</xref>], similar to the cases of high-<italic>T</italic>
<sub>c</sub> cuprates and iron arsenides. Therefore the electronic phase diagram shown in <xref ref-type="fig" rid="F4">Figure 4</xref> provides more information about the electronic states in (Li, Fe)OHFeSe system.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Electronic phase diagram of (Li,Fe)OHFeSe system [<xref ref-type="bibr" rid="B60 B63">60, 63</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>
<bold>(A,B)</bold> Temperature dependence of static magnetic susceptibility near the superconducting transitions, for the two sets of superconducting (Li,Fe)OHFeSe single crystals. <bold>(C)</bold> Antiferromagnetic (AFM) transition at &#x223c;125&#xa0;K is detectable for the superconducting (Tc &#x3c; &#x223c;38&#xa0;K) samples and non-superconducting samples. <bold>(D)</bold> The corresponding AFM signal size and the SC Meissner signal size are positively correlated (<xref ref-type="bibr" rid="B60">60</xref>).</p>
</caption>
<graphic xlink:href="fphy-08-586182-g005.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>The Link Between the Superconducting and Normal-State Properties in Fe<sub>1&#x2212;<italic>x</italic>
</sub>Se Single Crystals</title>
<p>The in-plane angular-dependent magnetoresistance (AMR) in the normal state was measured for the hydrothermal Fe<sub>1-<italic>x</italic>
</sub>Se single crystals [<xref ref-type="bibr" rid="B64">64</xref>]. <xref ref-type="fig" rid="F6">Figure 6</xref> shows the AMR at a 9&#xa0;T field for a representative sample with <italic>T</italic>
<sub>c</sub> &#x3d; 7.6&#xa0;K. The AMR displays a two-fold rotational symmetry emerging below a characteristic temperature <italic>T</italic>
<sub>sn</sub> &#x223c; 55&#xa0;K. This anisotropy in AMR is enhanced with decreasing temperature (left panel of <xref ref-type="fig" rid="F6">Figure 6</xref>). This enhancement in charge scatterings was also observed in the temperature-dependent magnetoresistance by an earlier study [<xref ref-type="bibr" rid="B89">89</xref>]. Moreover, a downward curvature starting below <italic>T</italic>
<sub>sn</sub> &#x223c; 55&#xa0;K was observed in our sample in the static magnetization under an in-plane magnetic field of 0.1&#xa0;T (<xref ref-type="fig" rid="F7">Figure 7A</xref>) [<xref ref-type="bibr" rid="B61">61</xref>]. Such a feature is strongly dependent on the magnitude and direction of the applied field (<xref ref-type="fig" rid="F7">Figures 7A</xref> vs <xref ref-type="fig" rid="F7">7B</xref>). This suggests that the strong quantum spin frustrations predominate in the iron planes. Although the orbital-nematic order associated with the structural transition at <italic>T</italic>
<sub>s</sub> &#x223c; 90&#xa0;K is also of a two-fold rotational symmetry, the obvious downward feature of in-plane static magnetization below <italic>T</italic>
<sub>sn</sub> &#x223c; 55&#xa0;K, which is far below <italic>T</italic>
<sub>s</sub>, suggests that the fourfold-rotational-symmetry breaking identified by our AMR measurements is closely related to the frustrated spins with anisotropic magnetic fluctuations. Therefore, a field-induced nematic state of a spin origin emerges below <italic>T</italic>
<sub>sn</sub>.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Temperature dependences of the angular-dependent magnetoresistance of FeSe crystal (<italic>T</italic>
<sub>c</sub> &#x3d; 7.6&#xa0;K), showing the twofold rotational symmetry below <italic>T</italic>
<sub>sn</sub> &#x223c; 55&#xa0;K [<xref ref-type="bibr" rid="B64">64</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g006.tif"/>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Temperature dependence of the static magnetization around <italic>T</italic>
<sub>sn</sub> under the in-plane and out-of-plane fields for the FeSe crystal shown in <xref ref-type="fig" rid="F6">
<bold>Figure 6</bold>
</xref> [<xref ref-type="bibr" rid="B61">61</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g007.tif"/>
</fig>
<p>By summarizing all the data of our samples, we found a remarkable linear relationship between <italic>T</italic>
<sub>c</sub> and <italic>T</italic>
<sub>sn</sub>, as shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. Moreover, the related data of <italic>T</italic>
<sub>c</sub> and <italic>T</italic>
<sub>sn</sub> available from literature [<xref ref-type="bibr" rid="B89">89</xref>&#x2013;<xref ref-type="bibr" rid="B91">91</xref>] also well satisfy this linear relationship. Namely, the linear relationship between superconducting <italic>T</italic>
<sub>c</sub> and characteristic <italic>T</italic>
<sub>sn</sub> of the field-induced spin-nematic state was observed to cover a wide range from far below to beyond <italic>T</italic>
<sub>s</sub>. This further suggests that the superconductivity is more likely related to the anisotropic magnetic fluctuations. These results of prototypal FeSe system are consistent with those of intercalated high-<italic>T</italic>
<sub>c</sub> (Li,Fe)OHFeSe presented above. It needs to be emphasized that, for nearly stoichiometric FeSe samples with a constant <italic>T</italic>
<sub>c</sub> &#x223c; 9.5&#xa0;K, both the spin-nematic ordering and orbital-nematic ordering (associated with the structural transition) happen to coincide with each other at &#x223c;90&#xa0;K, as shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. So it is difficult to distinguish these different ordering states in such samples. Our samples with different <italic>T</italic>
<sub>c</sub>&#x2019;s enable the disentanglement of the different states.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>The universal linear relationship between the superconducting transition temperature (<italic>T</italic>
<sub>c</sub>) and the field&#x2010;induced spin-nematic ordering temperature (<italic>T</italic>
<sub>sn</sub>) among various FeSe samples (the solid symbols) [<xref ref-type="bibr" rid="B64">64</xref>]. The hollow symbols in the vertical blue-shaded area represent the structure phase transition temperatures by the x-ray or neutron diffractions on various FeSe samples of different Tc&#x2019;s [<xref ref-type="bibr" rid="B30">30</xref>, <xref ref-type="bibr" rid="B52">52</xref>, <xref ref-type="bibr" rid="B55">55</xref>, <xref ref-type="bibr" rid="B86">86</xref>, <xref ref-type="bibr" rid="B92">92</xref>&#x2013;<xref ref-type="bibr" rid="B94">94</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g008.tif"/>
</fig>
<p>Most recently, we have studied the doping dependences of electronic correlation effect [<xref ref-type="bibr" rid="B9">9</xref>] and upper critical field behavior [<xref ref-type="bibr" rid="B62">62</xref>] in a series of hydrothermal Fe<sub>
<bold>1-<italic>x</italic>
</bold>
</sub>Se single crystals. Particularly in these binary Fe<sub>
<bold>1-<italic>x</italic>
</bold>
</sub>Se samples, the charge-doping level can be tuned simply by the non-stoichiometric <italic>x</italic>, from a strong electron dominance at <italic>x</italic> &#x223c; 0 to a strong hole dominance at higher <italic>x</italic> values. Importantly, we find that superconductivity of FeSe system emerges from the strongly correlated, hole-dominated Fe<sub>1&#x2212;<italic>x</italic>
</sub>Se as the non-stoichiometry is reduced to <italic>x</italic> &#x223c; 5.3% [<xref ref-type="bibr" rid="B9">9</xref>]. Interestingly, such an <italic>x</italic> threshold for superconductivity of the prototypal FeSe is similar to that (<italic>x</italic> &#x223c; 5% [<xref ref-type="bibr" rid="B65">65</xref>]) for high-<italic>T</italic>
<sub>c</sub> superconductivity of the intercalated (Li, Fe)OHFeSe sharing the common superconducting FeSe-blocks.</p>
</sec>
<sec id="s3-4">
<title>High Superconducting Critical Parameters of Un-Doped and Mn-Doped (Li,Fe)OHFeSe Crystals and Films</title>
<p>
<xref ref-type="fig" rid="F9">Figure 9</xref> shows the x-ray diffraction characterization of a representative (Li,Fe)OHFeSe film sample hydrothermally grown on LaAlO<sub>3</sub> substrate [<xref ref-type="bibr" rid="B16">16</xref>]. The observation of only (00<italic>l</italic>) reflections indicates a single preferred (001) orientation (<xref ref-type="fig" rid="F9">Figure 9A</xref>). Shown in <xref ref-type="fig" rid="F9">Figure 9B</xref> is the double-crystal x-ray rocking curve for the (006) Bragg reflection, with a small FWHM of 0.22&#xb0;. To our knowledge, this is the best FWHM value observed so far among various iron-based superconductor crystals and films, indicating a high sample quality. The <italic>&#x00D8;</italic>-scan of (101) plane shown in <xref ref-type="fig" rid="F9">Figure 9C</xref> exhibits four successive peaks with an equal interval of 90&#xb0;, consistent with the <italic>C</italic>
<sub>4</sub> symmetry of the (Li,Fe)OHFeSe film. These results clearly demonstrate an excellent in-plane orientation and epitaxial growth.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>XRD characterizations of the (Li,Fe)OHFeSe film on the LaAlO<sub>3</sub> (LAO) substrate. <bold>(A)</bold> The two theta scan detects only (00<italic>l</italic>) peaks. <bold>(B)</bold> The rocking curve of (006) reflection with an FWHM of 0.22&#xb0;. <bold>(C)</bold> The <italic>
<bold>&#x03D5;</bold>
</italic>-scan of the (101) plane. The 4-fold symmetry reveals an excellent epitaxial growth [<xref ref-type="bibr" rid="B16">16</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g009.tif"/>
</fig>
<p>High-quality superconducting films can play an important role in the application. Besides the high sample quality, the (Li,Fe)OHFeSe films also display excellent superconducting properties. The temperature dependence of in-plane resistivity is shown in <xref ref-type="fig" rid="F10">Figure 10A</xref>, with a superconducting zero-resistivity temperature up to 42.4&#xa0;K. <xref ref-type="fig" rid="F10">Figure 10B</xref> is the temperature dependences of upper critical field <italic>H</italic>
<sub>c2</sub> derived from systematic measurements of the in-plane and out-of-plane magnetoresistance. Based on WHH (Werthamer-Helfand-Hohenberg) model, the values of <italic>H</italic>
<sub>c2</sub>(0) are estimated as 79.5 and 443&#xa0;T at magnetic fields perpendicular and parallel to the <italic>ab</italic> plane, respectively. Moreover, a large critical current density <italic>J</italic>
<sub>c</sub> &#x3e; 0.5&#xa0;MA/cm<sup>2</sup> was achieved at &#x223c;20&#xa0;K, as shown in <xref ref-type="fig" rid="F10">Figure 10C</xref>. The high superconducting critical parameters are important for practical application. Additionally, as seen from <xref ref-type="fig" rid="F11">Figure 11</xref>, the critical temperature <italic>T</italic>
<sub>c</sub> of (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OHFe<sub>0.98</sub>Se single crystal can be further raised up to a value &#x3e;50&#xa0;K under a pressure of 12.5&#xa0;GPa in the superconducting phase II (SC-II) region. The SC-II phase develops with pressure at a critical <italic>P</italic>
<sub>c</sub> &#x3d; 5&#xa0;GPa, as the superconducting phase I (SC-I) is gradually suppressed.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>High superconducting critical parameters for (Li,Fe)OHFeSe film. <bold>(A)</bold> Temperature dependence of in-plane resistivity, with the onset of zero resistivity at 42.4&#xa0;K. <bold>(B)</bold> Temperature dependence of <italic>H</italic>
<sub>c2</sub> along the <italic>c</italic>-axis (circle) and within the <italic>ab</italic> plane (square). <bold>(C)</bold> The temperature dependence of <italic>J</italic>
<sub>c</sub>, exceeding 0.5&#xa0;MA/cm<sup>2</sup> at 20&#xa0;K [<xref ref-type="bibr" rid="B16">16</xref>].</p>
</caption>
<graphic xlink:href="fphy-08-586182-g010.tif"/>
</fig>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Temperature-pressure phase diagram of (Li<sub>0.84</sub>Fe<sub>0.16</sub>)OHFe<sub>0.98</sub>Se single crystal [<xref ref-type="bibr" rid="B70">70</xref>]. Pressure-dependence of <italic>T</italic>
<sub>c</sub> and contour plot of the normal-state resistivity exponent <italic>&#x3b1;</italic> are shown up to 12.5 GPa.</p>
</caption>
<graphic xlink:href="fphy-08-586182-g011.tif"/>
</fig>
<p>Very recently, we have successfully doped Mn into (Li,Fe)OHFeSe films [<xref ref-type="bibr" rid="B17">17</xref>]. As seen from <xref ref-type="fig" rid="F12">Figure 12A</xref>, the <italic>J</italic>
<sub>c</sub> value of high-<italic>T</italic>
<sub>c</sub> (Li,Fe)OHFeSe film is strongly enhanced by one order of magnitude, from the undoped 0.03 to Mn-doped 0.32&#xa0;MA/cm<sup>2</sup> under 33&#xa0;T at 5&#xa0;K. The vortex pinning force density <italic>F</italic>
<sub>p</sub> monotonically increases with field up to 106&#xa0;GN/m<sup>3</sup>, shown in <xref ref-type="fig" rid="F12">Figure 12B</xref>. To the best of our knowledge, these values are the records so far among all the iron-based superconductors. Such a superconducting (Li,Fe)OHFeSe film is not only important for the fundamental research, but also promising for high-field application.</p>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>Magnetic field dependence of <italic>J</italic>
<sub>c</sub> <bold>(A)</bold> and <italic>F</italic>
<sub>p</sub> <bold>(B)</bold> of several superconductors [<xref ref-type="bibr" rid="B17">17</xref>], including Mn-doped and pure (Li,Fe)OHFeSe films at 5&#xa0;K, SmFeAs(O,F) films [<xref ref-type="bibr" rid="B95">95</xref>], FeSe<sub>0.5</sub>Te<sub>0.5</sub> films [<xref ref-type="bibr" rid="B96">96</xref>], P-doped BaFe<sub>2</sub>As<sub>2</sub> films [<xref ref-type="bibr" rid="B97">97</xref>], and YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7&#x2212;&#x3b4;</sub> wires [<xref ref-type="bibr" rid="B98">98</xref>] at 4.2&#xa0;K under c-axis fields.</p>
</caption>
<graphic xlink:href="fphy-08-586182-g012.tif"/>
</fig>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>Conclusion</title>
<p>High-quality single crystals and single-crystalline films of iron-based superconductors play an important role in both the basic research and potential application. However, for the FeSe-based superconductor systems reviewed here, by the conventional high-temperature growth it is either hard to obtain the single crystals and films, or not easy to tune the electronic properties. These problems can be overcome by our recently developed soft-chemical hydrothermal growth methods, which are capable of producing the single crystals and films, and tuning the chemical stoichiometry thus the electronic properties. In addition, these methods may be applicable in other layered materials, providing a new route for the exploration of functional materials.</p>
<p>The successful crystal and film growth has enabled systematic studies of the FeSe-based superconductor systems. We have observed a strong electronic two-dimensionality towards <italic>T</italic>
<sub>c</sub>, and a nearly linear extracted magnetic susceptibility as well as a linear in&#x2010;plane resistivity both emerging below a Hall&#x2010;dip temperature <italic>T&#x002A;</italic> (&#x223c;120 K), in high-<italic>T</italic>
<sub>c</sub> intercalated (Li,Fe)OHFeSe system. We have also observed a linear relationship between <italic>T</italic>
<sub>c</sub> and characteristic temperature <italic>T</italic>
<sub>sn</sub> of a field&#x2010;induced spin nematicity in prototypal FeSe system. These results suggest the presence of magnetic fluctuations in the iron planes and their relevance to superconductivity. Importantly, we have found that superconductivity of the prototypal FeSe emerges from the strongly correlated, hole-dominated Fe<sub>1&#x2212;x</sub>Se at a non-stoichiometric <italic>x</italic> similar to that for the high-<italic>T</italic>
<sub>c</sub> superconductivity of the FeSe-based intercalate of (Li, Fe)OHFeSe. An electronic phase diagram has been established for (Li, Fe)OHFeSe system, with the observed coexistence of antiferromagnetism and superconductivity explained by electronic phase separation. On the other hand, the high superconducting critical current density achieved in Mn-doped high-<italic>T</italic>
<sub>c</sub> (Li,Fe)OHFeSe film is promising for high-field application. These FeSe-based superconductor systems deserve further experimental and theoretical studies, in both aspects of the underlying physics and potential application.</p>
</sec>
<sec id="s5">
<title>Author Contributions</title>
<p>All authors contribute to the writing of the manuscript.</p>
</sec>
<sec id="s6">
<title>Funding</title>
<p>This work was supported by National Natural Science Foundation of China (Nos. 11834016 and 11888101), the National Key Research and Development Program of China (Grant Nos. 2017YFA0303003, 2016YFA0300300), and the Strategic Priority Research Program and Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant Nos. XDB25000000, QYZDY-SSW-SLH001).</p>
</sec>
<sec id="s7">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
</body>
<back>
<ack>
<p>We are very thankful to all our collaborators for their valuable scientific contributions in the past 6 years, especially Huaxue Zhou, Dongna Yuan, Yulong Huang, Yiyuan Mao, Shunli Ni, Jinpeng Tian, Dong Li, and Peipei Shen for sample preparation and characterization. We are also very grateful to Kui Jin, Jie Yuan, Wei Hu, and Zhongpei Feng for electrical transport measurements and insightful discussions; Jinguang Cheng and Jianping Sun for high-pressure research; Zian Li, Huaixin Yang, and Jianqi Li for TEM and EELS studies; Guangming Zhang and Zhenyu Zhang for theoretical support; Xingjiang Zhou and Lin Zhao for ARPES studies; Donglai Feng and Tong Zhang for STM studies; Li Pi, Chuanying Xi, Zhaosheng Wang, and J. Wosnitza for high-field studies; Rustem Khasanov, Zurab Guguchia, and Alex Amato for &#x3bc;SR studies. We also thank Ping Zheng, Shaokui Su, and Lihong Yang for technical supports.</p>
</ack>
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