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 Select Pauli Radius of the Proton Zhu-Fang Cui, Daniele Binosi, Craig D Roberts, and Sebastian M Schmidt Chin. Phys. Lett.    2021, 38 (12): 121401 .   DOI: 10.1088/0256-307X/38/12/121401 Abstract   HTML   PDF (491KB) Using a procedure based on interpolation via continued fractions supplemented by statistical sampling, we analyze proton magnetic form factor data obtained via electron+proton scattering on $Q^2 \in [0.027,0.55]$ GeV$^2$ with the goal of determining the proton magnetic radius. The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto $Q^2\simeq 0$ for extraction of the form factor slope. In this way, we find $r_{\scriptscriptstyle {\rm M}} = 0.817(27)$ fm. Regarding the difference between proton electric and magnetic radii calculated in this way, extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors, $F_{1,2}(Q^2)$, are not truly independent observables; to wit, the difference $F_1^\prime(0)-F_2^\prime(0)/\kappa_{\rm p} = [1+\kappa_{\rm p}]/[4 m_{\rm p}^2]$, viz., the proton Foldy term.
 Select Unexpected Selective Absorption of Lithium in Thermally Reduced Graphene Oxide Membranes Jie Jiang, Liuhua Mu, Yu Qiang, Yizhou Yang, Zhikun Wang, Ruobing Yi, Yinwei Qiu, Liang Chen, Long Yan, and Haiping Fang Chin. Phys. Lett.    2021, 38 (11): 116802 .   DOI: 10.1088/0256-307X/38/11/116802 Abstract   HTML   PDF (1580KB) Lithium plays an increasingly important role in scientific and industrial processes, and it is extremely important to extract lithium from a high Mg$^{2+}$/Li$^{+}$ mass ratio brine or to recover lithium from the leachate of spent lithium-ion batteries. Conventional wisdom shows that Li$^{+}$ with low valence states has a much weaker adsorption (and absorption energy) with graphene than multivalent ions such as Mg$^{2+}$. Here, we show the selective adsorption of Li$^{+}$ in thermally reduced graphene oxide (rGO) membranes over other metal ions such as Mg$^{2+}$, Co$^{2+}$, Mn$^{2+}$, Ni$^{2+}$, or Fe$^{2+}$. Interestingly, the adsorption strength of Li$^{+}$ reaches up to 5 times the adsorption strength of Mg$^{2+}$, and the mass ratio of a mixed Mg$^{2+}$/Li$^{+}$ solution at a very high value of $500\!:\!1$ can be effectively reduced to $0.7\!:\!1$ within only six experimental treatment cycles, demonstrating the excellent applicability of the rGO membranes in the Mg$^{2+}$/Li$^{+}$ separation. A theoretical analysis indicates that this unexpected selectivity is attributed to the competition between cation–$\pi$ interaction and steric exclusion when hydrated cations enter the confined space of the rGO membranes.
 Select High $T_{\rm c}$ Superconductivity in Heavy Rare Earth Hydrides Hao Song, Zihan Zhang, Tian Cui, Chris J. Pickard, Vladimir Z. Kresin, and Defang Duan Chin. Phys. Lett.    2021, 38 (10): 107401 .   DOI: 10.1088/0256-307X/38/10/107401 Abstract   HTML   PDF (3378KB) Sulfur and lanthanum hydrides under compression display superconducting states with high observed critical temperatures. It has been recently demonstrated that carbonaceous sulfur hydride displays room temperature superconductivity. However, this phenomenon has been observed only at very high pressure. Here, we theoretically search for superconductors with very high critical temperatures, but at much lower pressures. We describe two of such sodalite-type clathrate hydrides, YbH$_{6}$ and LuH$_{6}$. These hydrides are metastable and are predicted to superconduct with $T_{\rm c} \sim 145$ K at 70 GPa and $T_{\rm c} \sim 273$ K at 100 GPa, respectively. This striking result is a consequence of the strong interrelationship between the $f$ states present at the Fermi level, structural stability, and the final $T_{\rm c}$ value. For example, TmH$_{6}$, with unfilled 4$f$ orbitals, is stable at 50 GPa, but has a relatively low value of $T_{\rm c}$ of 25 K. The YbH$_{6}$ and LuH$_{6}$ compounds, with their filled $f$-shells, exhibit prominent phonon “softening”, which leads to a strong electron-phonon coupling, and as a result, an increase in $T_{\rm c}$.
 Select Learning the Effective Spin Hamiltonian of a Quantum Magnet Sizhuo Yu, Yuan Gao, Bin-Bin Chen, and Wei Li Chin. Phys. Lett.    2021, 38 (9): 097502 .   DOI: 10.1088/0256-307X/38/9/097502 Abstract   HTML   PDF (9884KB) To understand the intriguing many-body states and effects in the correlated quantum materials, inference of the microscopic effective Hamiltonian from experiments constitutes an important yet very challenging inverse problem. Here we propose an unbiased and efficient approach learning the effective Hamiltonian through the many-body analysis of the measured thermal data. Our approach combines the strategies including the automatic gradient and Bayesian optimization with the thermodynamics many-body solvers including the exact diagonalization and the tensor renormalization group methods. We showcase the accuracy and powerfulness of the Hamiltonian learning by applying it firstly to the thermal data generated from a given spin model, and then to realistic experimental data measured in the spin-chain compound copper nitrate and triangular-lattice magnet TmMgGaO$_4$. The present automatic approach constitutes a unified framework of many-body thermal data analysis in the studies of quantum magnets and strongly correlated materials in general.
 Select Observation of a Ubiquitous ($\pi, \pi$)-Type Nematic Superconducting Order in the Whole Superconducting Dome of Ultra-Thin BaFe$_{2-x}$Ni$_x$As$_2$ Single Crystals Yu Dong, Yangyang Lv, Zuyu Xu, M. Abdel-Hafiez, A. N. Vasiliev, Haipeng Zhu, Junfeng Wang, Liang Li, Wanghao Tian, Wei Chen, Song Bao, Jinghui Wang, Yueshen Wu, Yulong Huang, Shiliang Li, Jie Yuan, Kui Jin, Labao Zhang, Huabing Wang, Shun-Li Yu, Jinsheng Wen, Jian-Xin Li, Jun Li, and Peiheng Wu Chin. Phys. Lett.    2021, 38 (9): 097401 .   DOI: 10.1088/0256-307X/38/9/097401 Abstract   HTML   PDF (3010KB) In iron-based superconductors, the ($0, \pi$) or ($\pi, 0$) nematicity, which describes an electronic anisotropy with a four-fold symmetry breaking, is well established and believed to be important for understanding the superconducting mechanism. However, how exactly such a nematic order observed in the normal state can be related to the superconducting pairing is still elusive. Here, by performing angular-dependent in-plane magnetoresistivity using ultra-thin flakes in the steep superconducting transition region, we unveil a nematic superconducting order along the ($\pi, \pi$) direction in electron-doped BaFe$_{2-x}$Ni$_x$As$_2$ from under-doped to heavily overdoped regimes with $x=0.065$–0.18. It shows superconducting gap maxima along the ($\pi, \pi$) direction rotated by 45$^\circ$ from the nematicity along ($0, \pi$) or ($\pi, 0$) direction observed in the normal state. A similar ($\pi, \pi$)-type nematicity is also observed in the under-doped and optimally doped hole-type Ba$_{1-y}$K$_y$Fe$_2$As$_2$, with $y = 0.2$–0.5. These results suggest that the ($\pi, \pi$) nematic superconducting order is a universal feature that needs to be taken into account in the superconducting pairing mechanism in iron-based superconductors.
 Select Magnetic Order and Its Interplay with Structure Phase Transition in van der Waals Ferromagnet VI$_{3}$ Yiqing Hao, Yiqing Gu, Yimeng Gu, Erxi Feng, Huibo Cao, Songxue Chi, Hua Wu, and Jun Zhao Chin. Phys. Lett.    2021, 38 (9): 096101 .   DOI: 10.1088/0256-307X/38/9/096101 Abstract   HTML   PDF (1534KB) Van der Waals magnet VI$_{3}$ demonstrates intriguing magnetic properties that render it great for use in various applications. However, its microscopic magnetic structure has not been determined yet. Here, we report neutron diffraction and susceptibility measurements in VI$_{3}$ that revealed a ferromagnetic order with the moment direction tilted from the $c$-axis by $\sim $$36^{\circ} at 4 K. A spin reorientation accompanied by a structure distortion within the honeycomb plane is observed, before the magnetic order completely disappears at T_{\rm C} = 50 K. The refined magnetic moment of \sim$$1.3 \mu_{\scriptscriptstyle {\rm B}}$ at 4 K is much lower than the fully ordered spin moment of $2\mu_{\scriptscriptstyle {\rm B}}$/V$^{3+}$, suggesting the presence of a considerable orbital moment antiparallel to the spin moment and strong spin–orbit coupling in VI$_{3}$. This results in strong magnetoelastic interactions that make the magnetic properties of VI$_{3}$ easily tunable via strain and pressure.
 Select Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu$_3$Zn(OH)$_6$FBr Yuan Wei, Xiaoyan Ma, Zili Feng, Yongchao Zhang, Lu Zhang, Huaixin Yang, Yang Qi, Zi Yang Meng, Yan-Cheng Wang, Youguo Shi, and Shiliang Li Chin. Phys. Lett.    2021, 38 (9): 097501 .   DOI: 10.1088/0256-307X/38/9/097501 Abstract   HTML   PDF (4042KB) We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.
 Select PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum Qianju Song, Shiwei Dai, Dezhuan Han, Z. Q. Zhang, C. T. Chan, and Jian Zi Chin. Phys. Lett.    2021, 38 (8): 084203 .   DOI: 10.1088/0256-307X/38/8/084203 Abstract   HTML   PDF (2264KB) It is well known that spatial symmetry in a photonic crystal (PhC) slab is capable of creating bound states in the continuum (BICs), which can be characterized by topological charges of polarization vortices. Here, we show that when a PT-symmetric perturbation is introduced into the PhC slab, a new type of BICs ($pt$-BICs) will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with $pt$-BICs embedded in these rings. Different from ordinary BICs, the $Q$-factor divergence rate of a $pt$-BIC is reduced and anisotropic in momentum space. Also, $pt$-BICs can even appear at off-high symmetry lines of the Brillouin zone. The $pt$-BICs also carry topological charges and can be created or annihilated with the total charge conserved. A unified picture on $pt$-BICs and the associated lasing threshold modes is given based on the temporal coupled mode theory. Our findings reveal the new physics arising from the interplay between PT symmetry and BIC in PhC slabs.