## Volume 39 Issue 2

#### Highlighted Articles

Editors' Suggestion

#### Probing a Dissipative Phase Transition with a Trapped Ion through Reservoir Engineering

M.-L. Cai, Z.-D. Liu, Y. Jiang, Y.-K. Wu, Q.-X. Mei, W.-D. Zhao, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan
Chin. Phys. Lett., 2022, 39 (2): 020502   PDF ( 218 )   HTML ( 77 )
Editors' Suggestion

#### High Temperature Melting Curve of Basaltic Glass by Laser Flash Heating

Yukai Zhuang, Junwei Li, Wenhua Lu, Xueping Yang, Zhixue Du, and Qingyang Hu
Chin. Phys. Lett., 2022, 39 (2): 020701   PDF ( 163 )   HTML ( 97 )
Editors' Suggestion

#### First-Principles Calculations about Elastic and Li$^{+}$ Transport Properties of Lithium Superoxides under High Pressure and High Temperature

Yufeng Li, Shichuan Sun, Yu He, and Heping Li
Chin. Phys. Lett., 2022, 39 (2): 026101   PDF ( 207 )   HTML ( 116 )
Express Letter

#### Evidence for a High-Pressure Isostructural Transition in Nitrogen

Chunmei Fan, Shan Liu, Jingyi Liu, Binbin Wu, Qiqi Tang, Yu Tao, Meifang Pu, Feng Zhang, Jianfu Li, Xiaoli Wang, Duanwei He, Chunyin Zhou, and Li Lei
Chin. Phys. Lett., 2022, 39 (2): 026401   PDF ( 405 )   HTML ( 332 )
Express Letter

#### A Theory for Anisotropic Magnetoresistance in Materials with Two Vector Order Parameters

X. R. Wang
Chin. Phys. Lett., 2022, 39 (2): 027301   PDF ( 262 )   HTML ( 222 )
Editors' Suggestion

#### Superconductivity with a Violation of Pauli Limit and Evidences for Multigap in $\eta$-Carbide Type Ti$_4$Ir$_2$O

Bin-Bin Ruan, Meng-Hu Zhou, Qing-Song Yang, Ya-Dong Gu, Ming-Wei Ma, Gen-Fu Chen, and Zhi-An Ren
Chin. Phys. Lett., 2022, 39 (2): 027401   PDF ( 190 )   HTML ( 180 )
Express Letter

#### Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate $\alpha$-RuCl$_3$

Kejing Ran, Jinghui Wang, Song Bao, Zhengwei Cai, Yanyan Shangguan, Zhen Ma, Wei Wang, Zhao-Yang Dong, P. Čermák, A. Schneidewind, Siqin Meng, Zhilun Lu, Shun-Li Yu, Jian-Xin Li, and Jinsheng Wen
Chin. Phys. Lett., 2022, 39 (2): 027501   PDF ( 487 )   HTML ( 456 )

#### Current Issue

GENERAL
 Select Multi-Type Solitons in Spin-Orbit Coupled Spin-1 Bose–Einstein Condensates Jun-Tao He, Ping-Ping Fang, and Ji Lin Chin. Phys. Lett. 2022, 39 (2): 020301 .   DOI: 10.1088/0256-307X/39/2/020301 Abstract   PDF(pc) (549KB) ( 119 ) PDF(mobile)(649KB) ( 23 ) HTML ( 119 )  Recently, research of solitons in Bose–Einstein condensates has become a popular topic. Here, we mainly study exact analytical solutions of Gross–Pitaevskii equations describing spin-orbit coupled spin-1 Bose–Einstein condensates. To begin with, we show the analytical relation between different types of one-dimensional spin-orbit coupling and Zeeman effect. In addition, we find a transformation that can simplify the three-component Gross–Pitaevskii equations with spin-orbit coupling into the nonlinear Schrödinger equation. The abundant stripe phase and dynamic characteristics of the system are investigated.
 Select Dynamics of Two Dark Solitons in a Polariton Condensate Yiling Zhang, Chunyu Jia, and Zhaoxin Liang Chin. Phys. Lett. 2022, 39 (2): 020501 .   DOI: 10.1088/0256-307X/39/2/020501 Abstract   PDF(pc) (806KB) ( 109 ) PDF(mobile)(919KB) ( 18 ) HTML ( 107 )  We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping, based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation. The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach. In particular, the analytical expression of the effective potential between two dark solitons is given. The resulting equation of motion captures how the open-dissipative character of a polariton Bose–Einstein condensate affects properties of dynamics of two-dark soliton, i.e., two-dark soliton relax by blending with the background at a finite time. We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity, in excellent agreement with the analytical results. The prediction of this work is sufficient for the experimental observations within current facilities.
 Select Probing a Dissipative Phase Transition with a Trapped Ion through Reservoir Engineering M.-L. Cai, Z.-D. Liu, Y. Jiang, Y.-K. Wu, Q.-X. Mei, W.-D. Zhao, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan Chin. Phys. Lett. 2022, 39 (2): 020502 .   DOI: 10.1088/0256-307X/39/2/020502 Abstract   PDF(pc) (1402KB) ( 218 ) PDF(mobile)(1636KB) ( 11 ) HTML ( 77 )  Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources in both quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms.
 Select High Temperature Melting Curve of Basaltic Glass by Laser Flash Heating Yukai Zhuang, Junwei Li, Wenhua Lu, Xueping Yang, Zhixue Du, and Qingyang Hu Chin. Phys. Lett. 2022, 39 (2): 020701 .   DOI: 10.1088/0256-307X/39/2/020701 Abstract   PDF(pc) (2446KB) ( 163 ) PDF(mobile)(2550KB) ( 17 ) HTML ( 97 )  Basalt is an igneous rock originating from the cooling and solidification of magma and covers approximately 70% of Earth's surface. Basaltic glass melting in the deep Earth is a fundamental subject of research for understanding geophysics, geochemistry, and geodynamic processes. In this study, we design a laser flash heating system using two-dimensional, four-color multi-wavelength imaging radiometry to measure the basaltic glass melting temperature under high pressure conditions in diamond anvil cells. Our experiment not only determines the temperature at the center of heating but also constructs a temperature distribution map for the surface heating area, and enables us to assess the temperature gradient. Through precise temperature measurements, we observe that the basaltic glass melting temperature is higher than those in previous reports, which is near the normal upper-mantle isotherm, approaching the hot geotherm. This suggests that basalt should not melt in most of the normal upper mantle and the basaltic melts could exist in some hot regions.
THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 Select Chiral Anomaly in Non-Relativistic Systems: Berry Curvature and Chiral Kinetic Theory Lan-Lan Gao and Xu-Guang Huang Chin. Phys. Lett. 2022, 39 (2): 021101 .   DOI: 10.1088/0256-307X/39/2/021101 Abstract   PDF(pc) (431KB) ( 94 ) PDF(mobile)(535KB) ( 9 ) HTML ( 67 )  Chiral anomaly and the novel quantum phenomena it induces have been widely studied for Dirac and Weyl fermions. In most typical cases, the Lorentz covariance is assumed and thus the linear dispersion relations are maintained. However, in realistic materials, such as Dirac and Weyl semimetals, the nonlinear dispersion relations appear naturally. We develop a kinetic framework to study the chiral anomaly for Weyl fermions with nonlinear dispersions using the methods of Wigner function and semi-classical equations of motion. In this framework, the chiral anomaly is sourced by Berry monopoles in momentum space and could be enhanced or suppressed due to the windings around the Berry monopoles. Our results can help understand the chiral anomaly-induced transport phenomena in non-relativistic systems.
ATOMIC AND MOLECULAR PHYSICS
 Select Identification of Above-Threshold Ionization by Imaging Photoelectrons from Ammonia Molecules in an Intense Femtosecond Laser Field Qin Yang, Jing Leng, Yan-Hui Wang, Ya-Nan Sun, Hai-Bin Du, Dong-Dong Zhang, Le-Le Song, Lan-Hai He, and Fu-Chun Liu Chin. Phys. Lett. 2022, 39 (2): 023301 .   DOI: 10.1088/0256-307X/39/2/023301 Abstract   PDF(pc) (753KB) ( 95 ) PDF(mobile)(860KB) ( 11 ) HTML ( 92 )  The above-threshold ionization process of ammonia molecules induced by a femtosecond laser field at 800 nm is studied in the intensity range from $1.6 \times 10^{13}$ to $5.7 \times 10^{13}$ W/cm$^{2}$. Channel switching under different laser intensities is observed and identified in the photoelectron kinetic energy spectra of ammonia. Based on the photoelectron kinetic energy distributions and the photoelectron angular distributions, the characteristic peaks observed are exclusively assigned to the multiphoton resonance through certain intermediate states, followed by multiphoton above-threshold ionization.
FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS)
 Select An All-Fiberized Chirped Pulse Amplification System Based on Chirped Fiber Bragg Grating Stretcher and Compressor Ming-Xiao Wang, Ping-Xue Li, Yang-Tao Xu, Yun-Chen Zhu, Shun Li, and Chuan-Fei Yao Chin. Phys. Lett. 2022, 39 (2): 024201 .   DOI: 10.1088/0256-307X/39/2/024201 Abstract   PDF(pc) (1505KB) ( 114 ) PDF(mobile)(1599KB) ( 13 ) HTML ( 235 )  We report an all-fiberized chirped pulse amplification system without any bulk devices. The stretcher and compressor are chirped fiber Bragg gratings inscribed in a 6/125 µm single-mode fiber and a 30/250 µm large-mode-area fiber. The fabrication system of chirped fiber Bragg gratings was designed and built by ourselves. The width of the linear exposure spot was controlled according to the different fiber sizes to improve the fabrication quality, and the parameters of chirped fiber Bragg gratings were fine-tuned during the fabrication to achieve the overall system's spectral matching. Two fiber circulators with the same fiber sizes as the chirped fiber Bragg gratings were employed to auxiliarily achieve the pulse stretching and compression. The dispersion accumulations provided by the stretcher and compressor are 129.8 ps and 90.8 ps. The power amplifiers were composed of the two-stage 10/130 µm fiber pre-amplifier and the 30/250 µm fiber main amplifier. The proposed chirped pulse amplification system with no spatial light is the true sense of an all-fiberized chirped pulse amplification structure and shows the main trend in development of ultrashort pulse fiber lasers.
PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
 Select Transverse Rutherford Scattering of Electron-Ion Collision in a Uniformly Magnetized Plasma Chang Jiang, Chao Dong, and Ding Li Chin. Phys. Lett. 2022, 39 (2): 025201 .   DOI: 10.1088/0256-307X/39/2/025201 Abstract   PDF(pc) (437KB) ( 85 ) PDF(mobile)(551KB) ( 7 ) HTML ( 83 )  Rutherford scattering formula plays an important role in plasma classical transport. It is urgent to investigate influence of magnetic field on the Rutherford scattering since the high magnetic field has been widely used in nowadays magnetic confinement fusion, inertial confinement fusion, and magneto-inertial fusion. In order to elucidate the magnetic field effect in a concise manner, we study the electron-ion collisions transverse to the magnetic field. The scattering angle is defined using the directions of electron velocity before and after collision, which is obtained analytically. It is found that the scattering angle can be influenced by finite magnetic field significantly. The theoretical results agree well with numerical calculation by checking the dependence of scattering angle on the magnetic field.
CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES
 Select First-Principles Calculations about Elastic and Li$^{+}$ Transport Properties of Lithium Superoxides under High Pressure and High Temperature Yufeng Li, Shichuan Sun, Yu He, and Heping Li Chin. Phys. Lett. 2022, 39 (2): 026101 .   DOI: 10.1088/0256-307X/39/2/026101 Abstract   PDF(pc) (2075KB) ( 207 ) PDF(mobile)(3026KB) ( 17 ) HTML ( 116 )  Lithium superoxides, Li$_{2}$O$_{3}$, LiO$_{2}$, and LiO$_{4}$, have been synthesized under high pressure. These materials have potential applications in energy storage devices. Here, we use first-principles calculations to investigate the elastic and Li$^{+}$ transport properties of these oxides at high pressure and high temperature. The elastic constants are calculated at 20–80 GPa, and they satisfy the Born stability criteria, indicating the good mechanical stability of these oxides. Their sound velocities calculated with elastic constants are close to each other, but difference in velocity anisotropy is obvious. LiO$_{2}$ presents significant shear sound wave anisotropy over 80%. The Li$^{+}$ transport properties are investigated using first principles molecular dynamics (FPMD) and climbing-image nudged elastic band methods. The lowest Li$^{+}$ migration barrier energies increase from 0.93, 0.86 and 1.22 eV at 20 GPa to 1.43, 1.12 and 1.77 eV at 50 GPa for Li$_{2}$O$_{3}$, LiO$_{2}$, and LiO$_{4}$, respectively. The most favorable path for LiO$_{2}$ and LiO$_{4}$ is along the [001] direction. The FPMD results suggest that these oxides become unstable with increasing temperature up to 2000 K due to O–O dimer clusters in these superoxides. Consequently, a superionic transition is not observed in the simulations.
 Select Evidence for a High-Pressure Isostructural Transition in Nitrogen Chunmei Fan, Shan Liu, Jingyi Liu, Binbin Wu, Qiqi Tang, Yu Tao, Meifang Pu, Feng Zhang, Jianfu Li, Xiaoli Wang, Duanwei He, Chunyin Zhou, and Li Lei Chin. Phys. Lett. 2022, 39 (2): 026401 .   DOI: 10.1088/0256-307X/39/2/026401 Abstract   PDF(pc) (2897KB) ( 405 ) PDF(mobile)(4876KB) ( 117 ) HTML ( 332 )  We observed an isostructural phase transition in the solid nitrogen $\lambda$-N$_{2}$ at approximately 50 GPa accompanied by anomalies in lattice parameters, atomic volume and Raman vibron modes. The anomalies are ascribed to a slight reorientation of the nitrogen molecules, which does not seem to affect the monoclinic symmetry (space group $P2_{1}/c$). Our ab initio calculations further confirm the phenomena, and suggest an optimized structure for the $\lambda$-N$_{2}$ phase. In addition, a new high-pressure amorphous phase of $\eta '$-N$_{2}$ was also discovered by a detailed investigation of the pressure-temperature phase diagram of nitrogen with the aim of probing the phase stability of $\lambda$-N$_{2}$. Our result may provide helpful information about the crystallographic nature of dissociation transitions in diatomic molecular crystals (H$_{2}$, O$_{2}$, N$_{2}$, etc).
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES
 Select A Theory for Anisotropic Magnetoresistance in Materials with Two Vector Order Parameters X. R. Wang Chin. Phys. Lett. 2022, 39 (2): 027301 .   DOI: 10.1088/0256-307X/39/2/027301 Abstract   PDF(pc) (304KB) ( 262 ) PDF(mobile)(426KB) ( 32 ) HTML ( 222 )  Anisotropic magnetoresistance (AMR) and related planar Hall resistance (PHR) are ubiquitous phenomena of magnetic materials. Although the universal angular dependences of AMR and PHR in magnetic polycrystalline materials with one order parameter are well known, no similar universal relation for other class of magnetic materials are known to date. Here a general theory of galvanomagnetic effects in magnetic materials is presented with two vector order parameters, such as magnetic single crystals with a dominated crystalline axis or polycrystalline non-collinear ferrimagnetic materials. It is shown that AMR and PHR have a universal angular dependence. In general, both longitudinal and transverse resistivity are non-reciprocal in the absence of inversion symmetry: Resistivity takes different values when the current is reversed. Different from simple magnetic polycrystalline materials where AMR and PHR have the same magnitude, and $\pi/4$ out of phase, the magnitudes of AMR and PHR of materials with two vector order parameters are not the same in general, and the phase difference is not $\pi/4$. Instead of $\pi$ periodicity of the usual AMR and PHR, the periodicities of materials with two order parameters are $2\pi$.
 Select Superconductivity with a Violation of Pauli Limit and Evidences for Multigap in $\eta$-Carbide Type Ti$_4$Ir$_2$O Bin-Bin Ruan, Meng-Hu Zhou, Qing-Song Yang, Ya-Dong Gu, Ming-Wei Ma, Gen-Fu Chen, and Zhi-An Ren Chin. Phys. Lett. 2022, 39 (2): 027401 .   DOI: 10.1088/0256-307X/39/2/027401 Abstract   PDF(pc) (2430KB) ( 190 ) PDF(mobile)(2621KB) ( 13 ) HTML ( 180 )  We report the synthesis, crystal structure, and superconductivity of Ti$_4$Ir$_2$O. The title compound crystallizes in an $\eta$-carbide type structure of the space group $Fd\bar{3}m$ (No. 227), with lattice parameters $a=b=c=11.6194(1)$ Å. The superconducting temperature $T_{\rm c}$ is found to be 5.1–5.7 K. Most surprisingly, Ti$_4$Ir$_2$O hosts an upper critical field of 16.45 T, which is far beyond the Pauli paramagnetic limit. Strong coupled superconductivity with evidences for multigap is revealed by the measurements of heat capacity and upper critical field. First-principles calculations suggest that the density of states near the Fermi level originates from the hybridization of Ti-3$d$ and Ir-5$d$ orbitals, and the effect of spin-orbit coupling on the Fermi surfaces is prominent. Large values of the Wilson ratio ($R_{\rm W} \sim 3.9$), the Kadowaki–Woods ratio [$A/\gamma^2 \sim 9.0 \times 10^{-6}$ $µ\Omega\cdot$cm/(mJ$\cdot$mol$^{-1}\cdot$K$^{-1}$)$^2$], and the Sommerfeld coefficient ($\gamma = 33.74$ mJ$\cdot$mol$^{-1}\cdot$K$^{-2}$) all suggest strong electron correlations (similar to heavy fermion systems) in Ti$_4$Ir$_2$O. The violation of Pauli limit is possibly due to a combination of strong-coupled superconductivity and large spin-orbit scattering. With these intriguing behaviors, Ti$_4$Ir$_2$O serves as a candidate for unconventional superconductor.
 Select Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate $\alpha$-RuCl$_3$ Kejing Ran, Jinghui Wang, Song Bao, Zhengwei Cai, Yanyan Shangguan, Zhen Ma, Wei Wang, Zhao-Yang Dong, P. Čermák, A. Schneidewind, Siqin Meng, Zhilun Lu, Shun-Li Yu, Jian-Xin Li, and Jinsheng Wen Chin. Phys. Lett. 2022, 39 (2): 027501 .   DOI: 10.1088/0256-307X/39/2/027501 Abstract   PDF(pc) (1105KB) ( 487 ) PDF(mobile)(1205KB) ( 36 ) HTML ( 456 )  It is known that $\alpha$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $\alpha$-RuCl$_3$ single crystals to explore the scattering continuum around the $\varGamma$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the $M$ point vanish above the transition temperature $T_{\rm N}$, the pure magnetic continuous excitations around the $\varGamma$ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the $K$–$\varGamma$ model, which involves with a ferromagnetic Kitaev interaction of $-7.2$ meV and an off-diagonal interaction of $5.6$ meV. We find this model can reproduce not only the spin-wave excitation spectra around the $M$ point, but also the non-spin-wave continuous magnetic excitations around the $\varGamma$ point. These results provide evidence for the existence of fractional excitations around the $\varGamma$ point originating from the Kitaev QSL state, and further support the validity of the $K$–$\varGamma$ model as the effective minimal spin model to describe $\alpha$-RuCl$_3$.
CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY
 Select Wet Mechanical Milling Induced Phase Transition to Cubic Anti-Perovskite Li$_{2}$OHCl Di-Xing Ni, Yao-Dong Liu, Zhi Deng, Dian-Cheng Chen, Xin-Xin Zhang, Tao Wang, Shuai Li, and Yu-Sheng Zhao Chin. Phys. Lett. 2022, 39 (2): 028201 .   DOI: 10.1088/0256-307X/39/2/028201 Abstract   PDF(pc) (990KB) ( 94 ) PDF(mobile)(1084KB) ( 15 ) HTML ( 133 )  Anti-perovskite solid-state electrolyte Li$_{2}$OHCl usually exhibits orthorhombic phase and low ionic conductivity at room temperature. However, its ionic conductivity increases greatly when the temperature is up to 40 ℃, while it goes through an orthorhombic-to-cubic phase transition. The cubic Li$_{2}$OHCl with high ionic conductivity is stabilized at room temperature and even lower temperature about 10 ℃ by a simple synthesis method of wet mechanical milling. The cubic Li$_{2}$OHCl prepared by this method performs an ionic conductivity of $4.27 \times 10^{-6}$ S/cm at room temperature, about one order of magnitude higher than that of the orthorhombic Li$_{2}$OHCl. The phase-transition temperature is decreased to around 10 ℃. Moreover, it can still remain cubic phase after heat treatment at 210 ℃. This work delivers a huge potential of fabricating high ionic conductivity phase anti-perovskite solid-state electrolyte materials by wet mechanical milling.
 Select Electrochemical Role of Transition Metals in Sn–Fe Alloy Revealed by Operando Magnetometry Le-Qing Zhang, Qing-Tao Xia, Zhao-Hui Li, Yuan-Yuan Han, Xi-Xiang Xu, Xin-Long Zhao, Xia Wang, Yuan-Yuan Pan, Hong-Sen Li, and Qiang Li Chin. Phys. Lett. 2022, 39 (2): 028202 .   DOI: 10.1088/0256-307X/39/2/028202 Abstract   PDF(pc) (1368KB) ( 33 ) PDF(mobile)(1500KB) ( 5 ) HTML ( 84 )  As promising materials, alloy-type anode materials have been intensively investigated in both academia and industry. To release huge volume expansion during alloying/dealloying process, they are usually doped with transition metals. However, the electrochemical role of transition metals has not been fully understood. Here, pure Sn$_{3}$Fe films were deposited by sputtering, and the electrochemical mechanism was systematically investigated by operando magnetometry. We confirmed that Fe particles liberated by Li insertion recombine partially with Sn during the delithiation, while the stepwise increase in magnetization with the cycles demonstrates growth of Fe nanoparticles. In addition, we also found an unconventional increase of magnetization in the charging process, which can be attributed to the space charge storage at the interface of Fe/Li$_{x}$Sn. These critical findings pave the way for the mechanism understanding and development of high-performance Sn based alloy electrode materials.
15 articles