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Motivated by the recent observations of various exotic quantum states in the equilateral triangular-lattice phosphates Na$_2$BaCo(PO$_4$)$_2$ with $J\rm_{eff}$ = 1/2 and Na$_2$BaNi(PO$_4$)$_2$ with $S$ = 1, the magnetic properties of spin-5/2 antiferromagnet Na$_2$BaMn(PO$_4$)$_2$, their classical counterpart, are comprehensively investigated experimentally. DC magnetization and specific heat measurements on polycrystalline samples indicate two successive magnetic transitions at $T\rm_{N1}$ $\approx$ 1.13 K and $T\rm_{N2}$ $\approx$ 1.28 K, respectively. Zero-field neutron powder diffraction measurement at 67 mK reveals a Y-like spin configuration as its ground-state magnetic structure, with both the $ab$-plane and $c$-axis components of the Mn$^{2+}$ moments long-range ordered. The incommensurate magnetic propagation vector $k$ shows a dramatic change for the intermediate phase between $T\rm_{N1}$ and $T\rm_{N2}$, in which the spin state is speculated to change into a collinear structure with only the $c$-axis moments ordered, as stabilized by thermal fluctuations. The successive magnetic transitions observed in Na$_2$BaMn(PO$_4$)$_2$ are in line with the expectation for a triangle-lattice antiferromagnet with an easy-axis magnetic anisotropy., Comment: 8 Pages, 6 figures

To realize ferromagnetic semiconductors with high Curie temperature TC is still a challenge in spintronics. Recent experiments have obtained two-dimensional (2D) room temperature ferromagnetic metals, such as monolayers MnSe2 and Cr3Te6. In this paper, by the density functional theory (DFT) calculations, we proposed a way to obtain 2D high TC ferromagnetic semiconductors through element replacement in these ferromagnetic metals. High TC ferromagnetic semiconductors are predicted in the monolayers (Mn, D)Se2 and (Cr, D)3Te6, where element D is taken as vacancy, 3d, 4d and 5d transition metal elements. For the concentrations of D from 1/9 to 1/3, there are about 10 ferromagnetic semiconductors with TC above 200 K, including (Cr5/6, W1/6)3Te6 and (Cr4/6, Mo2/6)3Te6 with TC above 300 K. In addition, Mn(Se6/8, Sb2/8)2 is also predicted to be a 2D ferromagnetic semiconductor with TC above 300 K. Considering the fast developments on fabrication and manipulation of 2D materials, our theoretical results propose a way to explore the high temperature ferromagnetic semiconductors from experimentally obtained 2D high temperature ferromagnetic metals through element replacement approach.

Loop current order has been suggested as a promising candidate for the spontaneous time-reversal symmetry breaking $2a_0 \times 2a_0$ charge density wave (CDW) revealed in vanadium-based kagom\'e metals \avs\ ($A$ = K, Rb, Cs) near van Hove filling $n_\text{vH} = 5/12$. Weak-coupling analyses and mean field calculations have demonstrated that nearest-neighbor Coulomb repulsion $V_1$ and next-nearest-neighbor Coulomb repulsion $V_2$ drives, respectively, real and imaginary bond-ordered CDW, with the latter corresponding to time-reversal symmetry breaking loop current CDW. It is important to understand the inter-layer correlation of these bond-ordered CDWs and its consequences in the bulk kagom\'e materials. To provide physical insights, we investigate in this paper the $c$-axis stacking of them, loop current CDW in particular, on the minimal bilayer kagom\'e lattice. The bare susceptibilities for stacking of real and imaginary bond orders are calculated for the free electrons on the bilayer kagom\'e lattice with inter-layer coupling $t_\perp=0.2t$, which splits the van Hove filling to $n_{+\text{vH}}=4.64/12$ and $n_{-\text{vH}}=5.44/12$. While real and imaginary bond-ordered CDWs are still favored, respectively, by $V_1$ and $V_2$, their inter-layer coupling is sensitive to band filling $n$. They tend to stack symmetrically near $n_{\pm\text{vH}}$ with identical bond orders in the two layers and give rise to a $2a_0 \times 2a_0 \times 1c_0$ CDW. On the other hand, they prefer to stack antisymmetrically around $n_\text{vH}$ with opposite bond orders in the two layers and lead to a $2a_0 \times 2a_0 \times 2c_0$ CDW. The concrete bilayer $t$-$t_\perp$-$V_1$-V$_2$ model is then studied. We obtain the mean-field ground states and determine the inter-layer coupling as a function of band filling at various interactions. The nontrivial topological properties of loop current CDWs are studied ..., Comment: 12 pages, 8 figures, 2 tables

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free $Z_2$ vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface. Potential realization of topological excitation cooling in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates., Comment: 10 pages, 4 figures; supplementary materials; to appear in Nat. Commun. (2024)

Identifying the exotic quantum spin liquid phase in Kitaev magnets has garnered great research interests and remains a significant challenge. In experiments, most of the proposed candidate materials exhibit an antiferromagnetic (AFM) order at low temperatures, thus the challenge transforms into the searching for a field-driven disordered phase that is distinct from the partially polarized paramagnetic phase after suppressing the AFM order. Recently, Na$_2$Co$_2$TeO$_6$ has been proposed as one of the prime candidates, where the Kitaev interaction is realized by the high-spin $t^{5}_{2g}e^2_g$ configuration, and spin-orbit entangled $J_{\rm eff} = 1/2$ state in a bond-edge shared honeycomb lattice. In this study, we identify an emergent intermediate disordered phase induced by an external field along the $c$-axis of the honeycomb plane. This phase is characterized through magnetization and magnetocaloric effect experiments in high magnetic fields. To explain the experimental results, we propose an effective spin model with large AFM Kitaev interaction, which yields results in good agreement with both our findings and previously reported data. We determine that the effective $K$-$J$-$\Gamma$-$\Gamma'$ model for Na$_2$Co$_2$TeO$_6$ is nearly dual to that of $\alpha$-RuCl$_3$ under an unitary transformation. Given the insignificant fragility of Na$_2$Co$_2$TeO$_6$ sample, further high-field experiments can be conducted to explore this intermediate-field quantum spin disordered phase., Comment: 12 pages, 8 figures

In recent years, nonlinear Hall effect has attracted great attention with three different terms contributed by Drude effect, Berry curvature dipole and Berry connection polarizability. In this work, we theoretically predict an intrinsic second order spin current induced by spin-dependent Berry curvature polarizability based on time-independent perturbation theory. We show other two second order spin conductivities contributed by the group velocity and spin-dependent Berry curvature dipole.A two-dimensional Rashba-Dresselhaus spin-orbit coupled system is studied as an example, and it is found that the intrinsic second order contribution plays a major role in the region of $\mu>0$, while current mainly comes from the extrinsic terms when $\mu<0$. Thus, the dependence of spin conductivity on chemical potential is expected to distinguish the extrinsic and intrinsic contributions experimentally., Comment: 13 pages,4 figures

The steam drum water level is a critical parameter that directly impacts the safety and efficiency of power plant operations. However, predicting the drum water level in boilers is challenging due to complex non-linear process dynamics originating from long-time delays and interrelations, as well as measurement noise. This paper investigates the application of Transformer-based models for predicting drum water levels in a steam boiler plant. Leveraging the capabilities of Transformer architectures, this study aims to develop an accurate and robust predictive framework to anticipate water level fluctuations and facilitate proactive control strategies. To this end, a prudent pipeline is proposed, including 1) data preprocess, 2) causal relation analysis, 3) delay inference, 4) variable augmentation, and 5) prediction. Through extensive experimentation and analysis, the effectiveness of Transformer-based approaches in steam drum water level prediction is evaluated, highlighting their potential to enhance operational stability and optimize plant performance., Comment: under review of IEEE PES ISGT Europe 2024 conference

A recent experiment has reported a nitrogen-doped lutetium hydride acheving a remarkable Tc of 294 K at just 1 GPa, significantly reducing the required pressure for obtaining room temperature superconductivity. However, subsequent experimental and theoretical investigations have encountered difficulties in replicating these results, leaving the structure of this Lu-H-N compound shrouded in uncertainty. Here, we propose a stable structure for Lu$_4$H$_7$N employing first-principles calculations. Our calculations reveal that Lu$_4$H$_7$N has a Tc of 1.044 K, which can be substantially enhanced to 11.721 K at 150 GPa, due to the increasing electron-phonon coupling (EPC). Notably, we delve into the nontrivial Z2 band topology of Lu$_4$H$_7$N, featuring discernible surface states near the Fermi level, and we explore its spin Hall conductivity characteristics. Furthermore, we find that the electron doping can enhance the EPC strength and Tc of Lu$_4$H$_7$N, such as the Lu$_4$H$_7$O structure we predict simulating electron doping for Lu$_4$H$_7$N with an impressive Tc of 3.837 K. This work demonstrates the coexistence of superconducting and topological properties in a Lu-H-N system compound, which holds the promise of guiding the search for novel topological superconducting materials.

Supersolid is an exotic quantum state of matter that spontaneously hosts the features of both solid and superfluid, which breaks the translation and U(1) gauge symmetries. Here we study the spin dynamics in the triangular-lattice compound Na$_2$BaCo(PO$_4$)$_2$, which is revealed in [Xiang et al., Nature 625, 270-275 (2024)] as a quantum magnetic analog of supersolid. We simulate the easy-axis Heisenberg model with tensor network approach and uncover unique dynamic traits. These features are manifested in two branches of excitations that can be associated with the spin solidity and superfluidity, respectively. One branch contains the U(1) Goldstone and roton modes, while the other comprises pseudo-Goldstone and roton modes. The gapless Goldstone modes of the in-plane superfluid order are confirmed by our inelastic neutron scattering measurements. Together with the evident out-of-plane solid order indicated by the magnetic Bragg peaks, our findings provide spectroscopic evidence for spin supersolidity in this easy-axis antiferromagnet. Akin to the role of phonon-roton modes -- Landau elementary excitations -- in shaping the helium superfluid thermodynamics, the intriguing double magnon-roton dispersion here determines the low-temperature thermodynamics of spin supersolid down to sub-Kelvin regime, explaining the recently observed giant magnetocaloric effect in Na$_2$BaCo(PO$_4$)$_2$., Comment: 8+9 pages, 4+9 figures

To control the magnon transport in magnetic systems is of great interest in magnonics. Due to the feasibility of electric field, how to generate and manipulate magnon with pure electrical method is one of the most desired goals. Here we propose that the magnon spin current is generated by applying time-dependent electric field, where the coupling between the magnon and electric field is invoked via Aharonov-Casher effect. In particular, the magnon spin current is dominated by electric field component which perpendicular to the magnetization direction. We apply our theory to 1D ferromagnetic SSH model and show that the generated magnon spin current is closely related to the band geometry. Our findings expands the horizons of magnonics and electric-control-magnon mechanisms., Comment: arXiv admin note: text overlap with arXiv:2307.10882

The geometric properties of parameter space are mostly described by Berry curvature and quantum metric, which are the imaginary and real part of quantum geometric tensor, respectively. In this work, we calculate the dressed Berry curvature and quantum metric containing eight Feynman diagrams, which are proportional to the leading-order of the concentration of impurities. For a two-band gapped graphene model, we find the disorder does not break the original symmetry but decrease (increase) the absolute value of Berry curvature and quantum metric in conduction (valence) band. We show how impurities affect the Berry curvature and quantum metric, deepening our understanding of the impurity effect on the electron transport properties in two-band gapped graphene., Comment: 14 pages,5 figures

The recent discovery of the spin supersolid candidate Na$_2$BaCo(PO$_4$)$_2$ stimulates numerous research interest on the triangular-lattice transition-metal phosphates. Here we report a comprehensive study on the structural, magnetic and magnetocaloric properties of polycrystalline Na$_2$$A$$T$(PO$_4$)$_2$ ($A$ = Ba, Sr; $T$ = Co, Ni, Mn). X-ray and neutron diffraction measurements confirm that Na$_2$Ba$T$(PO$_4$)$_2$ (NB$T$P) crystallizes in a trigonal structure, while Na$_2$Sr$T$(PO$_4$)$_2$ (NS$T$P) forms a monoclinic structure with a slight distortion of the triangular network of $T^{2+}$ ions. The dc magnetization data show that all six compounds order antiferromagnetically below 2 K, and the N\'{e}el temperatures of NS$T$P are consistently higher than those of NB$T$P for $T$ = Co, Ni, and Mn, due to the release of geometrical frustration by monoclinic distortions. Further magnetocaloric measurements show that trigonal NB$T$P can reach a lower temperature in the quasi-adiabatic demagnetization process and thus shows a better performance in the magnetic refrigeration, compared with monoclinic NS$T$P. Our findings highlight the outstanding magnetocaloric performances of the trigonal transition-metal phosphates, and disclose two necessary ingredients for a superior magnetic coolant that can reach an ultra-low temperature, including a perfect geometrically frustrated lattice and a small effective spin number associated with the magnetic ions., Comment: 10 Pages, 6 figures, accepted for publication in Physical Review Materials

La$_{3}$Ni$_{2}$O$_{7}$ has garnered widespread interest recently due to its high-temperature superconductivity under pressure, accompanied by charge density wave (CDW) ordering and metal-insulator (MI) transitions in the phase diagram. Here, we reveal with comprehensive calculations that La$_{3}$Ni$_{2}$O$_{7}$ possesses an antiferromagnetic ground state under both low and high pressures, with the strong Fermi surface nesting contributed by the flat band that leads to phonon softening and electronic instabilities. Several stable CDW orders with oxygen octahedral distortions are identified, which can trigger the MI transitions. The estimated CDW transition temperature ($\approx$120 K) at ambient pressure agrees nicely with experimental results. In the presence of apical oxygen vacancies, we identify two different phases, say, half distortion and full distortion phases, respectively, and their competition can lead to a pressure-induced MI transition, in good agreement with experimental observations. In addition, we find that the electron-phonon coupling is too small to contribute to superconductivity. These results appear to indicate an unconventional superconducting pairing mechanism mediated by antiferromagnetic fluctuations. A phase diagram that is consistent with the experimental results is given. The present results not only explain the origins of experimentally observed CDW and MI transitions, but also provide insight for deeply understanding the properties like superconductivity, CDW and the role of oxygen vacancies in pressurized La$_{3}$Ni$_{2}$O$_{7}$.

To realize room temperature ferromagnetic semiconductors is still a challenge in spintronics. Recent experiments have obtained two-dimensional (2D) room temperature ferromagnetic metals, such as monolayer MnSe2. In this paper, we proposed a way to obtain room temperature ferromagnetic semiconductors through metal-semiconductor transition. By the density functional theory calculations, a room temperature ferromagnetic semiconductor is obtained in monolayer MnSe2 with a few percent tensile strains, where a metal-semiconductor transition occurs with 2.2% tensile stain. The tensile stains raise the energy of d orbitals of Mn atoms and p orbitals of Se atoms near the Fermi level, making the Fermi level sets in the energy gap of bonding and antibonding states of these p and d orbitals, and opening a small band gap. The room temperature ferromagnetic semiconductors are also obtained in the heterostructures MnSe2/X (X = Al2Se3, GaSe, SiH, and GaP), where metal-semiconductor transition happens due to the tensile strains by interface of heterostructures. In addition, a large magneto-optical Kerr effect (MOKE) is obtained in monolayer MnSe2 with tensile strain and MnSe2-based heterostructures. Our theoretical results pave a way to obtain room temperature magnetic semiconductors from experimentally obtained 2D room temperature ferromagnetic metals through metal-semiconductor transitions.

Understanding the pairing mechanism in bilayer nickelate superconductors constitutes a fascinating quest. Using density matrix renormalization group for $T=0$ and thermal tensor networks for $T>0$ properties, along with density functional theory calculations, we investigate the intriguing interplay between the Hund's rule coupling and interorbital hybridization that explains the pressure-dependent high-$T_c$ superconductivity in bilayer nickelates. By studying a two-orbital model, we identify three distinct superconductive (SC) regimes: hybridization dominant, Hund's rule dominant, and the hybrid-Hund synergistic SC regimes. In these SC regimes, both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals exhibit algebraic pairing correlations with similar Luttinger parameters $K_{\rm SC}$. In particular, the former always exhibits a much stronger amplitude than the latter, with a distinctly higher SC characteristic temperature $T_c^*$. Below this temperature, the pairing susceptibility diverges as $\chi_{\rm SC}(T) \sim 1/T^{2-K_{\rm SC}}$. With realistic model parameters, we find the pressurized La$_3$Ni$_2$O$_7$ falls into the Hund's rule dominated SC regime. As hybridization further enhances under pressure, it leads to significant interorbital frustration and in turn suppresses the SC correlations, explaining the rise and fall of high-$T_c$ superconductivity under high pressure [J. Li, et al., arXiv:2404.11369 (2024)]. Our results offer a comprehensive understanding of the interlayer pairing in superconducting La$_3$Ni$_2$O$_7$., Comment: 5+2 pages, 4+3 figures

Doping nonmagnetic semiconductors with magnetic impurities is a feasible way to obtain diluted magnetic semiconductors (DMSs). It is generally accepted that for the most extensively studied DMS, (Ga, Mn)As, its highest Curie temperature T$_{\text{C}}$ was achieved at 200 K with a Mn concentration of approximately 16% in experiments. A recent experiment reported record-breaking high electron and hole mobilities in the semiconductor BAs [Science 377, 437 (2022)]. Since BAs shares the same zinc-blende structure with GaAs, here we predict four DMSs (B, Mn)X (X = N, P, As, Sb) by density functional theory calculations. Our results indicate that a significantly higher T$_{\text{C}}$ in the range of 254 K to 300 K for (B, Mn)As with a Mn concentration of around 15.6%, and even higher T$_{\text{C}}$ values above the room temperature for (B, Mn)N and (B, Mn)P with a Mn concentration exceeding 12.5%. Furthermore, we have predicted a large hole mobility of 1561 cm$^{\text{2}}$V$^{\text{-1}}$s$^{\text{-1}}$ at 300 K for (B, Mn)As with a Mn concentration of about 3.7%, which is three orders of magnitude larger than the hole mobility of 4 cm$^{\text{2}}$V$^{\text{-1}}$s$^{\text{-1}}$ at 300 K observed in the experiment for (Ga, Mn)As. Our findings predict the emergence of a new family of DMS, (B, Mn)X, and are expected to stimulate both experimental and theoretical studies of the DMS with high T$_{\text{C}}$ and high mobilities.

It is a critical challenge to simultaneously gain high interpretability and efficiency with the current schemes of deep machine learning (ML). Tensor network (TN), which is a well-established mathematical tool originating from quantum mechanics, has shown its unique advantages on developing efficient ``white-box'' ML schemes. Here, we give a brief review on the inspiring progresses made in TN-based ML. On one hand, interpretability of TN ML is accommodated with the solid theoretical foundation based on quantum information and many-body physics. On the other hand, high efficiency can be rendered from the powerful TN representations and the advanced computational techniques developed in quantum many-body physics. With the fast development on quantum computers, TN is expected to conceive novel schemes runnable on quantum hardware, heading towards the ``quantum artificial intelligence'' in the forthcoming future., Comment: 12 pages, 3 figures

To realize room temperature ferromagnetic (FM) semiconductors is still a challenge in spintronics. Many antiferromagnetic (AFM) insulators and semiconductors with high Neel temperature $T_N$ are obtained in experiments, such as LaFeO$_3$, BiFeO$_3$, etc. High concentrations of magnetic impurities can be doped into these AFM materials, but AFM state with very tiny net magnetic moments was obtained in experiments, because the magnetic impurities were equally doped into the spin up and down sublattices of the AFM materials. Here, we propose that the effective magnetic field provided by a FM substrate could guarantee the spin-dependent doping in AFM materials, where the doped magnetic impurities prefer one sublattice of spins, and the ferrimagnetic (FIM) materials are obtained. To demonstrate this proposal, we study the Mn-doped AFM insulator LaFeO$_3$ with FM substrate of Fe metal by the density functional theory (DFT) calculations. It is shown that the doped magnetic Mn impurities prefer to occupy one sublattice of AFM insulator, and introduce large magnetic moments in La(Fe,Mn)O$_3$. For the AFM insulator LaFeO$_3$ with high $T_N$ = 740 K, several FIM semiconductors with high Curie temperature $T_C >$ 300 K and the band gap less than 2 eV are obtained by DFT calculations, when 1/8 or 1/4 Fe atoms in LaFeO$_3$ are replaced by the other 3d, 4d transition metal elements. The large magneto-optical Kerr effect (MOKE) is obtained in these LaFeO$_3$-based FIM semiconductors. In addition, the FIM semiconductors with high $T_C$ are also obtained by spin-dependent doping in some other AFM materials with high $T_N$, including BiFeO$_3$, SrTcO$_3$, CaTcO$_3$, etc. Our theoretical results propose a way to obtain high $T_C$ FIM semiconductors by spin-dependent doping in high $T_N$ AFM insulators and semiconductors.

The advent of monochromated electron energy-loss spectroscopy has enabled atomic-resolution vibrational spectroscopy, which triggered interest in spatially localized or quasi-localized vibrational modes in materials. Here we report the discovery of phonon vortices at heavy impurities in two-dimensional materials. We use density-functional-theory calculations for two configurations of Si impurities in graphene, Si-C3 and Si-C4, to examine atom-projected phonon densities of states and display the atomic-displacement patterns for select modes that are dominated by impurity displacements. The vortices are driven by large displacements of the impurities, and reflect local symmetries. Similar vortices are found at phosphorus impurities in hexagonal boron nitride, suggesting that they may be a feature of heavy impurities in crystalline materials. Phonon vortices at defects are expected to play a role in thermal conductivity and other properties.

Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In this work, we propose an efficient and robust mixed-state tomography scheme based on the locally purified state ansatz. We demonstrate the efficiency and robustness of our scheme on various randomly initiated states with different purities. High tomography fidelity is achieved with much smaller numbers of positive-operator-valued measurement (POVM) bases than the conventional least-square (LS) method. On the superconducting quantum experimental circuit [Phys. Rev. Lett. 119, 180511 (2017)], our scheme accurately reconstructs the Greenberger-Horne-Zeilinger (GHZ) state and exhibits robustness to experimental noises. Specifically, we achieve the fidelity $F \simeq 0.92$ for the 10-qubit GHZ state with just $N_m = 500$ POVM bases, which far outperforms the fidelity $F \simeq 0.85$ by the LS method using the full $N_m = 3^{10} = 59049$ bases. Our work reveals the prospects of applying tensor network state ansatz and the machine learning approaches for efficient QST of many-body states., Comment: 7 pages, 6 figures

The recently discovered nickelate superconductor La$_3$Ni$_2$O$_7$ has a high transition temperature near 80 K under pressure, which offers additional avenues of unconventional superconductivity. Here with state-of-the-art tensor-network methods, we study a bilayer $t$-$J$-$J_\perp$ model for La$_3$Ni$_2$O$_7$ and find a robust $s$-wave superconductive (SC) order mediated by interlayer magnetic couplings. Large-scale density matrix renormalization group calculations find algebraic pairing correlations with Luttinger parameter of $K_{\rm SC} \simeq 1$. Infinite projected entangled-pair state method obtains a nonzero SC order directly in the thermodynamic limit, and estimates a strong pairing strength $\bar{\Delta}_z \sim \mathcal{O}(0.1)$. Tangent-space tensor renormalization group simulations further determine a high SC temperature $T_c^*/J \sim \mathcal{O}(0.1)$ and clarify the temperature evolution of SC order. Because of the intriguing orbital selective behaviors and strong Hund's rule coupling in the compound, $t$-$J$-$J_\perp$ model has strong interlayer spin exchange (while negligible interlayer hopping), which greatly enhances the SC pairing in the bilayer system. Such a magnetically mediated strong pairing has also been observed recently in the optical lattice of ultracold atoms. Our accurate and comprehensive tensor-network calculations reveal robust SC order in the bilayer $t$-$J$-$J_\perp$ model and shed light on the high-$T_c$ superconductivity in the pressurized nickelate La$_3$Ni$_2$O$_7$., Comment: 5 + 6 pages, 4 + 8 figures

Magnons are electrically neutral bosonic quasiparticles emerging as collective spin excitations of magnetically ordered materials, and play a central role in the next-generation spintronics owing to its obviating Joule heating. A difficult obstacle for quantum magnonics is that the magnons do not couple to the external electric field directly so that a direct electric manipulation via bias or gate voltage as in conventional charge-based devices seems not applicable. In this work, we propose a new mechanism in which magnons can be excited and controlled by electric field of light directly. Since the electric field of light can be tuned in a wide and easy way, the proposal is of great interest in realistic applications. We call it as the magnon spin photogalvanic effect (SPGE), which comes from five contributions: the Drude, Berry curvature dipole (BCD), injection, shift, and rectification, with distinct geometric origins. We further show that the responses to linearly-polarized or circularly-polarized light are determined by band-resolved quantum metric or Berry curvature, the two combined together just comprise of a quantum geometric tensor. The proposed magnon SPGE can be measured by a characterized topological phase transition. We also discuss a breathing kagome-lattice model of ferromagnets and suggest possible candidate materials to implement it.

The recently discovered ATi$_3$Bi$_5$ (A=Cs, Rb) exhibit intriguing quantum phenomena including superconductivity, electronic nematicity, and abundant topological states, which provide promising platforms for studying kagome superconductivity, band topology, and charge orders. In this work, we comprehensively study various properties of ATi$_3$Bi$_5$ including superconductivity under pressure and doping, band topology under pressure, thermal conductivity, heat capacity, electrical resistance, and spin Hall conductivity (SHC) using first-principles calculations. Calculated superconducting transition temperature ($\mathrm{ T_{c}}$) of CsTi$_3$Bi$_5$ and RbTi$_3$Bi$_5$ at ambient pressure are about 1.85 and 1.92K. When subject to pressure, $\mathrm{ T_{c}}$ of CsTi$_3$Bi$_5$ exhibits a special valley and dome shape, which arises from quasi-two-dimensional to three-dimensional isotropic compression within the context of an overall decreasing trend. Furthermore, $\mathrm{ T_{c}}$ of RbTi$_3$Bi$_5$ can be effectively enhanced up to 3.09K by tuning the kagome van Hove singularities (VHSs) and flat band through doping. Pressure can also induce abundant topological surface states at the Fermi energy ($\mathrm{E}_{\mathrm{F}}$) and tune VHSs across $\mathrm{E}_{\mathrm{F}}$. Additionally, our transport calculations are in excellent agreement with recent experiments, confirming the absence of charge density wave. Notably, SHC of CsTi$_3$Bi$_5$ can reach as large as 226$ \hbar\cdot (e\cdot \Omega \cdot cm) ^{-1} $ at $\mathrm{E}_{\mathrm{F}}$. Our work provides a timely and detailed analysis of the rich physical properties for ATi$_3$Bi$_5$, offering valuable insights for further explorations and understandings on these intriguing superconducting materials., Comment: 11 pages, 5 figures

The nature of the 1/9-magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to the exotic physical properties and high complexity induced by the geometrical frustration. Instead of a Z3 quantum spin liquid revealed on a cylinder, we show on an infinite-size lattice that the 1/9 plateau can be described by a valence bond crystal (VBC) that breaks spatial translational invariance. Consistent results are achieved by two accurate tensor network methods, namely the full-update infinite projected-entangled pair states and the projected-entangled simplex states. The VBC exhibits an hourglass pattern with $\sqrt{3}\times\sqrt{3}$ spatial symmetry, demonstrated by magnetizations, bond energies, and three-body correlators. The spatial inversion symmetry in the $\sqrt{3}\times\sqrt{3}$ VBC is instantly broken with the presence of the difference between the coupling strengths in the up and down triangles, suggesting the existence of gapless excitations. The gapless nature of the 1/9 plateau is further indicated by the scaling behaviors of the entanglement entropy and the correlation length, which indicate a c=1 conformal field theory., Comment: 6 pages, 5 figures, Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.107.L220401

${\gamma}$-GeSe is a new type of layered bulk material that was recently successfully synthesized. By means of density functional theory first-principles calculations, we systematically studied the physical properties of two-dimensional (2D) few-layer ${\gamma}$-GeSe. It is found that few-layer ${\gamma}$-GeSe are semiconductors with band gaps decreasing with increasing layer number; and 2D ${\gamma}$-GeSe with layer number $n \geq 2$ are ferroelectric with rather low transition barriers, consistent with the sliding ferroelectric mechanism. Particularly, spin-orbit coupling induced spin splitting is observed at the top of the valence band, which can be switched by the ferroelectric reversal; furthermore, their negative piezoelectricity also enables the regulation of spin splitting by strain. Finally, excellent optical absorption was also revealed. These intriguing properties make 2D few-layer ${\gamma}$-GeSe promising in spintronic and optoelectric applications., Comment: 18 pages,6 figures

Artificial intelligence (AI) has brought tremendous impacts on biomedical sciences from academic researches to clinical applications, such as in biomarkers' detection and diagnosis, optimization of treatment, and identification of new therapeutic targets in drug discovery. However, the contemporary AI technologies, particularly deep machine learning (ML), severely suffer from non-interpretability, which might uncontrollably lead to incorrect predictions. Interpretability is particularly crucial to ML for clinical diagnosis as the consumers must gain necessary sense of security and trust from firm grounds or convincing interpretations. In this work, we propose a tensor-network (TN)-ML method to reliably predict lung cancer patients and their stages via screening Raman spectra data of Volatile organic compounds (VOCs) in exhaled breath, which are generally suitable as biomarkers and are considered to be an ideal way for non-invasive lung cancer screening. The prediction of TN-ML is based on the mutual distances of the breath samples mapped to the quantum Hilbert space. Thanks to the quantum probabilistic interpretation, the certainty of the predictions can be quantitatively characterized. The accuracy of the samples with high certainty is almost 100$\%$. The incorrectly-classified samples exhibit obviously lower certainty, and thus can be decipherably identified as anomalies, which will be handled by human experts to guarantee high reliability. Our work sheds light on shifting the ``AI for biomedical sciences'' from the conventional non-interpretable ML schemes to the interpretable human-ML interactive approaches, for the purpose of high accuracy and reliability., Comment: 10 pages, 7 figures

We propose the linear and nonlinear planar Hall effect (PHE) in tilted Weyl semimetals in the presence of an in-plane magnetic and electric field, where the field-induced Berry connection (FBC) plays a key role. We show that the PHE is ascribed to the quantum metric, distinct from the well-known chiral anomaly-induced PHE arising from the Berry curvature. Using a tilting vector to describe the model, we demonstrate the constrains on the linear and nonlinear PHE by the tilting directions. The linear PHE is intrinsic that is determined by the topological properties of energy bands, whereas the nonlinear PHE is extrinsic. The predicted linear and nonlinear PHE are inherently different from others and may shed light on a deeper understanding on transport nature of the tilted Weyl semimetals.

Second-order nonlinear optical responses, including photogalvanic effect (PGE) and second harmonic generation (SHG), are important physical phenomena in nonlinear optics. The PGE (SHG) related to linearly and circularly polarized light are called the linear and circular PGE (LPGE and CPGE) [linear and circular SHG (LSHG and CSHG)], respectively. In this work, we use the quantum kinetics under relaxation time approximation to study the dependence of second-order nonlinear optical responses on Fermi level and frequency under different out-of-plane electric fields in WTe$_2$ monolayer from radio to infrared region. We find that the maximum frequency at which the Berry curvature dipole mechanism for the nonlinear Hall effect plays a major role is about 1 THz. In radio and microwave regions, two large peaks of nonlinear conductivities occur when the Fermi level is equal to the energy corresponding to gap-opening points. In terms of frequency, in radio region, LPGE and SHG conductivities maintain a large constant while the CPGE conductivity disappears. In microwave region, LPGE and SHG start to decrease with increasing frequency while the CPGE is large. In 125-300 THz region and in y direction, the presence of DC current without the disturbance of second harmonic current under circularly polarized light may be useful for fabricating new optoelectronic devices. Moreover, we illustrate that when calculating the nonlinear optical responses of practical materials, the theories in the clean limit fail and it is necessary to use a theory that considers scattering effects. We also point out that for materials with femtosecond-scale relaxation times and complex energy band structures, the quantum kinetics is more accurate than the semi-classical Boltzmann equation method. Besides, phenomenological expressions of PGE and SHG are provided.

Inspired by recent experimental measurements [Guo \textit{et al.}, Phys. Rev. Lett.~\textbf{124}, 206602 (2020); Jim\'enez \textit{et al.}, Nature \textbf{592}, 370 (2021)] on frustrated quantum magnet SrCu$_2$(BO$_3$)$_2$ under combined pressure and magnetic fields, we study the related spin-$1/2$ Shastry-Sutherland (SS) model using state-of-the-art tensor network methods. By calculating thermodynamics, correlations and susceptibilities, we find, in zero magnetic field, not only a line of first-order plaquette-singlet (PS) to dimer-singlet phase transition ending with a critical point, but also signatures of the ordered PS transition with its critical endpoint terminating on this first-order line. Moreover, we uncover prominent magnetic barocaloric responses, a novel type of quantum correlation induced cooling effect, in the strongly fluctuating supercritical regime. Under finite fields, we identify a quantum phase transition from the PS phase to the spin supersolid phase that breaks simultaneously lattice translational and spin rotational symmetries. The present findings on the SS model are accessible in current experiments and would shed new light on exotic critical and supercritical phenomena in archetypal frustrated quantum magnets., Comment: Close to the published version. 7 pages, 4 figures (SM 9 pages, 12 figures)

By performing experiment and model studies on a triangular-lattice dipolar magnet KBaGd(BO$_3$)$_2$ (KBGB), we find the highly frustrated magnet with a planar anisotropy hosts a strongly fluctuating dipolar spin liquid (DSL), which originates from the intriguing interplay between dipolar and Heisenberg interactions. The DSL constitutes an extended regime in the field-temperature phase diagram, which gets lowered in temperature as field increases and eventually ends with an unconventional quantum critical point (QCP) at $B_c\simeq 0.75$~T. Based on dipolar Heisenberg model calculations, we identify the DSL as a Berezinskii-Kosterlitz-Thouless (BKT) phase with emergent U(1) symmetry. Due to the tremendous entropy accumulation that can be related to the strong BKT and quantum fluctuations, unprecedented magnetic cooling effects are observed in the DSL regime and particularly near the QCP, making KBGB a superior dipolar coolant to commercial Gd-based refrigerants. We establish the phase diagram for triangular-lattice dipolar quantum magnets where emergent symmetry plays an essential role, and provide a basis and opens an avenue for their applications in sub-Kelvin refrigeration., Comment: 7 pages and 4 figures in main text, 5 pages and 4 figures in Supplementary Materials

The two-dimensional (2D) van der Waals ferromagnetic semiconductors, such as CrI$_3$ and Cr$_2$Ge$_2$Te$_6$, and the 2D ferromagnetic metals, such as Fe$_3$GeTe$_2$ and MnSe$_2$, have been obtained in recent experiments and attracted a lot of attentions. The superexchange interaction has been suggested to dominate the magnetic interactions in these 2D magnetic systems. In the usual theoretical studies, the expression of the 2D Heisenberg models were fixed by hand due to experiences. Here, we propose a method to determine the expression of the 2D Heisenberg models by counting the possible superexchange paths with the density functional theory (DFT) and Wannier function calculations. With this method, we obtain a 2D Heisenberg model with six different nearest-neighbor exchange coupling constants for the 2D ferromagnetic metal Cr$_3$Te$_6$, which is very different for the crystal structure of Cr atoms in Cr$_3$Te$_6$. The calculated Curie temperature Tc = 328 K is close to the Tc = 344 K of 2D Cr$_3$Te$_6$ reported in recent experiment. In addition, we predict two stable 2D ferromagnetic semiconductors Cr$_3$O$_6$ and Mn$_3$O$_6$ sharing the same crystal structure of Cr$_3$Te$_6$. The similar Heisenberg models are obtained for 2D Cr$_3$O$_6$ and Mn$_3$O$_6$, where the calculated Tc is 218 K and 208 K, respectively. Our method offers a general approach to determine the expression of Heisenberg models for these 2D magnetic semiconductors and metals, and builds up a solid basis for further studies.

A kagome lattice of 3d transition metals hosts flat bands, Dirac fermions and saddle points. It provides a versatile platform for achieving topological superconductivity, anomalous Hall effect, unconventional density wave order and quantum spin liquid when the strong correlation, spin-orbit coupling or magnetic order are involved in such a lattice. Here, using laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations, we investigate the electronic structure of the newly discovered kagome superconductor CsTi$_3$Bi$_5$, which is isostructural to the AV$_3$Sb$_5$ (A=K, Rb or Cs) kagome superconductors and possesses a perfect two-dimensional kagome network of Titanium. We directly observed a strikingly flat band derived from the local destructive interferences of Bloch wave functions within the kagome lattices. We also identify the type-II Dirac nodal loops around the Brillouin zone center, the type-III Dirac nodal loops around the zone corners and type-III Dirac nodal lines along the k$_z$ direction. In addition, around the Brillouin zone center, Z2 nontrivial topological surface states are also observed which is formed from the band inversion due to strong spin orbital coupling. The simultaneous existence of such multi-sets of nontrivial band structures in one kagome superconductor not only provides good opportunities to study related physics in the kagome lattice but also makes CsTi$_3$Bi$_5$ an ideal system to realize noval quantum phenomena by manipulating its chemical potential with chemical doping or pressure.

Fabrication of new types of superconductors with novel physical properties has always been a major thread in the research of superconducting materials. An example is the enormous interests generated by the cascade of correlated topological quantum states in the newly discovered vanadium-based kagome superconductors AV3Sb5 (A=K, Rb, and Cs) with a Z2 topological band structure. Here we report the successful fabrication of single-crystals of titanium-based kagome metal CsTi3Bi5 and the observation of superconductivity and electronic nematicity. The onset of the superconducting transition temperature Tc is around 4.8 K. In sharp contrast to the charge density wave superconductor AV3Sb5, we find that the kagome superconductor CsTi3Bi5 preserves translation symmetry, but breaks rotational symmetry and exhibits an electronic nematicity. The angular-dependent magnetoresistivity shows a remarkable two-fold rotational symmetry as the magnetic field rotates in the kagome plane. The scanning tunneling microscopy and spectroscopic imaging detect rotational-symmetry breaking C2 quasiparticle interference patterns (QPI) at low energies, providing further microscopic evidence for electronic nematicity. Combined with first-principle calculations, we find that the nematic QPI is orbital-selective and dominated by the Ti dxz and dyz orbitals, possibly originating from the intriguing orbital bond nematic order. Our findings in the new "135" material CsTi3Bi5 provide new directions for exploring the multi-orbital correlation effect and the role of orbital or bond order in the electron liquid crystal phases evidenced by the symmetry breaking states in kagome superconductors.

Topological superconductors (TSC) become a focus of research due to the accompanying Majorana fermions. However, the experimentally reported TSC are extremely rare. The recent experiments reported the kagome TSC AV$_{3}$Sb$_{5}$ (A=K, Rb, Cs), which exhibit unique superconductivity, topological surface states (TSS), and Majorana bound states. More recently, the first titanium-based kagome superconductor CsTi$ _{3} $Bi$ _{5} $ with nontrivial topology was successfully synthesized as a perspective TSC. Given that Cs contributes little to the electronic structures of CsTi$ _{3} $Bi$ _{5} $ and binary compounds may be easier to be synthesized, here, by density functional theory calculations, we predict five stable non-magnetic kagome compounds Ti$ _{6} $X$ _{4} $ (X = Bi, Sb, Pb, Tl, In) which exhibit superconductivity with critical temperature Tc = 3.8$ - $5.1 K, nontrivial $\mathbb{Z}$$_2$ band topology, and TSS close to the Fermi level. In addition, the large intrinsic spin Hall effect is obtained in Ti$ _{6} $X$ _{4} $, which is caused by gapped Dirac nodes and nodal lines due to a strong spin-orbit coupling. This work offers new platforms for TSC and spintronic devices.

Recently, robust $d$-wave superconductive (SC) order has been unveiled in the ground state of the 2D $t$-$t'$-$J$ model -- with both nearest-neighbor ($t$) and next-nearest-neighbor ($t'$) hoppings -- by density matrix renormalization group studies. However, there is currently a debate on whether the $d$-wave SC holds up strong on both $t'/t>0$ and $t'/t<0$ cases for the $t$-$t'$-$J$ model, which correspond to the electron- and hole-doped sides of the cuprate phase diagram, respectively. Here we exploit state-of-the-art thermal tensor network approach to accurately obtain the phase diagram of the $t$-$t'$-$J$ model on cylinders with widths up to $W=6$ and down to low temperature as $T/J \simeq 0.06$, pushing the boundaries of contemporary finite-$T$ calculations. For $t'/t>0$, we find a dome-like SC regime with a diverging $d$-wave pairing susceptibility, $\chi_\textrm{SC} \propto 1/T^\alpha$ below a characteristic temperature $T_c^*$. Near optimal doping, $T_c^*$ reaches its highest value of about $0.15 J$. Above $T_c^*$ yet below a higher crossover temperature $T^*$, the magnetic susceptibility becomes suppressed, which can be related to the onset of pseudogap (PG) behaviors. On the other hand, for $t'/t<0$ we find the pairing correlations are much weaker, although there exhibits a node-antinode structure in the PG regime as observed in the hole-doped cuprates. The thermal tensor network calculations of the $t$-$t'$-$J$ model underscore both the similarities and differences in the finite-temperature phase diagram between the fundamental model and cuprates, yielding unique insights into their intricate behaviors., Comment: 8+8 pages, 4+12 figures

The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\alpha$-RuCl$_3$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations, and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K$-$J$-$\Gamma$-$\Gamma'$ model for $\alpha$-RuCl$_3$ [1], we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, and the magnetotropic susceptibility, etc, under a magnetic field with a tilting angle $\theta$ to the $c^*$-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\alpha$-RuCl$_3$ and other candidate Kitaev magnets., Comment: 10 pages, 6 figures (including Appendices)

Recently, charge or spin nonlinear transport with nontrivial topological properties in crystal materials has attracted much attention. In this paper, we perform a comprehensive symmetry analysis for all 122 magnetic point groups (MPGs) and provide a useful dictionary for charge and spin nonlinear transport from Berry curvature dipole, Berry connection polarization and Drude term with nontrivial topological nature. The results are obtained by making a full symmetry investigation on matrix representations of six nonlinear response tensors. We further identify every MPG that can accommodate two or three of the nonlinear tensors. The present work gives a solid theoretical basis for overall understanding the second-order nonlinear responses in realistic materials., Comment: 5 pages, 2 figures

Since the discovery of a new family of vanadium-based kagome superconductor AV3Sb5 (A=K, Rb, and Cs) with topological band structures, extensive effort has been devoted to exploring the origin of superconducting states and the intertwined orders. Meanwhile, searching for new types of superconductors with novel physical properties and higher superconducting transition temperatures has always been a major thread in the history of superconductor research. Here we report a successful fabrication and the topological states of a Titanium-based kagome metal CsTi3Bi5 (CT3B5) crystal. The as-grown CT3B5 crystal is of high quality and possesses a perfect two-dimensional kagome net of Titanium. The superconductivity of the CT3B5 crystal shows that the critical temperature Tc is of ~4.8 K. First-principle calculations predict that the CT3B5 has robust topological surface states, implying that CT3B5 is a Z2 topological kagome superconductor. This finding provides a new type of superconductors and the base for exploring the origin of superconductivity and topological states in kagome superconductors.

Superconductivity in transition metal nitrides (TMNs) has been investigated for a long time, such as zirconium nitride (ZrN) with a superconducting transition temperature Tc of 10 K. Recently, a phase diagram has been revealed in ZrNx with different nitrogen concentrations, which is very similar to that of high-temperature copper oxide superconductors. Here, we study the TMNs with face-centered cubic lattice, where ZrN and HfN have been experimentally obtained, and predict eight new stable superconductors by the first-principle calculations. We find that CuN has a high Tc of 30 K with a very strong electron-phonon coupling (EPC) strength. In contrast to ZrN, CuN has softening acoustic phonons at the high symmetry point L, which accounts for its much stronger EPC. In addition, the highly symmetrical structure leads to topological protected nodal points and lines, such as the hourglass Weyl loop in kx/y/z = 0 plane and Weyl points in kx/y/z = 2{\pi}/a plane, as well as quadratic band touch at {\Gamma} point. CuN could be a topological superconductor. Our results expand the transition metal nitrides superconductor family and would be helpful to guide the search for high temperature topological superconductors., Comment: 5 pages, 4 figures, 2 tables