arXiv subjects

Zhijun Tu

Publications and source records attributed to Zhijun Tu.

48 records · Page 3Linked to original sources

arXiv2022

Charge order breaks time-reversal symmetry in CsV$_3$Sb$_5$

The recently discovered vanadium-based kagome metals $A$V$_{3}$Sb$_{5}$ ($A$~=~K,~Rb,~Cs) exhibit superconductivity at low-temperatures and charge density wave (CDW) order at high-temperatures. A prominent feature of the charge ordered state in this family is that it breaks time-reversal symmetry (TRSB), which is connected to the underlying topological nature of the band structure. In this work, a powerful combination of zero-field and high-field muon-spin rotation/relaxation is used to study the signatures of TRSB of the charge order in CsV$_3$Sb$_5$, as well as its anisotropic character. By tracking the temperature evolution of the in-plane and out-of-plane components of the muon-spin polarization, an enhancement of the internal field width sensed by the muon-spin ensemble was observed below $T_{\rm TRSB}=T_{\rm CDW}\simeq95$~K. Additional increase of the internal field width, accompanied by a change of the local field direction at the muon site from the $ab$-plane to the $c$-axis, was detected below $T^\ast\simeq30$~K. Remarkably, this two-step feature becomes well pronounced when a magnetic field of 8~T is applied along the crystallographic $c-$axis, thus indicating a field-induced enhancement of the electronic response at the CDW transition. These results point to a TRSB in CsV$_3$Sb$_5$ by charge order with an onset of ${\simeq}~95$~K, followed by an enhanced electronic response below ${\simeq}~30$~K. The observed two-step transition is discussed within the framework of different charge-order instabilities, which, in accordance with density functional theory calculations, are nearly degenerate in energy.

cond-mat.str-el↗

arXiv2022

Two types of charge order in the superconducting kagome material CsV$_3$Sb$_5$

The kagome metals of the family $A$V$_3$Sb$_5$, featuring a unique structural motif, harbor an array of intriguing phenomena such as chiral charge order and superconductivity. CsV$_3$Sb$_5$ is of particular interest because it displays a double superconducting dome in the region of the temperature-pressure phase diagram where charge order is still present. However, the microscopic origin of such an unusual behavior remains an unsolved issue. Here, to address it, we combine high-pressure, low-temperature muon spin relaxation with first-principles calculations. We observe a pressure-induced threefold enhancement of the superfluid density, which also displays a double peak feature, similar to the superconducting critical temperature. This leads to three distinct regions in the phase diagram, each of which features distinct slopes of the linear relation between superfluid density and the critical temperature. These results are attributed to a possible evolution of the charge order pattern from the superimposed tri-hexagonal Star-of-David phase at low pressures (within the first dome) to the staggered tri-hexagonal phase at intermediate pressures (between the first and second domes). Our findings suggest a change in the nature of the charge ordered state across the phase diagram of CsV$_3$Sb$_5$, with varying degrees of competition with superconductivity.

cond-mat.supr-con↗

arXiv2022

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV$_{3}$Sb$_{5}$

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV$_3$Sb$_5$. The spectra around $\bar{K}$ is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below $E_{\rm F}$. The peak-dip-hump lineshape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to $E_{\rm F}$ in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of $\sim$0.4 meV is observed on both the electron band around $\barΓ$ and the flat band around $\bar{K}$, implying the multiband superconductivity. The finite density of states (DOS) at $E_{\rm F}$ in the CDW phase are most likely in favor of the emergence of multiband superconductivity, particularly the enhanced DOS associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

cond-mat.supr-con↗

arXiv2021

Tri-Hexagonal charge order in kagome metal CsV$_{3}$Sb$_{5}$ revealed by $^{121}$Sb NQR

We report $^{121}$Sb nuclear quadrupole resonance (NQR) measurements on kagome superconductor CsV$_3$Sb$_5$ with $T_{\rm c}=2.5$ K. $^{121}$Sb NQR spectra split after a charge density wave (CDW) transition at $94$ K, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between $91$ K and $94$ K manifests that it is a first order phase transition. The CDW order exhibits Tri-Hexagonal deformation with a lateral shift between the adjacent kagome layers, which is consistent with $2 \times 2 \times 2$ superlattice modulation. The superconducting state coexists with CDW order and shows a conventional s-wave behavior in the bulk state.

cond-mat.str-el↗

arXiv2021

Structures and physical properties of V-based kagome metals CsV$_{6}$Sb$_{6}$ and CsV$_{8}$Sb$_{12}$

We report two new members of V-based kagome metals CsV$_{6}$Sb$_{6}$ and CsV$_{8}$Sb$_{12}$. The most striking structural feature of CsV$_{6}$Sb$_{6}$ is the V kagome bilayers. For CsV$_{8}$Sb$_{12}$, there is an intergrowth of two-dimensional V kagome layers and one-dimensional V chains and the latter lead to the orthorhombic symmetry of this material. Further measurements indicate that these two materials exhibit metallic and Pauli paramagnetic behaviors. More importantly, different from CsV$_{3}$Sb$_{5}$, the charge density wave state and superconductivity do not emerge in CsV$_{6}$Sb$_{6}$ and CsV$_{8}$Sb$_{12}$ when temperature is above 2 K. Small magnetoresistance with saturation behavior and linear field dependence of Hall resistivity at high field and low temperature suggest that the carriers in both materials should be uncompensated with much different concentrations. The discovery of these two new V-based kagome metals sheds light on the exploration of correlated topological materials based on kagome lattice.

cond-mat.supr-con↗

arXiv2021

Quantum transport evidence of topological band structures of kagome superconductor CsV3Sb5

We report the transport properties of kagome superconductor CsV$_{3}$Sb$_{5}$ single crystals at magnetic field up to 32 T. The Shubnikov de Haas (SdH) oscillations emerge at low temperature and four frequencies of $F_α=$ 27 T, $F_β=$ 73 T, $F_ε=$ 727 T, and $F_η=$ 786 T with relatively small cyclotron masses are observed. For $F_β$ and $F_ε$, the Berry phases are close to $π$, providing a clear evidence of nontrivial topological band structures of CsV$_{3}$Sb$_{5}$. Furthermore, the consistence between theoretical calculations and experimental results implies that these frequencies can be assigned to the Fermi surfaces locating near the boundary of Brillouin zone and confirms that the structure with an inverse Star of David distortion could be the most stable structure at charge density wave state. These results will shed light on the nature of correlated topological physics in kagome material CsV$_{3}$Sb$_{5}$.

cond-mat.supr-con↗

arXiv2021

Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal

The transition-metal kagome lattice materials host frustrated, correlated, and topological quantum states of matter. Recently, a new family of vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band structures has been discovered. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that CsV3Sb5 exhibits a V-shaped pairing gap Δ~0.5 meV and is a strong-coupling superconductor (2Δ/kBTc~5) that coexists with 4a0 unidirectional and 2a0X2a0 charge order. Remarkably, we discover a 3Q PDW accompanied by bidirectional 4a0/3 spatial modulations of the superconducting gap, coherence peak and gap-depth in the tunneling conductance. We term this novel quantum state a roton-PDW associated with an underlying vortex-antivortex lattice that can account for the observed conductance modulations. Probing the electronic states in the vortex halo in an applied magnetic field, in strong-field that suppresses superconductivity, and in zero-field above Tc reveals that the PDW is a primary state responsible for an emergent pseudogap and intertwined electronic order. Our findings show striking analogies and distinctions to the phenomenology of high-Tc cuprate superconductors, and provide groundwork for understanding the microscopic origin of correlated electronic states and superconductivity in vanadium-based kagome metals.

cond-mat.supr-con↗

arXiv2021

Evolution of electronic structure in pristine and hole-doped kagome metal RbV$_3$Sb$_5$

We report on in situ low-temperature (4 K) scanning tunneling microscope measurements of atomic and electronic structures of the cleaved surfaces of an alkali-based kagome metal RbV$_3$Sb$_5$ single crystals. We find that the dominant pristine surface exhibits Rb-1x1 structure, in which a unique unidirectional $\sqrt{3}a_0$ charge order is discovered. As the sample temperature slightly rises, Rb-$\sqrt{3}$x1 and Rb-$\sqrt{3}$x$\sqrt{3}$ reconstructions form due to desorption of surface Rb atoms. Our conductance mapping results demonstrate that Rb desorption not only gives rise to hole doping, but also renormalizes the electronic band structures. Surprisingly, we find a ubiquitous gap opening near the Fermi level in tunneling spectra on all the surfaces despite their large differences of hole-carrier concentration, indicating an orbital-selective band reconstruction in RbV$_3$Sb$_5$.

cond-mat.supr-con↗

arXiv2021

Charge-density-wave-induced bands renormalization and energy gaps in a kagome superconductor RbV3Sb5

Recently discovered Z2 topological kagome metals AV3Sb5 (A = K, Rb, and Cs) exhibit charge density wave (CDW) phases and novel superconducting paring states, providing a versatile platform for studying the interplay between electron correlation and quantum orders. Here we directly visualize CDW-induced bands renormalization and energy gaps in RbV3Sb5 using angle-resolved photoemission spectroscopy, pointing to the key role of tuning van Hove singularities to the Fermi energy in mechanisms of ordering phases. Near the CDW transition temperature, the bands around the Brillouin zone (BZ) boundary are shifted to high-binding energy, forming an "M"-shape band with singularities near the Fermi energy. The Fermi surfaces are partially gapped and the electronic states on the residual ones should be possibly dedicated to the superconductivity. Our findings are significant in understanding CDW formation and its associated superconductivity.

cond-mat.supr-con↗

arXiv2021

s-wave superconductivity in kagome metal CsV$_{3}$Sb$_{5}$ revealed by $^{121/123}$Sb NQR and $^{51}$V NMR measurements

We report $^{121/123}$Sb nuclear quadrupole resonance (NQR) and $^{51}$V nuclear magnetic resonance (NMR) measurements on kagome metal CsV$_3$Sb$_5$ with $T_{\rm c}=2.5$ K. Both $^{51}$V NMR spectra and $^{121/123}$Sb NQR spectra split after a charge density wave (CDW) transition, which demonstrates a commensurate CDW state. The coexistence of the high temperature phase and the CDW phase between $91$ K and $94$ K manifests that it is a first order phase transition. At low temperature, electric-field-gradient fluctuations diminish and magnetic fluctuations become dominant. Superconductivity emerges in the charge order state. Knight shift decreases and $1/T_{1}T$ shows a Hebel--Slichter coherence peak just below $T_{\rm c}$, indicating that CsV$_3$Sb$_5$ is an s-wave superconductor.

cond-mat.supr-con↗

arXiv2021

Superconductivity and normal-state properties of kagome metal RbV3Sb5 single crystals

We report the discovery of superconductivity and detailed normal-state physical properties of RbV3Sb5 single crystals with V kagome lattice. RbV3Sb5 single crystals show a superconducting transition at Tc ~ 0.92 K. Meanwhile, resistivity, magnetization and heat capacity measurements indicate that it exhibits anomalies of properties at T* ~ 102 - 103 K, possibly related to the formation of charge ordering state. When T is lower than T*, the Hall coefficient RH undergoes a drastic change and sign reversal from negative to positive, which can be partially explained by the enhanced mobility of hole-type carriers. In addition, the results of quantum oscillations show that there are some very small Fermi surfaces with low effective mass, consistent with the existence of multiple highly dispersive Dirac band near the Fermi energy level.

cond-mat.supr-con↗

arXiv2018

Design Space Exploration of Neural Network Activation Function Circuits

The widespread application of artificial neural networks has prompted researchers to experiment with FPGA and customized ASIC designs to speed up their computation. These implementation efforts have generally focused on weight multiplication and signal summation operations, and less on activation functions used in these applications. Yet, efficient hardware implementations of nonlinear activation functions like Exponential Linear Units (ELU), Scaled Exponential Linear Units (SELU), and Hyperbolic Tangent (tanh), are central to designing effective neural network accelerators, since these functions require lots of resources. In this paper, we explore efficient hardware implementations of activation functions using purely combinational circuits, with a focus on two widely used nonlinear activation functions, i.e., SELU and tanh. Our experiments demonstrate that neural networks are generally insensitive to the precision of the activation function. The results also prove that the proposed combinational circuit-based approach is very efficient in terms of speed and area, with negligible accuracy loss on the MNIST, CIFAR-10 and IMAGENET benchmarks. Synopsys Design Compiler synthesis results show that circuit designs for tanh and SELU can save between 3.13-7.69 and 4.45-8:45 area compared to the LUT/memory-based implementations, and can operate at 5.14GHz and 4.52GHz using the 28nm SVT library, respectively. The implementation is available at: https://github.com/ThomasMrY/ActivationFunctionDemo.

cs.NE↗