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Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)0031-900710.1103/PhysRevLett.130.147101], we demonstrated that the correct critical behaviors of EP in infinite dimensions (complete graph) can be accurately extracted using the event-based method, with finite-size scaling behaviors still described by the standard finite-size scaling theory. We perform an extensive simulation of EPs on hypercubic lattices ranging from dimensions d=2 to 6, and find that the critical behaviors consistently obey the standard finite-size scaling theory. Consequently, we obtain a high-precision determination of the percolation thresholds and critical exponents, revealing that EPs governed by the product and sum rules belong to different universality classes. Remarkably, despite the mean of the dynamic pseudocritical point T_{L} deviating from the infinite-lattice criticality by a distance determined by the d-dependent correlation-length exponent, T_{L} follows a normal (Gaussian) distribution across all dimensions, with a standard deviation proportional to 1/sqrt[V], where V denotes the system volume. A theoretical argument associated with the central-limit theorem is further proposed to understand the probability distribution of T_{L}. These findings offer a comprehensive understanding of critical behaviors in EPs across various dimensions, revealing a different dimension-dependence compared to standard bond percolation.

Two-dimensional (2D) superconducting systems are of great importance for exploring exotic quantum physics. The recent development of fabrication techniques has stimulated studies of high-quality single-crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here, we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity) in 4-monolayer (ML) to 6-ML crystalline Pb films grown on striped incommensurate Pb layers on Si(111) substrates by molecular beam epitaxy. An anomalously large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that, in superconducting heterostructures, the interface can induce Zeeman-type spin-orbit interactions and modulate the superconductivity.

Three-dimensional topological Dirac semimetals have a linear dispersion in 3D momentum space and are viewed as the 3D analogues of graphene. Here, we report angle-dependent magnetotransport on the newly revealed Cd_{3}As_{2} single crystals and clearly show how the Fermi surface evolves with crystallographic orientations. Remarkably, when the magnetic field lies in the [112] or [441[over ¯]] axis, magnetoresistance oscillations with only single period are present. However, the oscillation shows double periods when the field is applied along the [11[over ¯]0] direction. Moreover, aligning the magnetic field at certain directions also gives rise to double period oscillations. We attribute the observed anomalous oscillation behavior to the sophisticated geometry of Fermi surface and illustrate a complete 3D Fermi surface with two nested anisotropic ellipsoids around the Dirac points. Additionally, a submillimeter mean-free path at 6 K is found in Cd_{3}As_{2} crystals, indicating ballistic transport in this material. By measuring the magnetoresistance up to 60 T, we reach the quantum limit (n=1 Landau level) at about 43 T. These results improve the knowledge of the Dirac semimetal material Cd_{3}As_{2} and also pave the way for proposing new electronic applications based on 3D Dirac materials.

We presented a high-sensitivity temperature detection using an implanted single nitrogen-vacancy (NV) center array in diamond. The high-order thermal Carr-Purcell-Meiboom-Gill (TCPMG) method was performed on the implanted single NV center in diamond in a static magnetic field. We demonstrated that under small detunings for the two driving microwave frequencies, the oscillation frequency of the induced fluorescence of the NV center equals approximately the average of the detunings of the two driving fields. On the basis of the conclusion, the zero-field splitting D for the NV center and the corresponding temperature could be determined. The experiment showed that the coherence time for the high-order TCPMG was effectively extended, particularly up to 108 μs for TCPMG-8, about 14 times the value 7.7 μs for thermal Ramsey method. This coherence time corresponded to a thermal sensitivity of 10.1 mK/Hz1/2. We also detected the temperature distribution on the surface of a diamond chip in three different circumstances by using the implanted NV center array with the TCPMG-3 method. The experiment implies the feasibility of using implanted NV centers in high-quality diamonds to detect temperatures in biology, chemistry, materials science, and microelectronic systems with high sensitivity and nanoscale resolution. [ABSTRACT FROM AUTHOR]

We investigate the geometric properties of percolation clusters by studying square-lattice bond percolation on the torus. We show that the density of bridges and nonbridges both tend to 1/4 for large system sizes. Using Monte Carlo simulations, we study the probability that a given edge is not a bridge but has both its loop arcs in the same loop and find that it is governed by the two-arm exponent. We then classify bridges into two types: branches and junctions. A bridge is a branch iff at least one of the two clusters produced by its deletion is a tree. Starting from a percolation configuration and deleting the branches results in a leaf-free configuration, whereas, deleting all bridges produces a bridge-free configuration. Although branches account for ≈43% of all occupied bonds, we find that the fractal dimensions of the cluster size and hull length of leaf-free configurations are consistent with those for standard percolation configurations. By contrast, we find that the fractal dimensions of the cluster size and hull length of bridge-free configurations are given by the backbone and external perimeter dimensions, respectively. We estimate the backbone fractal dimension to be 1.643 36(10). [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of the bond- and site-directed (oriented) percolation models in (d+1) dimensions on simple-cubic and body-centered-cubic lattices, with 2=d=7. A dimensionless ratio is defined, and an analysis of its finite-size scaling produces improved estimates of percolation thresholds. We also report improved estimates for the standard critical exponents. In addition, we study the probability distributions of the number of wet sites and radius of gyration, for 1=d=7. [ABSTRACT FROM AUTHOR]

We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L = 512, and estimate the percolation thresholds to be pc(bond) = 0.248 811 82(10) and pc(site) = 0.311 607 7(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/v = 1.1410(15), ß/v = 0.47705(15), the leading correction exponent y, = -1.2(2), and the shortest-path exponent dmin = 1.3756(3). Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent ≈--2, rather than y, ≈ --1.2. [ABSTRACT FROM AUTHOR]

We report on high magnetic field studies of magnetization, electric polarization, and specific heat on single crystals of Ni3V2O8, which is an S = 1 kagome compound. The magnetization process exhibits multistep magnetic transitions when the magnetic field is parallel to the magnetic easy axis. An apparent magnetization plateau was observed at half the height of the saturation magnetization Ms ~ 2.39µ B/Ni. In addition, the magnetization transitions at higher fields are quantized at 2/3, 3/4, and 8/9 of Ms. These results are unusual for the one-third magnetization plateaus that theories have predicted for conventional kagome antiferromagnets. We find that the high magnetic field suppresses the spontaneous polarization, leading to a different high-field phase where the magnetic structure is collinear or coplanar with the underlying lattice. The resulting high-field phase diagram explores several magnetic phases and sheds light on recent experimental findings. Analytical arguments have been presented to discuss these high-field phases. [ABSTRACT FROM AUTHOR]

We have studied the magnetization of CeOs2Al10 in high magnetic fields up to 55 T for H ∥ a and constructed the magnetic phase diagram for H ∥ a. The magnetization curve shows a concave H dependence below Tmax ∼ 40 K, which is higher than the transition temperature T0 ∼ 29 K. The magnetic susceptibility along the a axis, χa, shows a smooth and continuous decrease down to ∼20 K below Tmax ∼ 40 K without showing an anomaly at T0. From these two results, a Kondo singlet is formed below Tmax and coexists with the antiferromagnetic order below T0. We also propose that the larger suppression of the spin degrees of freedom along the a axis than along the c axis below Tmax is associated with the origin of the antiferromagnetic component. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of the geometric properties of Fortuin-Kasteleyn (FK) clusters of the Ising model on square [two-dimensional (2D)] and simple-cubic [three-dimensional (3D)] lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on a torus, is found to suffer from smaller finite-size corrections than the well-known Binder ratio and yields a high-precision critical coupling as Kc(3D)=0.221654631(8). We then study other geometric properties of FK clusters at criticality. It is demonstrated that the distribution of the critical largest-cluster size C1 follows a single-variable function as P(C1,L)dC1=˜P(x)dx with x≡C1/LdF (L is the linear size), where the fractal dimension dF is identical to the magnetic exponent. An interesting bimodal feature is observed in distribution ˜P(x) in three dimensions, and attributed to the different approaching behaviors for K→Kc+0±. To characterize the compactness of the FK clusters, we measure their graph distances and determine the shortest-path exponents as dmin(3D)=1.25936(12) and dmin(2D)=1.0940(2). Further, by excluding all the bridges from the occupied bonds, we obtain bridge-free configurations and determine the backbone exponents as dB(3D)=2.1673(15) and dB(2D)=1.7321(4). The estimates of the universal wrapping probabilities for the 3D Ising model and of the geometric critical exponents dmin and dB either improve over the existing results or have not been reported yet. We believe that these numerical results would provide a testing ground in the development of further theoretical treatments of the 3D Ising model. [ABSTRACT FROM AUTHOR]

We study critical bond percolation on a seven-dimensional hypercubic lattice with periodic boundary conditions (7D) and on the complete graph (CG) of finite volume (number of vertices) V. We numerically confirm that for both cases, the critical number density n(s,V) of clusters of size s obeys a scaling form n(s,V)~s-τn(s/Vd*f) with identical volume fractal dimension d*f=2/3 and exponent τ=1+1/d*f=5/2. We then classify occupied bonds into bridge bonds, which includes branch and junction bonds, and nonbridge bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree. Deleting branch bonds from percolation configurations produces leaf-free configurations, whereas deleting all bridge bonds leads to bridge-free configurations composed of blobs. It is shown that the fraction of nonbridge (biconnected) bonds vanishes, ρn,CG→0, for large CGs, but converges to a finite value, ρn,7D=0.0061931(7), for the 7D hypercube. Further, we observe that while the bridge-free dimension d*bf=1/3 holds for both the CG and 7D cases, the volume fractal dimensions of the leaf-free clusters are different: d*lf,7D=0.669(9)≈2/3 and d*lf,CG=0.3337(17)≈1/3. On the CG and in 7D, the whole, leaf-free, and bridge-free clusters all have the shortest-path volume fractal dimension d*min≈1/3, characterizing their graph diameters. We also study the behavior of the number and the size distribution of leaf-free and bridge-free clusters. For the number of clusters, we numerically find the number of leaf-free and bridge-free clusters on the CG scale as ~lnV, while for 7D they scale as ~V. For the size distribution, we find the behavior on the CG is governed by a modified Fisher exponent τ'=1, while for leaf-free clusters in 7D, it is governed by Fisher exponent τ=5/2. The size distribution of bridge-free clusters in 7D displays two-scaling behavior with exponents τ=4 and τ'=1. The probability distribution P(C1,V)dC1 of the largest cluster of size C1 for whole percolation configurations is observed to follow a single-variable function P(x)dx, with x≡C1/Vd*f for both CG and 7D. Up to a rescaling factor for the variable x, the probability functions for CG and 7D collapse on top of each other within the entire range of x. The analytical expressions in the x→0 and x→∞ limits are further confirmed. Our work demonstrates that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts. [ABSTRACT FROM AUTHOR]

By efficient nanoscale plasma etching, the nitrogen-vacancy (NV) centers in diamond were brought to the sample surface step by step successfully. At each depth, we measured the ratios of spin coherence times before and after applying external spins on the surface, which reflected the contribution of external spins to the decoherence, and then investigated the relationships between depth and ratios. The values of ratios declined and then rose with the decreasing depth, which was attributed to the decoherence influenced by external spins, surface spins, discrete surface spin effects, and electric field noise. Moreover, our work experimentally and theoretically revealed a characteristic depth at which the NV center would experience relatively the strongest decoherence caused by external spins in consideration of inevitable surface spins. And the characteristic depth was found depending on the local environments of NV centers and the density of surface spins. [ABSTRACT FROM AUTHOR]

We report the electrical transport properties for Weyl semimetal TaAs in an intense magnetic field. Strong temperature-dependent anomalies occur in the Hall signals and longitudinal magnetoresistance at low temperatures when the Weyl electrons are confined into the lowest Landau level. The temperature-dependent behaviors indicate that electron-hole pairing instability may be the origin of the anomalies. Our measurements show that the ultraquantum regime for the Weyl semimetals is not featureless. [ABSTRACT FROM AUTHOR]

We report large magnetoresistance (MR) at low temperatures in single-crystalline nonmagnetic compounds TaAs2 and NbAs2. Both compounds exhibit parabolic-field-dependent MR larger than 5 ? 10³ in a magnetic field of 9 Tesla at 2 K. The MR starts to deviate from parabolic dependence above 10 T and intends to be saturated in 45 T for TaAs2 at 4.2 K. The Hall resistance measurements and band structure calculations reveal their compensated semimetal characteristics. Their large MR at low temperatures is ascribed to an effect for compensation of electrons and holes with large mobilities. After discussing the MR for different samples of TaAs2 and other semimetals, we found that the magnitudes of MR are strongly dependent on the samples' quality for different compounds. [ABSTRACT FROM AUTHOR]

HfTe5 is predicted to be a promising platform for studying topological phases. Here through an electrical transport study, we present an observation of chiral anomaly and ultrahigh mobility in HfT e5 crystals. Negative magnetoresistivity in HfT e5 is observed when the external magnetic and electrical fields are parallel (B//E) and quickly disappears once B deviates from the direction of E. Quantitative fitting further confirms the chiral anomaly as the underlying physics. Moreover, by analyzing the conductivity tensors of longitudinal and Hall traces, ultrahigh mobility and ultralow carrier density are revealed in HfT e5, which paves the way for potential electronic applications. [ABSTRACT FROM AUTHOR]

We report extremely large magnetoresistance (MR) in an extended temperature regime from 1.5 K to 300 K in nonmagnetic binary compounds TaP and NbP. TaP exhibits linear MR around 1.8×104 at 2 K in a magnetic field of 9 T, which further follows its linearity up to 1.4×105 in a magnetic field of 56 T at 1.5 K. At room temperature the MR for TaP and NbP follows a power law of the exponent about 1.5 with the values larger than 300% in a magnetic field of 9 T. Such large MR in a wide temperature regime is likely not only due to a resonance of the electron-hole balance, but also indicates a complicated mechanism underneath. [ABSTRACT FROM AUTHOR]