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Bilayer moir\'e structures have attracted significant attention recently due to their spatially modulated layer degrees of freedom. However, the layer-dependent transport mechanism in the moir\'e structures is still a problem to be explored. Here we investigate the layer-dependent transport properties regulated by the strain, the interlayer bias and the number of moir\'e periods in a strained moir\'e homobilayer TMDs nanoribbon based on low-energy efficient models. The charge carriers can pass perfectly through the scattering region with the moir\'e potential. While, it is noted that the overall transmission coefficient is mainly contributed from either intralayer or interlayer transmissions. The transition of transport mechanism between intralayer and interlayer transmissions can be achieved by adjusting the strain. The intralayer transmissions are suppressed and one of the interlayer transmissions can be selected by a vertical external electric field, which can cause a controllable layer polarization. Moreover, the staggered intralayer and interlayer minigaps are formed as the number of moir\'e periods increases in the scattering region due to the overlap of the wave functions in two adjacent moir\'e periods. Our finding points to an opportunity to realize layer functionalities by the strain and electric field., Comment: 10 pages, 6 figures

Since the discovery of the fascinating properties in magic-angle graphene, the exploration of moir\'e systems in other two-dimensional materials has garnered significant attention and given rise to a field known as 'moir\'e physics'. Within this realm, magnetic van der Waals heterostructure and the magnetic proximity effect in moir\'e superlattices have also become subjects of great interest. However, the spin-polarized transport property in this moir\'e structures is still a problem to be explored. Here, we investigate the spin-polarized transport properties in a moir\'e superlattices formed by a two-dimensional ferromagnet CrI_3 stacked on a monolayer BAs, where the spin degeneracy is lifted because of the magnetic proximity effect associated with the moir\'e superlattices. We find that the conductance exhibits spin-resolved miniband transport properties at a small twist angle because of the periodic moir\'e superlattices. When the incident energy is in the spin-resolved minigaps, the available states are spin polarized, thus providing a spin-polarized current from the superlattice. Moreover, only a finite number of moir\'e period is required to obtain a net spin polarization of 100\%. In addition, the interlayer distance of the heterojunction is also moir\'e modifiable, so a perpendicular electric field can be applied to modulate the intensity and direction of the spin polarization. Our finding points to an opportunity to realize spin functionalities in magnetic moir\'e superlattices., Comment: 7 pages, 5 figures

Searching for compact objects (black holes, neutron stars, or white dwarfs) in the Milky Way is essential for understanding the stellar evolution history, the physics of compact objects, and the structure of our Galaxy. Compact objects in binaries with a luminous stellar companion are perfect targets for optical observations. Candidate compact objects can be achieved by monitoring the radial velocities of the companion star. However, most of the spectroscopic telescopes usually obtain stellar spectra at a relatively low efficiency, which makes a sky survey for millions of stars practically impossible. The efficiency of a large-scale spectroscopic survey, the Large Sky Area Multi-Object Fiber Spectroscopy Telescope (LAMOST), presents a specific opportunity to search for compact object candidates, i.e., simply from the spectroscopic observations. Late-type K/M stars are the most abundant populations in our Galaxy. Owing to the relatively large Keplerian velocities in the close binaries with a K/M-dwarf companion, a hidden compact object could be discovered and followed-up more easily. In this study, compact object candidates with K/M-dwarf companions are investigated with the LAMOST low-resolution stellar spectra. Based on the LAMOST Data Release 5, we obtained a sample of $56$ binaries, each containing a K/M-dwarf with a large radial velocity variation $\Delta V_{\rm R} > 150~{\rm km~s}^{-1}$. Complemented with the photometric information from the Transiting Exoplanet Survey Satellite, we derived a sample of $35$ compact object candidates, among which, the orbital periods of $16$ sources were revealed by the light curves. Considering two sources as examples, we confirmed that a compact object existed in the two systems by fitting the radial velocity curve. This study demonstrates the principle and the power of searching for compact objects through LAMOST., Comment: 20 pages, 7 figures, 4 tables, Science China Physics, Mechanics & Astronomy, Vol.65 No.2:229711

Optical time-domain surveys can unveil and characterize exciting but less-explored non-accreting and/or non-beaming neutron stars (NS) in binaries. Here we report the discovery of such a NS candidate using the LAMOST spectroscopic survey. The candidate, designated LAMOST J112306.9+400736 (hereafter J1123), is in a single-lined spectroscopic binary containing an optically visible M star. The star's large radial velocity variation and ellipsoidal variations indicate a relatively massive unseen companion. Utilizing follow-up spectroscopy from the Palomar 200-inch telescope and high-precision photometry from TESS, we measure a companion mass of $1.24_{-0.03}^{+0.03}~M_{\odot}$. Main-sequence stars with this mass are ruled out, leaving a NS or a massive white dwarf (WD). Although a massive WD cannot be ruled out, the lack of UV excess radiation from the companion supports the NS hypothesis. Deep radio observations with FAST yielded no detections of either pulsed or persistent emission. J1123 is not detected in numerous X-ray and gamma-ray surveys. These non-detections suggest that the NS candidate is not presently accreting and pulsing. Our work exemplifies the capability of discovering compact objects in non-accreting close binaries by synergizing the optical time-domain spectroscopy and high-cadence photometry., Comment: 53 pages, 15 figures, publication in Nature Astronomy

In this work, a modified Nambu-Jona-Lasinio (NJL) model with proper-time regularization is employed to study the structure of nonstrange quark stars. The coupling constant of four-fermion interaction in the conventional NJL model is modified as $G=G_1+G_2\langle\bar{\psi}\psi\rangle$ to highlight the feedback of quark propagator to gluon propagator. To study the dependence of the equation of state (EOS) on this modification as well as the vacuum pressure, we choose nine representative EOSs for comparison. It is found that a smaller $G_1$ leads to a stiffer EOS, and a higher vacuum pressure (i.e., a smaller bag constant) yields a softer EOS at low energy density. It is further shown that the heaviest quark star under this modified NJL model satisfies not only the recent mass measurement of PSR J0740+6620, but also the radius constraints from X-ray timing observations. The corresponding tidal deformability is also in agreement with the observations of GW170817., Comment: 9 pages, 9 figures

Valley degree of freedom besides spin is a promising candidate as a carrier of information. Spintronics has come a long way and spin modulation can be realized by quantum interference and spin-orbit coupling effect. However, the control of valley degree of freedom using quantum interference is still a problem to be explored. Here we discover a mechanism of producing valley polarization in a monolayer transition metal dichalcogenides nanoribbon with attached stubs, in which valley-resolved Fano resonance are formed due to the quantum interference of intervalley backscattering. When the quantum interference occurs between the localized states at the edge of the stubs and the continuous channels in the nanoribbon, the transmission dips of Fano effect is valley-polarized. As the number of stubs increases, the valley-polarized transmission dips will split and valley-resolved minigaps are formed by Fano resonance with intervalley backscattering in stub superlattice. When the electron incident energy is in these valley-resolved gaps of the superlattice, even with several stubs, the transmission can have a significant valley polarization. Our finding points to an opportunity to realize valley functionalities by quantum interference., Comment: 8 pages, 6 figures

The central engine of gamma-ray bursts (GRBs) remains an open and forefront topic in the era of multimessenger astrophysics. The X-ray plateaus appear in some GRB afterglows, which are widely considered to originate from the spindown of magnetars. According to the stable magnetar scenario of GRBs, an X-ray plateau and a decay phase as $\sim t^{-2}$ should appear in X-ray afterglows. Meanwhile, the ``normal'' X-ray afterglow is produced by the external shock from GRB fireball. We analyze the Neil Gehrels \emph{Swift} GRB data, then find three gold samples, which have an X-ray plateau and a decay phase as $\sim t^{-2}$ superimposed on the jet-driven normal component. Based on these features of the lightcurves, we argue that the magnetars should be the central engines of these three GRBs. Future joint multimessenger observations might further test this possibility, then which can be beneficial to constrain GRB physics., Comment: 6 pages, 3 figures, 1 table, accepted for publication in ApJ

Manipulating the valley degree of freedom to encode information for potential valleytronic devices has ignited a new direction in solid-state physics. A significant, fundamental challenge in the field of valleytronics is how to generate and regulate valley-polarized currents by practical ways. Here, we discover a new mechanism of producing valley polarization in a monolayer transition metal dichalcogenides superlattice, in which valley-resolved gaps are formed at the supercell Brillouin zone boundaries and centers due to the intervalley scattering. When the energy of the incident electron is in the gaps, the available states are valley polarized, thus providing a valley-polarized current from the superlattice. We show that the direction and strength of the valley polarization may further be tuned by varying the potential applied the superlattice. The transmission can have a net valley polarization of 55% for a 4-period heterojunction. Moreover, such two valley filters in series may function as an electrostatically controlled giant valleyresistance device, representing a zero magnetic field counterpart to the familiar giant magnetoresistance device., Comment: 14 pages, 4 figures

Most dynamically confirmed stellar-mass black holes and the candidates were originally selected from X-ray outbursts. In the present work, we search for black hole candidates in the LAMOST survey by using the spectra along with photometry from the ASAS-SN survey, where the orbital period of the binary may be revealed by the periodic light curve, such as the ellipsoidal modulation type. Our sample consists of 9 binaries, where each source contains a giant star with large radial velocity variation ($\Delta V_{\rm R} > 70~{\rm km~s^{-1}}$) and periods known from light curves. We focus on the 9 sources with long periods ($T_{\rm ph} > 5$ days) and evaluate the mass $M_2$ of the optically invisible companion. Since the observed $\Delta V_{\rm R}$ from only a few repeating spectroscopic observations is a lower limit of the real amplitude, the real mass $M_2$ can be significantly higher than the current evaluation. It is likely an efficient method to place constraints on $M_2$ by combining $\Delta V_{\rm R}$ from LAMOST and $T_{\rm ph}$ from ASAS-SN, particularly by the ongoing LAMOST Medium Resolution Survey., Comment: 12 pages, 3 figures, accepted for publication in Astronomical Journal

We propose a method to search for stellar-mass black hole (BH) candidates with giant companions from spectroscopic observations. Based on the stellar spectra of LAMOST Data Release 6, we obtain a sample of seven giants in binaries with large radial velocity variation $\Delta V_R > 80~{\rm km~s^{-1}}$. With the effective temperature, surface gravity, and metallicity provided by LAMOST, and the parallax given by {\it Gaia}, we can estimate the mass and radius of the giant, and therefore evaluate the possible mass of the optically invisible star in the binary. We show that the sources in our sample are potential BH candidates, and are worthy of dynamical measurement by further spectroscopic observations. Our method may be particularly valid for the selection of BH candidates in binaries with unknown orbital periods., Comment: 13 pages, 2 figures, accepted for publication in ApJ Letters

The occurrence rates of bright X-ray flares in z<1 gamma-ray bursts (GRBs) with or without observed supernovae (SNe) association were compared. Our Sample I: the z<1 long GRBs (LGRBs) with SNe association (SN-GRBs) and with early Swift/X-Ray Telescope (XRT) observations, consists of 18 GRBs, among which only two GRBs have bright X-ray flares. Our Sample II: for comparison, all the z<1 LGRBs without observed SNe association and with early Swift/XRT observations, consists of 45 GRBs, among which 16 GRBs present bright X-ray flares. Thus, the study indicates a lower occurrence rate of bright X-ray flares in Sample I (11.1%) than in Sample II (35.6%). In addition, if dim X-ray fluctuations are included as flares, then 16.7% of Sample I and 55.6% of Sample II are found to have flares, again showing the discrepancy between these two samples. We examined the physical origin of these bright X-ray flares and found that most of them are probably related to the central engine reactivity. To understand the discrepancy, we propose that such a lower occurrence rate of flares in the SN-GRB sample may hint at an energy partition among the GRB, SNe, and X-ray flares under a saturated energy budget of massive star explosion., Comment: 10 pages, 4 figures, accepted for publication in MNRAS

Short gamma-ray bursts may originate from the merger of double neutron stars (NS) or that of a black hole (BH) and an NS. We propose that the bright X-ray flare related to the central engine reactivity may hint a BH-NS merger, since such a merger can provide more fall-back materials and therefore a more massive accretion disk than the NS-NS merger. Based on the observed 49 short bursts with Swift/X-ray Telescope follow-up observations, we find that three bursts have bright X-ray flares, among which three flares from two bursts are probably related to the central engine reactivity. We argue that these two bursts may originate from the BH-NS merger rather than the NS-NS merger. Our suggested link between the central engine-powered bright X-ray flare and the BH-NS merger event can be checked by the future gravitational wave detections from advanced LIGO and Virgo., Comment: 15 pages, 6 figures, accepted for publication in ApJ

Outflows launched from a remnant disc of compact binary merger may have essential contribution to the kilonova emission. Numerical calculations are conducted in this work to study the structure of accretion flows and outflows. By the incorporation of limited-energy advection in the hyper-accretion discs, outflows occur naturally from accretion flows due to imbalance between the viscous heating and the sum of the advective and radiative cooling. Following this spirit, we revisit the properties of the merger outflow ejecta. Our results show that around $10^{-3} \sim 10^{-1} M_\odot$ of the disc mass can be launched as powerful outflows. The amount of unbound mass varies with the disc mass and the viscosity. The outflow-contributed peak luminosity is around $10^{40} \sim 10^{41}$ erg/s. Such a scenario can account for the observed kilonovae associated with short gamma-ray bursts, including the recent event AT2017gfo (GW170817)., Comment: 8 pages, 6 figures, accepted for publication in MNRAS

Central engine of gamma-ray bursts (GRBs) may be intermittent and launch several episodes of ejecta separated by a long quiescent interval. In this scenario, an external shock is formed due to the propagation of the first launched ejecta into the circum-burst medium and the later launched ejecta may interact with the external shock at later period. Owing to the internal dissipation, the later launched ejecta may be observed at a later time ($t_{\rm{jet}}$). In this paper, we study the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$, where $t_{\rm{b}}$ is the collision time of the later launched ejecta with the formed external shock. It is found that the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$ depends on the bulk Lorentz factor ($\Gamma_{\rm{jet}}$) of the later launched ejecta and the density ($\rho$) of the circum-burst medium. If the value of $\Gamma_{\rm{jet}}$ or $\rho$ is low, the $t_{\rm{b}}$ would be significantly larger than $t_{\rm{jet}}$. However, the $t_{\rm{b}}\sim t_{\rm{jet}}$ can be found if the value of $\Gamma_{\rm{jet}}$ or $\rho$ is significantly large. Our results can explain the large lag of the optical emission relative to the $\gamma$-ray/X-ray emission in GRBs, e.g., GRB~111209A. For GRBs with a precursor, our results suggest that the energy injection into the external shock and thus more than one external-reverse shock may appear in the main prompt emission phase. According to our model, we estimate the Lorentz factor of the second launched ejecta in GRB~160625B., Comment: 10 pages, 4 figures, accepted for publication in ApJ

Two plateaus and one following bump in the X-ray light curve of GRB 170714A have been detected by the \textit{Swift}/X-Ray Telescope, which could be very meaningful for the central engine of gamma-ray bursts (GRBs), implying that the origin of this burst might be different from that of other ultra-long GRBs. We propose that merging two neutron stars into a hyper-massive quark star (QS) and then collapsing into a black hole (BH), with a delay time around $10^4$~s, could be responsible for those X-ray components. The hyper-massive QS is initially in a fluid state, being turbulent and differentially rotating, but would be solidified and release its latent heat injected into the GRB fireball (lasting about $10^3$~s during the liquid-solid phase transition). Magnetic field as high as $\sim 10^{15}$~G could be created by dynamo action of the newborn liquid QS, and a magnetar-like central engine (after solidification) supplies significant energy for the second plateau. More energy could be released during a fall-back accretion after the post-merger QS collapses to a BH, and the X-ray bump forms. This post-merger QS model might be tested by future observations, with either advanced gravitational wave detectors (e.g., advanced LIGO and VIRGO) or X-ray/optical telescopes., Comment: 6 pages, 1 figure, 1 table, accepted for publication in ApJ

We derive a simple analytical formula to describe the evolution of spectral index $\beta$ in the steep decay phase shaped by the curvature effect with assumption that the spectral parameters and Lorentz factor of jet shell is the same for different latitude. Here, the value of $\beta$ is estimated in 0.3$-$10keV energy band. For a spherical thin shell with a cutoff power law (CPL) intrinsic radiation spectrum, the spectral evolution can be read as a linear function of observer time. For the situation with Band function intrinsic radiation spectrum, the spectral evolution may be complex. If the observed break energy of radiation spectrum is larger than 10keV, the spectral evolution is the same as that shaped by jet shells with a CPL spectrum. If the observed break energy is less than 0.3keV, the value of $\beta$ would be a constant. Others, the spectral evolution can be approximated as a logarithmal function of the observer time in generally., Comment: 24 pages, 13 figures, accepted for publication in ApJ

The curvature effect may be responsible for the steep decay phase observed in gamma-ray bursts. For testing the curvature effect with observations, the zero time point $t_0$ adopted to plot observer time and flux on a logarithmic scale should be appropriately selected. In practice, however, the true $t_0$ cannot be directly constrained from the data. Then, we move $t_0$ to a certain time in the steep decay phase, which can be easily identified. In this situation, we derive an analytical formula to describe the flux evolution of the steep decay phase. The analytical formula is read as $F_\nu\propto (1+\tilde t_{\rm obs}/{\tilde t_c})^{-\alpha}$ with $\alpha(\tilde{t}_{\rm obs})=2+{\int_{0}^{\log (1+\tilde{t}_{\rm obs}/{\tilde{t}_c})} {\beta(\tau)d[\log(1+\tau/{\tilde{t}_c})]}}/{\log (1 + {\tilde t}_{\rm obs}/{{\tilde t}_c})}$, where $F_\nu$ is the flux observed at frequency $\nu$, $\tilde t_{\rm obs}$ is the observer time by setting zero time point $t_0$ at a certain time in the steep decay phase, $\beta$ is the spectral index estimated around $\nu$, and ${\tilde t}_c$ is the decay timescale of the phase with $\tilde{t}_{\rm obs}{\geqslant}0$. We test the analytical formula with the data from numerical calculations. It is found that the analytical formula presents a well estimation about the evolution of flux shaped by the curvature effect. Our analytical formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase., Comment: 28 pages, 18 figures, accepted for publication in ApJ

Recent simulations on super-Eddington accretion flows have shown that, apart from the diffusion process, the vertical advection based on magnetic buoyancy can be a more efficient process to release the trapped photons in the optically thick disk. As a consequence, the radiative luminosity from the accretion disk can be far beyond the Eddington value. Following this spirit, we revisit the structure and radiation of hyper-accretion disks with mass accretion rates in the range $10^{-3}\sim 10~M_{\sun}~{\rm s}^{-1}$. Our results show that, due to the strong cooling through the vertical advection, the disk temperature becomes lower than that in the classic model without the vertical advection process, and therefore the neutrino luminosity from the disk is lower. On the other hand, the gamma-ray photons released through the vertical advection can be extremely super-Eddington. We argue that the large amount of escaped gamma-ray photons may have more significant contribution to the primordial fireball than the neutrino annihilation, and may hint a link between gamma-ray bursts and kilonovae in the black hole hyper-accretion scenario., Comment: 13 pages, 7 figures, accepted for publication in ApJ

High temperature superconducting coated conductor (CC) could be practically applied in electric equipment due to its favorable mechanical properties and the critical current performance of YBCO superconducting layer. It is well known that CC could be easily delaminated because of its poor stress tolerance in thickness direction, i.e. along the c-axis of YBCO. Commonly, a stack including YBCO layer and silver stabilizer could be obtained after the delamination. It would be interesting to investigate the superconducting properties of the delaminated stack, since it could also be considered as a new type of CC with the silver stabilizer as the buffer layer, which is quite different from the oxide buffer layers in the traditional CC and might lead to new applications. In this study, a CC sample was delaminated by liquid nitrogen immersing. A Hall probe scanning system was employed to measure the critical current (IC) distribution of the original sample and the obtained stack. It was found that IC could be partially preserved after the delamination. Dense and crack-free morphologies of the delaminated surfaces were observed by scanning electron microscopy, and the potential application of the obtained stack in superconducting joint technology was discussed., Comment: 4 pages, 5 figures

This work focuses on a sample of seven extremely late-time X-ray flares with peak time $t_{\rm p} > 10^4 {\rm s}$, among which two flares can be confirmed as the late-time activity of central engine. The main purpose is to investigate the mechanism of such late-time flares based on the internal origin assumption. In the hyper-accreting black hole (BH) scenario, we study the possibility of two well-known mechanisms as the central engine to power such X-ray flares, i.e., the neutrino-antineutrino annihilation and the Blandford-Znajek (BZ) process. Our results show that the annihilation luminosity is far below the observational data. Thus, the annihilation mechanism cannot account for such late-time flares. For the BZ process, if the role of outflows is taken into consideration, the inflow mass rate near the horizon will be quite low such that the magnetic field will probably be too weak to power the observed X-ray flares. We therefore argue that, for the late-time flares with internal origin, the central engine is unlikely to be associated with BHs. On the contrary, a fast rotating neutron star with strong bipolar magnetic fields may be responsible for such flares., Comment: 16 pages, 6 figures, accepted for publication in ApJ

We present time-resolved spectral analysis of the steep decay segments of 29 bright X-ray flares of gamma-ray bursts (GRBs) observed with the Swift/X-ray telescope, and model their lightcurves and spectral index evolution behaviors with the curvature effect model. Our results show that the observed rapid flux decay and strong spectral index evolution with time can be well fit with this model, and the derived characteristic timescales ($t_c$) are in the range of $33\sim 264$ seconds. Using an empirical relation between the peak luminosity and the Lorentz factor derived from the prompt gamma-rays, we estimate the Lorentz factors of the flares ($\Gamma_{\rm X}$). We obtain $\Gamma_{\rm X}=17\sim 87$ with a median value of $52$, which is smaller than the initial Lorentz factors of prompt gamma-ray fireballs. With the derived $t_c$ and $\Gamma_{\rm X}$, we constrain the radiating regions of 13 X-ray flares, yielding $R_{\rm X}=(0.2\sim 1.1)\times 10^{16}$ cm, which are smaller than the radii of the afterglow fireballs at the peak times of the flares. A long evolution feature from prompt gamma-ray phase to the X-ray epoch is found by incorporating our results with a sample of GRBs whose initial Lorentz factors are available in literatures, i.e., $\Gamma\propto [t_{p}/(1+z)]^{-0.69\pm 0.06}$. These results may shed lights on the long term evolution of GRB central engines., Comment: 28 pages, 33 figures, accepted for publication in ApJ

The emission from black hole binaries (BHBs) and active galactic nuclei (AGNs) displays significant aperiodic variabilities. The most promising explanation for these variabilities is the propagating fluctuations in the accretion flow. It is natural to expect that the mechanism driving variabilities in BHBs and AGNs may operate in a black hole hyper-accretion disk, which is believed to power gamma-ray bursts (GRBs). We study the variabilities of jet power in GRBs based on the model of propagating fluctuations. It is found that the variabilities of jet power and the temporal profile of erratic spikes in this scenario are similar to those in observed light curves of prompt gamma-ray emission of GRBs. Our results show that the mechanism driving X-ray variabilities in BHBs and AGNs may operate in the central engine to drive the variabilities of GRBs., Comment: 6 pages, 2 figures, accepted for publication in MNRAS

X-ray flares are generally supposed to be produced by the later central engine activities, and may share the similar physical origin with prompt emission of gamma-ray bursts (GRBs). In this paper, we have analyzed all significant X-ray flares from the GRBs observed by {\em Swift} from April 2005 to March 2015. The catalog contains 468 bright X-ray flares, including 200 flares with redshifts. We obtain the fitting results of X-ray flares, such as start time, peak time, duration, peak flux, fluence, peak luminosity, and mean luminosity. The peak luminosity decreases with peak time, following a power-law behavior $L_p \propto T_{peak,z}^{-1.27}$. The flare duration increases with peak time. The 0.3-10 keV isotropic energy of X-ray flares distribution is a lognormal peaked at $10^{51.2}$ erg. We also study the frequency distributions of flare parameters, including energies, durations, peak fluxes, rise times, decay times and waiting times. Power-law distributions of energies, durations, peak fluxes, and waiting times are found in GRB X-ray flares and solar flares. These distributions could be well explained by a fractal-diffusive, self-organized criticality model. Some theoretical models basing on magnetic reconnection have been proposed to explain X-ray flares. Our result shows that the relativistic jets of GRBs may be Poynting-flux dominated., Comment: 36 pages, 10 figures, 2 tables, accepted for publication in ApJS

The variability of accretion rate, which is believed to induce the aperiodic variability of X-ray emission from disk, may affect the energy injection into the jet. In this spirit, a correlation between disk emission and jet emission can be formed even if the mean luminosity of disk emission keeps constant. In this work, these correlations are found in the situation that the luminosity of disk emission is variable and kept with a constant mean value. The obtained correlations may be shallower than that of the fundamental plane of black hole activity. In addition, the slope of correlation may increase with increasing observed frequency of jet emission. For the luminosities spacing with three days, the slope of correlation decreases with increasing black hole mass. The deviation of our found correlations from that of the fundamental plane is related to the suppression of variability in the jet emission in comparison with that in the disk emission. This mechanism may work in some sources in which shallower correlations have been reported. Moreover, it implies that luminosities used to estimate the relation of fundamental plane should cover an appropriate timescale, in which the variability of jet emission is not significantly suppressed., Comment: 19 pages, 5 figures, accepted for publication in ApJ