Dimensionality is a central concept in developing the theory of low-dimensional physics. However, previous research on dimensional crossover in the context of a Bose–Einstein condensate (BEC) has focused on the single-component BEC. To our best knowledge, further consideration of the two-component internal degrees of freedom on the effects of dimensional crossover is still lacking. In this work, we are motivated to investigate the dimensional crossover in a three-dimensional (3D) Rabi-coupled two-component BEC. The spin degrees of freedom consist of the Rabi-like and inter- and intra- interaction coupling constants. The dimensional crossovers from 3D to 2D or 1D are controlled by the continuous increase of 1D or 2D lattice depth respectively. Then we analyze how the dimensionality of the model system combined with spin degrees of freedom can affect quantum fluctuations. Accordingly, the analytical expressions of the ground-state energy and quantum depletion of the system are obtained. Our results show that the dimensional crossover induces a characteristic 3D to quasi-2D or 1D crossover in the behavior of quantum fluctuations, with an emphasis on the separated effects of Rabi-like and inter- and intra- interaction coupling constants on the quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Using the Monte Carlo method, the compensation temperature and hysteresis loops of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising-type graphene-like bilayer are investigated induced by different physical parameters such as crystal field, exchange coupling, external magnetic field, and temperature. The variations of magnetization, magnetic susceptibility, specific heat, and internal energy with the change of temperature are discussed. In addition, we also plot the phase diagrams including transition temperature and compensation temperature. Finally, multiple hysteresis loops under certain parameters are given.

As a very simple model, the Ising model plays an important role in statistical physics. In the paper, with the help of quantum Liouvillian statistical theory, we study the one-dimensional non-Hermitian Ising model at finite temperature and give its analytical solutions. We find that the non-Hermitian Ising model shows quite different properties from those of its Hermitian counterpart. For example, the 'pseudo-phase transition' is explored between the 'topological' phase and the 'non-topological' phase, at which the Liouvillian energy gap is closed rather than the usual energy gap. In particular, we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field. This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.

To some extent, the operational quickness of semiconductor devices depends on the transmission time of an electron through semiconductor nanostructures. However, the calculation of transmission time is very difficult, thanks to both the contentious definition of the transmission time in quantum mechanics and the complicated effective potential functions experienced by electrons in semiconductor devices. Here, based on an improved transfer matrix method to numerically solve the Schrödinger equation and H G Winful's relationship to calculate the dwell time, we develop a numerical approach to evaluate the transmission time of an electron in semiconductor devices. Compared to the exactly resolvable case of the rectangular potential barrier, the established numerical approach possesses high precision and small error, which may be employed to explore the dynamic response and operating speed of semiconductor devices. This proposed numerical method is successfully applied to the calculation of dwell time for an electron in double rectangular potential barriers and the dependence of transmission time on the number of potential barriers is revealed.

As is well known, any condition change in a network model will affect the research method and result. This paper studies an arbitrary m × n apple surface network with a pair of non-uniform boundary resistors, which is a complex network that has not been solved before. The research process of this paper consists of four strict basic steps according to RT-V theory. With the breakthrough of matrix transformation and eigenvector solution, two exact potential function formulae and two equivalent resistance formulae are derived. A series of applications and special cases are given to help readers understand the results. In particular, we have drawn eight visualized potential function images, which can intuitively understand the changing characteristics of potential function. The establishment of theoretical results provides a new theoretical basis for related interdisciplinary research.

The Heisenberg–Kitaev (HK) model on various lattices has attracted a lot of attention because it may lead to exotic states such as quantum spin liquid and topological orders. The rare-earth-based kagome lattice (KL) compounds ${\mathrm{Mg}}_{2}{\mathrm{RE}}_{3}{\mathrm{Sb}}_{3}{{\rm{O}}}_{14}$ $(\mathrm{RE}=\mathrm{Gd},\ \mathrm{Er})$ and $(\mathrm{RE}=\mathrm{Nd})$ have q = 0, 120° order and canted ferromagnetic (CFM) order, respectively. Interestingly, the HK model on the KL has the same ground state long-range orders. In the theoretical phase diagram, the CFM phase resides in a continuous parameter region and there is no phase change across special parameter points, such as the Kitaev ferromagnetic (KFM) point, the ferromagnetic (FM) point and its dual FM point. However, a ground state property cannot distinguish a system with or without topological nontrivial excitations and related phase transitions. Here, we study the topological magnon excitations and related thermal Hall conductivity in the HK model on the KL with CFM order. The CFM phase can be divided into two regions related by the Klein duality, with the self dual KFM point as their boundary. We find that the scalar spin chirality, which is intrinsic in the CFM order, changes sign across the KFM point. This leads to the opposite Chern numbers of corresponding magnon bands in the two regions, and also the sign change of the magnon thermal Hall conductivity.

We investigate the topological properties of an antiferromagnetic (AFM) chain with an on-site periodic potential, considering the intrinsic spin–orbit coupling and an external Zeeman field along with the nanowire. Our results indicate that Majorana zero modes (MZMs) can be observed by adjusting the strength of the periodic potential. We have calculated the energy spectrum, the wave-function and transport properties, and all these results support the existence of MZMs in the AFM chain. Additionally, multiple topological phase transitions occur as the strength of the periodic potential changes, and several regions support MZMs.

Any changes in resistor conditions will increase the difficulty of resistor network research. This paper considers a new model of a generalized 2 × n resistor network with an arbitrary intermediate axis that was previously unsolved. We investigate the potential function and equivalent resistance of the 2 × n resistor network using the RT-I theory. The RT-I method involves four main steps: (1) establishing difference equations on branch currents, (2) applying a matrix transform to study the general solution of the differential equation, (3) obtaining a current analysis of each branch according to the boundary constraints, and (4) deriving the potential function of any node of the 2 × n resistor network by matrix transformation, and the equivalent resistance formula between any nodes. The article concludes with a discussion of a series of special results, comparing and verifying the correctness of the conclusions. The work establishes a theoretical basis for related scientific research and application.

In this article a new achievement of fractional-order 3 × n Fan networks is presented. In the first step, the RT-I method is used to derive the general formulae of the equivalent impedance of fractional-order 3 × n Fan networks. In the second part, the effects of five system parameters (L, C, n, α and β) on amplitude-frequency and phase-frequency characteristics are analyzed. At the same time, the amplitude-frequency and phase-frequency characteristics of the fractional order 3 × n Fan network are revealed by Matlab drawing. This work has important theoretical and practical significance for resistor network models in the field of natural science and engineering technology.

The third-harmonic generation (THG) coefficient for a spherical quantum dot system with inversely quadratic Hellmann plus inversely quadratic potential is investigated theoretically, considering the regulation of quantum size, confinement potential depth and the external environment. The numerical simulation results indicate that the THG coefficient can reach the order of 10⁻¹² m² V^–2, which strongly relies on the tunable factor, with its resonant peak experiencing a redshift or blueshift. Interestingly, the effect of temperature on the THG coefficient in terms of peak location and size is consistent with the quantum dot radius but contrasts with the hydrostatic pressure. Thus, it is crucial to focus on the influence of internal and external parameters on nonlinear optical effects, and to implement the theory in practical experiments and the manufacture of optoelectronic devices.

The fundamental I–V formula of an organic field effect transistor (OFET) is improved to overcome the divergence of the integrand, so it is very convenient for both numerical calculations and analytic derivations. The analytic I–V formulae are derived based on the exponential mobility model and power-function mobility model, respectively, and the derived analytic formulae are applied to three OFET devices. The results calculated from the reformulated analytic I–V formulae taking in exponential and power function mobility models are all in good agreement with the experimental I–V data. The parameters μ₀ and γ that are extracted from the mobility model and fitted by experimental data show simple Arrhenius temperature dependence and inverse linear relationship with temperature, respectively. These findings are very useful for practical applications and device simulations.

Based on the Monte Carlo method, we examined the dynamic magnetic behaviors and magnetocaloric effect of a Kagome lattice subjected to the influence of time-dependent oscillating and time-independent magnetic fields. We used the Ising model to describe the Kagome lattice and study the dynamic order parameters, blocking temperature, internal energy, and phase diagrams. The results revealed that exchange coupling increases the stability of the system and the bias field induces order; however, the time-dependent oscillating magnetic field induces disorder. In addition, the magnetocaloric properties, changes in magnetic entropy, and relative cooling power of the Kagome lattice were investigated.

This paper theoretically studies the impurity states and the effects of impurity concentration and configuration on the optical, electrical, and statistical properties of CdSe nanoplatelets (NPLs). An image charge-based model of electron-impurity interaction is proposed. The charge-carrier energy spectra and corresponding wave functions depending on the impurity number and configuration are calculated. The electron binding energies are calculated for different NPL thicknesses. It is shown that the image charge-based interaction potential that arises due to the dielectric constants mismatch is much stronger than the interaction potential that does not take such a mismatch into account. Also, it is demonstrated that the binding energies are increasing with the number of impurities. We calculate the canonical partition function using the energy levels of the electron, which in turn is used to obtain the mean energy, heat capacity, and entropy of the non-interacting electron gas. The thermodynamic properties of the non-interacting electron gas that depend on the geometric parameters of the NPL, impurity number, configuration, and temperature are studied.

This study introduces an innovative dual-tunable absorption film with the capability to switch between ultra-wideband and narrowband absorption. By manipulating the temperature, the film can achieve multi-band absorption within the 30–45 THz range or ultra-wideband absorption spanning 30–130 THz, with an absorption rate exceeding 0.9. Furthermore, the structural parameters of the absorption film are optimized using the particle swarm optimization (PSO) algorithm to ensure the optimal absorption response. The absorption response of the film is primarily attributed to the coupling of guided-mode resonance and local surface plasmon resonance effects. The film's symmetric structure enables polarization incoherence and allows for tuning through various means such as doping/voltage, temperature and structural parameters. In the case of a multi-band absorption response, the film exhibits good sensitivity to refractive index changes in multiple absorption modes. Additionally, the absorption spectrum of the film remains effective even at large incidence angles, making it highly promising for applications in fields such as biosensing and infrared stealth.

The polaron phenomenon is commonly observed in low-dimensional semiconductor materials and is known to have unique effects on conductive material properties. Furthermore, the phonon dragging effect, which leads to the polaron energy level, is less than the electron energy level. A decay magnetic field also affects the polaron effect, which causes polaron energy level changes. We demonstrate the unique electron–phonon coupling properties of this polaron using numerical calculations. Our findings have strong implications for theories of polaron properties and provide compelling evidence for a semiconductor device that industrial manufacturers use for new low-dimensional materials.

The successful discovery of borophene has opened a new door for the development of 2D materials. Due to its excellent chemical, electronic and thermal properties, borophene has shown considerable potential in supercapacitors, hydrogen storage and batteries. In this paper, the thermodynamic characteristics and magnetocaloric effect of borophene are specifically studied using the Monte Carlo method. We find that there is an opposite impact between the spin quantum number and the crystal field on the magnetization, magnetic susceptibility, specific heat and magnetic entropy of the system. Moreover, increasing the spin quantum number or decreasing the absolute value of the crystal field can improve the relative cooling power, the coercivity (h_c), and the remanence (M_R) and the area of the loop.

We investigate the size effect and boundary states based on a circular non-Hermitian chain under the nonreciprocal intra-cell coupling and inter-cell coupling regimes. We find that the circular non-Hermitian chain exhibits an even–odd effect on the unit cell corresponding to a large chain, which is different from the open non-Hermitian chain only exhibiting the same effect for a small chain. Moreover, we find that the originally localized bulk states become totally extended via designing the boundary coupling strength appropriately. The extended bulk states reveal the fact of the disappearance of the non-Hermitian skin effect. In particular, we show that the circular non-Hermitian chain also possesses the analogous edge states under some parameter regimes, which is pretty counterintuitive since the circular chain usually cannot define a boundary. Our investigations supply the different non-Hermitian phenomena in a circular non-Hermitian chain.

We present a family of graphical representations for the O(N) spin model, where N ≥ 1 represents the spin dimension, and N = 1, 2, 3 corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter 0 ≤ ℓ ≤ N/2, each configuration is the coupling of ℓ copies of subgraphs consisting of directed flows and N − 2ℓ copies of subgraphs constructed by undirected loops, which we call the XY and Ising subgraphs, respectively. On each lattice site, the XY subgraphs satisfy the Kirchhoff flow-conservation law and the Ising subgraphs obey the Eulerian bond condition. Then, we formulate worm-type algorithms and simulate the O(N) model on the simple-cubic lattice for N from 2 to 6 at all possible ℓ. It is observed that the worm algorithm has much higher efficiency than the Metropolis method, and, for a given N, the efficiency is an increasing function of ℓ. Besides Monte Carlo simulations, we expect that these graphical representations would provide a convenient basis for the study of the O(N) spin model by other state-of-the-art methods like the tensor network renormalization.

Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose-Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau-Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z₂ × Z₃. We call the transition a 'shamrock transition', due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.

We carry out a theoretical investigation of the low-temperature phase diagram of muonium hydride in two dimensions, using numerical simulations. It is shown that the phase diagram of this substance is qualitatively different in two and three dimensions. Specifically, while in three dimensions it is essentially identical to that of parahydrogen, i.e., only displaying a single (crystalline) phase. In two dimensions it is very similar to that of ⁴He, with an equilibrium liquid phase that turns superfluid at a temperature as high as ∼2.2 K, and crystallizes under applied pressure. This is a well-described case of a continuous-space condensed matter system whose ground state equilibrium phase is qualitatively altered by dimensional reduction.

This research paper provides valuable insight into the electronic, mechanical and transport properties of the Sr₂RuO₂F₂ compound. The study shows that the Sr₂RuO₄ compound exhibits a metallic ground state and that the energy gap widens with oxygen substitution with fluorine. The concept of absolute deformation potential and its correlation with band energies and strains is explained using deformation potential theory. The paper also examines the mechanical features of Sr₂RuO₂F₂ using the Voigt–Reuss–Hill approximation method and analyzes its elastic constants, bulk modulus and shear modulus, indicating flexibility and suitability for optoelectronic applications. The role of acoustic phonons in scattering rates and carrier mobility in Sr₂RuO₂F₂ and its potential for phonon-mediated superconductivity is investigated. The intrinsic resistivity of electrons and holes under strain and its potential impact on superconductivity and electrical resistivity are also discussed. The insight provided by this study contributes to the current understanding of Sr₂RuO₂F₂, and its potential applications.

We revisit the problem of adsorption of a single ⁴He layer on graphene, focusing on the commensurate (C_1/3) crystalline phase, specifically on whether it may possess a nonzero superfluid response, and on the existence of superfluid phases, either (metastable) liquid or vacancy-doped crystalline. We make use of canonical quantum Monte Carlo simulations at zero and finite temperature, based on a realistic microscopic model of the system. Our results confirm the absence of any superfluid response in the commensurate crystal, and that no thermodynamically stable uniform phase exists at lower coverage. No evidence of a possibly long-lived, metastable superfluid phase at C_1/3 coverage is found. Altogether, the results of ground-state projection methods and finite-temperature simulations are entirely consistent.

Most path integral expressions for quantum open systems are formulated with diagonal system-bath coupling, where the influence functional is a functional of scalar-valued trajectories. This formalism is enough if only a single bath is under consideration. However, when multiple baths are present, non-diagonal system-bath couplings need to be taken into consideration. In such a situation, using an abstract Liouvillian method, the influence functional can be obtained as a functional of operator-valued trajectories. The value of the influence functional itself also becomes a superoperator rather than an ordinary scalar, whose meaning is ambiguous at first glance and its connection to the conventional understanding of the influence functional needs extra careful consideration. In this article, we present another concrete derivation of the superoperator-valued influence functional based on the straightforward Trotter–Suzuki splitting, which can provide a clear picture to interpret the superoperator-valued influence functional.

Solar energy has always been a kind of energy with large reserves and wide application. It is well utilized through solar absorbers. In our study, the finite difference time domain method (FDTD) is used to simulate the absorber composed of refractory metal materials, and its absorption performance and thermal emission performance are obtained. The ultra-wide band of 200 nm–3000 nm reaches 95.93% absorption efficiency, of which the bandwidth absorption efficiency of 2533 nm (200 nm–2733 nm) is greater than 90%. The absorption efficiency in the whole spectrum range (200 nm–2733 nm) is 97.17% on average. The multilayer nanodisk structure of the absorber allows it to undergo strong surface plasmon resonance and near-field coupling when irradiated by incident light. The thermal emission performance of the absorber enables it to also be applied to the thermal emitter. The thermal emission efficiency of 95.37% can be achieved at a high temperature of up to 1500 K. Moreover, the changes of polarization and incident angle do not cause significant changes in absorption. Under the gradual change of polarization angle (0°–90°), the absorption spectrum maintains a high degree of consistency. As the incident angle increases from 0° to 60°, there is still 85% absorption efficiency. The high absorption efficiency and excellent thermal radiation intensity of ultra-wideband enable it to be deeply used in energy absorption and conversion applications.

Long-range magnetic order appears on a side decorated Heisenberg spin nanoribbon at nonzero temperature, although no spontaneous magnetization exists in a one- or two-dimensional isotropic Heisenberg model at any nonzero temperature according to the Mermin–Wagner theorem. By use of the spin Green's function method, we calculated the magnetizations of Heisenberg nanoribbons decorated by side spins with single-ion anisotropy and found that the system exhibits a nonzero transition temperature, whether the decorated edge spins of the system link together or separate from each other. When the width of the nanoribbon achieves infinite limit, the transition temperatures of the system tend to the same finite constant eventually whether one edge or both edges are decorated by side spins in the nanoribbon. The results reveal that the magnetism of a low-dimensional spin system is different from that of a three-dimensional spin system. When the single-ion anisotropy of edge spins in a Heisenberg spin nanoribbon can be modulated by an electric field experimentally, various useful long-range magnetic orders of the system can be obtained. This work can provide a detailed theoretical basis for designing and fabricating next-generation low-dimensional magnetic random-access memory.

Nanorod is a unique low-dimensional nanometer structure in which the Landau level arrangement of polaron is essential for understanding its quasiparticle system. However, the stability of the polaron level is susceptible to external factors, such as changing magnetic fields. In this manuscript, the Pekar variational method is employed to calculate the external magnetic field’s effect on the nanorod’s polaron Landau level. It was found that different magnetic fields have different effects on the polaron energy levels of the nanorod, which demonstrated that the external environment had critical effects on the polaron energy levels. This study provides a theoretical basis for regulating the interaction between electrons and phonons in low-dimensional nanomaterials.

The field of terahertz devices is important in terahertz technology. However, most of the current devices have limited functionality and poor performance. To improve device performance and achieve multifunctionality, we designed a terahertz device based on a combination of VO₂ and metamaterials. This device can be tuned using the phase-transition characteristics of VO₂, which is included in the triple-layer structure of the device, along with SiO₂ and Au. The terahertz device exhibits various advantageous features, including broadband coverage, high absorption capability, dynamic tunability, simple structural design, polarization insensitivity, and incident-angle insensitivity. The simulation results showed that by controlling the temperature, the terahertz device achieved a thermal modulation range of spectral absorption from 0 to 0.99. At 313 K, the device exhibited complete reflection of terahertz waves. As the temperature increased, the absorption rate also increased. When the temperature reached 353 K, the device absorption rate exceeded 97.7% in the range of 5–8.55 THz. This study used the effective medium theory to elucidate the correlation between conductivity and temperature during the phase transition of VO₂. Simultaneously, the variation in device performance was further elucidated by analyzing and depicting the intensity distribution of the electric field on the device surface at different temperatures. Furthermore, the impact of various structural parameters on device performance was examined, offering valuable insights and suggestions for selecting suitable parameter values in real-world applications. These characteristics render the device highly promising for applications in stealth technology, energy harvesting, modulation, and other related fields, thus showcasing its significant potential.

This study explores the presence of diverse phase diagrams and hysteresis characteristics, as well as their dependencies on segment dilution, in an Ising-type core/shell segmented nanostructure. The magnetic and hysteretic behavior of the nanostructure was carefully investigated by employing the effective-field theory and its respective diluted parameters. The phase diagrams reveal characteristic phenomena that are influenced by the dilution parameters. Specifically, this study examined the variations in phase transitions and tricritical points by altering the dilution and physical parameters of the segments. The investigation also encompasses an examination of the hysteresis characteristics, including the hysteresis loop, coercivity, and remanence, in relation to the segment dilution dependence of the segmented nanowire. It was discovered that as the temperature rises, the hysteresis loop areas diminish. However, intriguingly, at specific dilution and crystal area values, the hysteresis loop areas exhibit an augmentation.

With the Becchi–Rouet–Stora–Tyutin (BRST) quantization of gauge theory, we solve the long-standing difficult problem of the local constraint conditions, i.e. the single occupation of a slave particle per site, in the slave particle theory. This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_i which ensures the constraint: in the Hamiltonian formalism of the theory, λ_i is time-independent and commutes with the Hamiltonian while in the Lagrangian formalism, λ_i(t) becomes time-dependent and plays a role of gauge field. This implies that the redundant degrees of freedom of λ_i(t) are introduced and must be removed by the additional constraint, the gauge fixing condition (GFC) ∂_tλ_i(t) = 0. In literature, this GFC was missed. We add this GFC and use the BRST quantization of gauge theory for Dirac’s first-class constraints in the slave particle theory. This GFC endows λ_i(t) with dynamics and leads to important physical results. As an example, we study the Hubbard model at half-filling and find that the spinon is gapped in the weak U and the system is indeed a conventional metal, which resolves the paradox that the weak coupling state is a superconductor in the previous slave boson mean field (MF) theory. For the t–J model, we find that the dynamic effect of λ_i(t) substantially suppresses the d-wave pairing gap and then the superconducting critical temperature may be lowered at least a factor of one-fifth of the MF value which is of the order of 1000 K. The renormalized T_c is then close to that in cuprates.

This work focuses on the ground-state phase diagram, the compensation temperatures and the critical behaviors of a ferrimagnetic graphene-like trilayer induced by crystal fields and exchange couplings. The simulation results show that a negative decrease in crystal field or an increase in exchange coupling can increase the critical temperature. More importantly, an M curve with double compensation temperatures can be observed, which is not predicted by the ${\rm{N}}\acute{{\rm{e}}}\mathrm{el}$ theory. This remarkable compensation phenomenon has potential application value in the field of magnetic recording.

In this article, we investigate the nonrelativistic quantum motion of a charged particle within a rotating frame, taking into account the Aharonov–Bohm (AB) effect and a uniform magnetic field. Our analysis entails the derivation of the equation of motion and the corresponding radial equation to describe the system. Solving the resulting radial equation enables us to determine the eigenvalues and eigenfunctions, providing a clear expression for the energy levels. Furthermore, our numerical analysis highlights the substantial influence of rotation on both energy levels and optical properties. Specifically, we evaluate the photoionization cross-section with and without the effects of rotation. To elucidate the impact of rotation on the photoionization process of the system, we present graphics that offer an appealing visualization of the intrinsic nature of the physics involved.

Using the modified Blonder–Tinkham–Klapwijk (BTK) theory, the interplay between the lifetime of quasi particles and the magnetic gap in a topological insulator-based ferromagnet/f-wave superconductor (TI-based FM/f–wave SC) tunnel structure is theoretically studied. Two symmetries of f₁ and f₂ waves are considered for superconducting pairing states. The results indicate that reducing the finite quasi-particle lifetime will induce a transformation of energy-gap peaks into a zero-bias peak in tunneling conductance spectrum, as well as a transformation of energy-gap dips into a zero-bias dip in shot noise spectrum, ultimately resulting in the smoothing of the zero-bias conductance peak and the zero-bias shot noise dip. An increase in magnetic gap will suppress the tunnel conductance and shot noise when the conventional Andreev retro-reflection dominates, but will enhance them when the specular Andreev reflection is dominant. Both specular Andreev reflection and conventional Andreev retro-reflection will be enhanced as the quasi-particle lifetime increases. When Fermi energy equals the magnetic gap, shot noise and tunneling conductance vanish across all energy ranges. These findings not only contribute to a better understanding of specular Andreev reflection in the FM/f–wave SC junction based on TIs but also provide insights for experimentally determining the f-wave pairing symmetry.