Effect Of Coulomb Repulsion Research Articles

Universal chemical formula dependence of ab initio low-energy effective Hamiltonian in single-layer carrier-doped cuprate superconductors: Study using a hierarchical dependence extraction algorithm

We explore the possibility to control the superconducting transition temperature at optimal hole doping Tcopt in cuprates by tuning the chemical formula (CF). Tcopt can be theoretically predicted from the parameters of the low-energy effective Hamiltonian with one antibonding (AB) Cu3dx2−y2/O2pσ orbital per Cu atom in the CuO2 plane, notably the nearest-neighbor hopping amplitude |t1| and the ratio u=U/|t1|, where U is the onsite effective Coulomb repulsion. However, the CF dependence of |t1| and u is a highly nontrivial question. In this paper, we propose the universal dependence of |t1| and u on the CF and structural features in hole doped cuprates with a single CuO2 layer sandwiched between block layers. To do so, we perform extensive calculations of |t1| and u and analyze the results by employing a machine-learning method called hierarchical dependence extraction (HDE). The main results are (a) |t1| has a main-order dependence on the radii RX and RA of the apical anion X and cation A in the block layer. (|t1| increases when RX or RA decreases.) (b) u has a main-order dependence on the ionic charge ZX of X and the hole doping δ of the AB orbital. (u decreases when |ZX| increases or δ increases.) We elucidate and discuss the microscopic mechanism of items (a) and (b). We demonstrate the predictive power of the HDE by showing the consistency between items (a) and (b) and results from previous works. The present results provide a basis for optimizing superconducting properties in cuprates and possibly akin materials. Also, the HDE method offers a general platform to identify dependencies between physical quantities. Published by the American Physical Society 2024

Dome structure in pressure dependence of superconducting transition temperature for HgBa2Ca2Cu3O8 : Studies by ab initio low-energy effective Hamiltonian

The superconducting (SC) cuprate HgBa2Ca2Cu3O8 (Hg1223) has the highest SC transition temperature Tc among cuprates at ambient pressure Pamb, namely, Tcopt≃138 K experimentally at the optimal hole doping concentration. Tcopt further increases under pressure P and reaches 164 K at optimal pressure Popt≃30 GPa, then Tcopt decreases with increasing P>Popt generating a dome structure [Gao , ]. This nontrivial and nonmonotonic P dependence of Tcopt calls for a theoretical understanding and mechanism. To answer this open question, we consider the low-energy effective Hamiltonian (LEH) for the antibonding (AB) Cu3dx2−y2/O2pσ band derived generally for the cuprates. In the AB LEH for cuprates with Nℓ≤2 laminated CuO2 planes between block layers, it was proposed that Tcopt is determined by a universal scaling Tcopt≃0.16|t1|FSC [Schmid , ], where t1 is the nearest-neighbor hopping, and the SC order parameter at optimal hole doping FSC mainly depends on the ratio u=U/|t1| where U is the onsite effective Coulomb repulsion: The u dependence of FSC has a peak at uopt≃8.5 and a steep decrease with decreasing u in the region u<uopt irrespective of materials dependent on other parameters. In this paper, we show that |t1| increases with P, whereas u decreases with P in the Hamiltonian of Hg1223. Based on these facts, we show that the domelike P dependence of Tcopt can emerge at least qualitatively if we assume Hg1223 with Nℓ=3 follows the same universal scaling for Tcopt, and Hg1223 is located at the slightly strong coupling region u≳uopt at Pamb and u≃uopt at Popt by taking account of expected corrections to our calculation. The consequence of these assumptions is the following: With increasing P within the range P<Popt, the increase in Tcopt is accounted for by the increase in |t1|, whereas FSC is insensitive to the decrease in u around ≃uopt and hence to P as well. At P>Popt, the decrease in Tcopt is accounted for by the decrease in u below uopt, which causes a rapid decrease in FSC dominating over the increase in |t1|. We further argue the appropriateness of these assumptions based on the insight from studies on other cuprate compounds in the literature. In addition, we discuss the dependencies of u and |t1| on each crystal parameter (CP), which provides hints for design of even higher Tcopt materials. Published by the American Physical Society 2024

The effect of f-electrons on the structural phase transition, mechanical and electronic properties in light rare-earth bismuthides

ABSTRACT The electronic structure, phase transition pressure and mechanical properties of light rare-earth bismuthides (PrBi, NdBi, PmBi and SmBi) have been investigated by full geometry optimization using Vienna Ab-Initio Simulation Package (VASP) which has been used in combination with the projector augmented wave (PAW) method and the generalized gradient approximation (GGA) over the local density approximation (LDA) for exchange-correlation functional. We focus our attention on the lattice constants and elastic constants of these compounds. These compounds undergo a phase transition from the NaCl (B1) structure to the body-centered tetragonal (BCT) structure. We also report the density of states (DOS) of these rare earth bismuthides. In the case of PrBi and NdBi, the 4f states are treated as valence states. The effects of on-site Coulomb repulsion and the spin-orbit coupling (SOC) on the electronic structure are also studied.

The effect of Coulomb repulsion on Seebeck coefficient of NiCl2 monolayer

The Seebeck effect of NiCl2 has been explored by using first-principles calculations under the LDA+U to include the Coulomb repulsion. The exploration was conducted for two cases, namely, close to the critical temperature and room temperature. We found the slight difference of the peaks of Seebeck coefficients, i.e., the highest peak has been observed near the critical temperature. As the Coulomb repulsion was considered, the peak was shifted both two cases. It suggested that the Seebeck effect was influenced by the Coulomb repulsion.

Yu-Shiba-Rusinov states assisted by asymmetric Coulomb repulsion in a bipartite molecular device

Interfacing magnetism with superconducting condensates are promising candidates holding Majorana bound states with which fault-tolerant quantum computation could be implemented. Within this field, understanding the detailed dynamics is important both for fundamental reasons and for the development of innovative quantum technologies. Herein, motivated by a molecular magnet Tb2Pc3 interacting with a superconducting Pb(111) substrate, which results in spin-orbital Yu-Shiba-Rusinov (YSR) states, as is affirmed by a theoretical simulation with the aid of the numerical renormalization group technique (see Xia et al 2022 Nat. Commun. 13 6388), we study the YSR states and quantum phase transitions (QPTs) in a bipartite molecular device adsorbed on an wave superconducting substrate. We highlight the effect of asymmetric Coulomb repulsion by computing the spectrum function and spin correlation function in various parameter regimes. We demonstrate that if one impurity is non-interacting, there are no YSR states in both impurities with any repulsion value in the other impurity. Whereas if the repulsion in one impurity is strong, the YSR states are observed in both impurities, and a QPT arises as the repulsion in the other impurity sweeps, assisted by the competition between the superconducting singlet (Cooper pair) and the Kondo singlet. The evolution of YSR states distinguishes from the single impurity case and can be well interpreted by the energy scales of the isotropic superconducting gap parameter, as well as the two Kondo temperatures. Our findings provide theoretical insights into the phase diagram of two magnetic impurities on a superconducting host and shine light on the effects induced by asymmetric Coulomb repulsion on many-body interactions.

Coupled topological flat and wide bands: Quasiparticle formation and destruction.

Flat bands amplify correlation effects and are of extensive current interest. They provide a platform to explore both topology in correlated settings and correlation physics enriched by topology. Recent experiments in correlated kagome metals have found evidence for strange-metal behavior. A major theoretical challenge is to study the effect of local Coulomb repulsion when the band topology obstructs a real-space description. In a variant to the kagome lattice, we identify an orbital-selective Mott transition in any system of coupled topological flat and wide bands. This was made possible by the construction of exponentially localized and Kramers-doublet Wannier functions, which, in turn, leads to an effective Kondo-lattice description. Our findings show how quasiparticles are formed in such coupled topological flat-wide band systems and, equally important, how they are destroyed. Our work provides a conceptual framework for the understanding of the existing and emerging strange-metal properties in kagome metals and beyond.

Ionization efficiency at sub-keV energies for crystals and noble liquids

We study the ionization and light yields produced by nuclear recoils at low energies in pure crystals and noble liquids in the context of Lindhard’s integral equation, incorporating the effects of binding energy, improved modeling of the electronic stopping, and electronic straggling. We consider three different models for the electronic stopping power that incorporate Coulomb repulsion effects at low energies, and Bohr electronic stripping for high energies. Finally, we discuss possible new effects near threshold.

Superconductivity in type II layered Weyl semi-metals

Novel ‘quasi 2D’ typically layered (semi)metals offer a unique opportunity to control the density and even the topology of electronic matter. In intercalated MoTe 2 type II Weyl semi-metal the tilt of the dispersion relation cones is so large that topologically the Fermi surface is distinct from a more conventional type I. Superconductivity observed recently in this compound (Zhang et al 2022 2D Mater. 9 045027) demonstrated two puzzling phenomena. The gate voltage has no impact on critical temperature, in a wide range of density, while it is very sensitive to the inter-layer distance. A phonon theory of pairing in a layered Weyl material including the effects of Coulomb repulsion is constructed, which explains the above two features in MoTe 2. The first feature turns out to be a general one for any type II topological material, while the second reflects properties of the intercalated materials affecting the Coulomb screening.

Interatomic Coulomb repulsion in epitaxial carbon nanostructures on metals: Account of “excitonic” mean values

Anomalous, or “excitonic” mean values (EMV) corrections to the Coulomb repulsion effects on electronic and electron-phonone characteristics of the epitaxial single-layer and carbine are studied. It is demonstrated that in-plane and in-chain EMV correction to the nearest neighbor electron hopping energy is small, while for the Coulomb interaction between these nanostructures and metallic substrate can be significant. This conclusion can be applied to some other carbon nanostructures.

Asymmetric Alternative Current Electrochemical Method Coupled with Amidoxime-Functionalized Carbon Felt Electrode for Fast and Efficient Removal of Hexavalent Chromium from Wastewater

A large amount of Cr (VI)-polluted wastewater produced in electroplating, dyeing and tanning industries seriously threatens water ecological security and human health. Due to the lack of high-performance electrodes and the coulomb repulsion between hexavalent chromium anion and cathode, the traditional DC-mediated electrochemical remediation technology possesses low Cr (VI) removal efficiency. Herein, by modifying commercial carbon felt (O-CF) with amidoxime groups, amidoxime-functionalized carbon felt electrodes (Ami-CF) with high adsorption affinity for Cr (VI) were prepared. Based on Ami-CF, an electrochemical flow-through system powered by asymmetric AC was constructed. The mechanism and influencing factors of efficient removal of Cr (VI) contaminated wastewater by an asymmetric AC electrochemical method coupling Ami-CF were studied. Scanning Electron Microscopy (SEM), Fourier Transform Infrared (FTIR), and X-ray photoelectron spectroscopy (XPS) characterization results showed that Ami-CF was successfully and uniformly loaded with amidoxime functional groups, and the adsorption capacity of Cr (VI) was more than 100 times higher than that of O-CF. In particular, the Coulomb repulsion effect and the side reaction of electrolytic water splitting were inhibited by the high-frequency anode and cathode switching (asymmetric AC), the mass transfer rate of Cr (VI) from electrode solution was increased, the reduction efficiency of Cr (VI) to Cr (III) was significantly promoted and a highly efficient removal of Cr (VI) was achieved. Under optimal operating conditions (positive bias 1 V, negative bias 2.5 V, duty ratio 20%, frequency 400 Hz, solution pH = 2), the asymmetric AC electrochemistry based on Ami-CF can achieve fast (30 s) and efficient removal (>99.11%) for 0.5-100 mg·L-1 Cr (VI) with a high flux of 300 L h-1 m-2. At the same time, the durability test verified the sustainability of the AC electrochemical method. For Cr (VI)-polluted wastewater with an initial concentration of 50 mg·L-1, the effluent concentration could still reach drinking water grade (<0.05 mg·L-1) after 10 cycling experiments. This study provides an innovative approach for the rapid, green and efficient removal of Cr (VI) containing wastewater at low and medium concentrations.

Ab initio low-energy effective Hamiltonians for the high-temperature superconducting cuprates Bi2Sr2CuO6, Bi2Sr2CaCu2O8, HgBa2CuO4, and CaCuO2

We derive $ab$ $initio$ low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi$_2$Sr$_2$CuO$_6$ (Bi2201, $N_{\ell}=1$, $T_c^{\rm exp} \sim 10$ K), Bi$_2$Sr$_2$CaCu$_2$O$_8$ (Bi2212, $N_{\ell}=2$, $T_c^{\rm exp} \sim 84$ K), HgBa$_2$CuO$_4$ (Hg1201, $N_{\ell}=1$, $T_c^{\rm exp} \sim 90$ K) and CaCuO$_2$ (Ca11, $N_{\ell}=\infty$, $T_c^{\rm exp} \sim 110$ K), with different experimental optimal SC transition temperature $T_c^{\rm exp}$ and number $N_{\ell}$ of laminated CuO$_2$ planes between the two neighboring block layers. We apply the latest methodology of the multiscale $ab$ $initio$ scheme for correlated electron systems (MACE), and focus on the LEH consisting of one antibonding (AB) Cu$3d_{x^2-y^2}$/O$2p_{\sigma}$ orbital centered on each Cu atom. We discuss prominent features of this LEH: (1) The ratio $U/|t_1|$ between the onsite effective Coulomb repulsion (ECR) $U$ and amplitude of nearest neighbour hopping $t_1$ increases with $T^{\rm exp}_c$ and $N_{\ell}$, consistently with the expected increase in $d$-wave SC correlation function $P_{dd}$ with $U/|t_1|$. One possible cause of the increase of $U/|t_1|$ is the replacement of apical O atoms by Cu atoms from neighbouring CuO$_2$ planes when $N_{\ell}$ increases. Furthermore, we show that the increase in distance between Cu and apical O atoms decreases the effective screening (ES) by electrons outside of the LEH and increases $U/|t_1|$. (2) For Hg1201 and Ca11, we show that $U/|t_1|$ decreases when hole doping per AB orbital $\delta$ increases, which may partly account for the disappearance of SC when $\delta$ exceeds the optimal value in experiment. (3) For $N_{\ell} \geq 2$, off-site inter-CuO$_2$ plane ECR is comparable to off-site intra-CuO$_2$ plane ECR. We discuss contributions of inter-CuO$_2$ plane ECR to both $P_{dd}$ and the stability of the SC state.

DFT study of the effect of impurity defects on the inner-layer adsorption of hydrated Al(OH)2+ on the kaolinite (0 0 1) surface

Impurity defects are ubiquitous on the kaolinite surface. Density functional theory (DFT) was used to study the adsorption mechanism of Al3+ dihydroxy hydrate on ideal and impurity-doped kaolinite (001) Al-OH surfaces, and the influence of three common impurity defects, namely Mg, Ca, and Fe, on the surface properties. In addition, the effects of van der Waals forces and effective Coulomb repulsion on DFT calculations results are compared. The results show that the stable hydration configuration of Al(OH)2+ is Al(OH)2(H2O)4+. Hydrated Al(OH)2+ tends to be adsorbed at the Ot site and Al-Os are filled with bonding orbitals. Compared with the ideal kaolinite surface, hydrated Al(OH)2+ is more easily adsorbed on the Mg-doped surface. Mg and Ca doping enhanced the activity of surface O atoms and made the hydrated Al(OH)2+ more easily adsorbed on the surface, while Fe doping decreased the activity of surface O atoms. The van der Waals force has little effect on the surface properties and adsorption configuration. Since the effective Coulomb repulsion parameter U takes into account the Coulomb repulsion between local electrons with opposite spins on the Fe atom, the Fe-doped system can be described more accurately. The research results reveal the change of properties of kaolinite surface after doping and the adsorption mechanism of impurity Al on the doped kaolinite surface, which provides a reference for the development of high-efficiency ionic rare earth ore leaching agent.

Two-stage superconductivity in the Hatsugai–Kohomoto-BCS model

Superconductivity in strongly correlated electrons can emerge out from a normal state that is beyond the Landau’s Fermi liquid paradigm, often dubbed as ‘non-Fermi liquid’. While the theory for non-Fermi liquid is still not yet conclusive, a recent study on the exactly-solvable Hatsugai–Kohomoto (HK) model has suggested a non-Fermi liquid ground state whose Green’s function resembles the Yang–Rice–Zhang ansatz for cuprates (2020 Phillips et al Nat. Phys. 16 1175). Similar to the effect of on-site Coulomb repulsion in the Hubbard model, the repulsive interaction in the HK model divides the momentum space into three parts: empty, single-occupied and double-occupied regions, that are separated from each other by two distinct Fermi surfaces. In the presence of an additional Bardeen–Cooper–Schrieffer-type pairing interaction of a moderate strength, we show that the system exhibits a ‘two-stage superconductivity’ feature as temperature decreases: a first-order superconducting transition occurs at a temperature T c that is followed by a sudden increase of the superconducting order parameter at a lower temperature . At the first stage, , the pairing function arises and the entropy is released only in the vicinity of the two Fermi surfaces; while at the second stage, , the pairing function becomes significant and the entropy is further released in deep (single-occupied) region in the Fermi sea. The phase transitions are analyzed within the Ginzburg–Landau theory. Our work sheds new light on unconventional superconductivity in strongly correlated electrons.

Enhanced Spin Transfer Torque in Single Barrier Model Tunnel Junctions Containing Disordered Interface

We investigate the role of magnetic impurities in the barrier region in enhancing the torque transferred to the free ferromagnet layer in a non-collinear model tunnel junction. The tunnel junction is modeled using the non-equilibrium Green’s function formalism within the tight-binding approximation. The position of the impurity which is described by the single impurity Anderson model is found to have a profound impact on the trends observed in the spin transfer torque. The parallel ([Formula: see text]) torque is observed to have a switch on-off step-like bias behavior while the perpendicular ([Formula: see text]) torque exhibits a change in sign between the switch-on bias voltages. The spin transfer torque is found to be dramatically enhanced when the impurity is positioned at the interface of a five-layer barrier which is three orders of magnitude larger even at temperatures as high as 200[Formula: see text]K. With this formulation the effect of Coulomb repulsion at the impurity site on the torque could be deduced and the obtained results are explained in terms of the region-wise electronic density of states in the junction.

Ultrafast modification of the electronic structure of a correlated insulator

A non-trivial balance between Coulomb repulsion and kinematic effects determines the electronic structure of correlated electron materials. The use electromagnetic fields strong enough to rival these native microscopic interactions allows us to study the electronic response as well as the timescales and energies involved in using quantum effects for possible applications. We use element-specific transient x-ray absorption spectroscopy and high-harmonic generation to measure the response to ultrashort off-resonant optical fields in the prototypical correlated electron insulator NiO. Surprisingly, fields of up to 0.22 V/{\AA} leads to no detectable changes on the correlated Ni 3d-orbitals contrary to previous predictions. A transient directional charge transfer is uncovered, a behavior that is captured by first-principles theory. Our results highlight the importance of retardation effects in electronic screening, and pinpoints a key challenge in functionalizing correlated materials for ultrafast device operation.

Carbon and vacancy centers in hexagonal boron nitride

Creation of defect with predetermined optical, chemical and other characteristics is a powerful tool to enhance the functionalities of materials. Herewith, we utilize density functional theory to understand the microscopic mechanisms of formation of defects in hexagonal boron nitride based on vacancies and substitutional atoms. Through in-depth analysis of the defect-induced band structure and formation energy in varying growth conditions, we uncovered a dominant role of interdefect electron paring in stabilization of defect complexes. The electron reorganization modifies the exchange component of the electronic interactions which dominates over direct Coulomb repulsion or structural relaxation effects making the combination of acceptor- and donor-type defect centers energetically favorable. Based on an analysis of a large number of defect complexes we develop a simple picture of the inheritance of electronic properties when individual defects are combined together to form more complex centers.

Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers

We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moir\'eless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Bernal bilayer graphene and rhombohedral trilayer graphene, and we further predict existence of superconductivity in ABCA tetralayer graphene arising from electron-phonon interactions. In particular, we demonstrate that the acoustic-phonon-mediated superconductivity prevails over a wide range of doping in rhombohedral trilayer graphene and ABCA tetralayer graphene while superconductivity exists only in a narrow range of doping near the Van Hove singularity in Bernal bilayer graphene. Key features of our theory are the inclusion of realistic band structures with the appropriate Van Hove singularities and Coulomb repulsion effects (the so-called "$\mu^*$ effect") opposing the phonon-induced superconducting pairing. We also discuss how intervalley scatterings can suppress the spin-triplet spin-polarized superconductivity. Our work provides detailed prediction based on electron-acoustic-phonon-interaction-induced graphene superconductivity, which should be investigated in future experiments.

Functional Regulation and Stability Engineering of Three-Dimensional Covalent Organic Frameworks.

ConspectusAs one of the most attractive members in the porous materials family, covalent organic frameworks (COFs) have been reported thousands of times since their first discovery in 2005, covering their design, synthesis, and applications. However, an overwhelming majority of these COFs are based on two-dimensional (2D) topologies while three-dimensional (3D) COFs are numbered fewer than 100 up to date. In fact, baring enhanced specific surface area, interconnected channels, well-exposed functional moieties, and highly adjustable structures, 3D COFs are often more competitive in various application fields like adsorption, separation, chemical sensing, and heterogeneous catalysis compared with their 2D counterparts. However, significant crystallization problems and poor chemical stabilities, which might be attributed to the highly void frameworks and the absence of π-π stacking, have raised severe limitations over the research and application of 3D COFs. To solve these problems, more elaborate synthesis regulations or more moderate functionalization conditions are required. More importantly, the strategies for enhancing chemical stabilities of 3D COFs are of vital importance for their further development and practical applications.In this Account, we review the design principles, functional approaches, and stability regulation methods toward functional 3D COFs. We begin the discussion with some essential elements in the construction of 3D COF structures, including topologies, interpenetrations, linkages, and synthetic methods. After that, we focus on several strategies for the functionalization of 3D COFs, including in situ approaches (utilizing in situ generated COF linkages as the active sites), bottom-up synthesis (embedding functional moieties from predesigned building blocks), and postsynthesis modification (covalent modification or metalation of pristine frameworks). At last, we highlight some approaches toward the durable amplification of 3D COFs, which is highly important for framework functionalization and practical application. This target could be achieved through not only the introduction of some extra strengthening force, such as hydrophobic effects, coulomb repulsion, and steric hindrance effects, but also the utilization of robust linkages, which could enhance the stability from material nature.Due to their high surface area, various interpenetrated channels, multifarious functionalities, and promising stabilities, 3D COFs demonstrated excellent performance and have great potential in a wide range of application fields including adsorption and separation, heterogeneous catalysis, energy storage, and so on. Although the development of these materials has been limited by serious crystallization problems and stability restriction, great efforts have been devoted by researchers in the past decade, and a mass of strategies have been developed in synthesis control, functionalization regulation, and stability enhancement for 3D COFs. We expect 3D COFs to be practically utilized in the future with further advances in the design, preparation, and functionalization of these materials.

Structural and electronic properties of wide band gap charge transfer insulator Hg2Cl2: Insights from the first-principle calculations

The structural and electronic properties of Mercurous Chloride (Hg2Cl2) in its tetragonal (I4/mmm) phase at room temperature have been investigated from the first principle calculations. Detail calculations within the framework of density functional theory (DFT) upon incorporation of spin-orbit coupling (SOC) reveal that Hg2Cl2 is a wide band gap charge transfer (CT) insulator with band gap energy (Eg) ∼ 3.96 eV. Despite being a CT insulator, the orbital resolved PDOS of Hg2Cl2 compound exhibit energy dispositions that do not obey the Zaanen – Sawatzky – Allen (ZSA) diagram. The effect of on-site Coulomb repulsion (Hubbard +Udd) on the band gap of the compound has also been studied in detail. The Mulliken bond population, electronic charge density distribution and Bader charges analyses have been explored to unveil the covalent and ionic interactions between Hg and Cl atoms of the Hg2Cl2 compound. The Natural Bond Orbital (NBO) analyses have been performed to gain deeper insights on the CT interactions between Hg and Cl atoms of Hg2Cl2. The rationale behind the distortions of the octahedral domains within Hg2Cl2 crystal has also been elucidated in detail.

Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion

In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin–orbit Rashba coupling and the Coulomb repulsion. The spin–orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. Topological phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The region of existence of the zero energy Majorana states tends to zero at the point of the Mott phase transition. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model).