Semimetal State Research Articles

Electron-phonon correlations inducing excitonic excitations in semimetal and semiconducting materials

The influence of phonons on the low-energy excitonic excitations at zero temperature in the extended Falicov-Kimball model has been investigated. In the framework of the unrestricted Hartree-Fock approximation, a set of self-consistent equations for the excitonic condensate order parameter and a lattice distortion is derived when both electron-phonon coupling and electron-hole Coulomb interaction are treated on an equal footing. The low-energy excitation properties of the excitonic condensate are addressed in signatures of the optical conductivity and the dynamical excitonic susceptibility function. The real part of the optical conductivity is evaluated by the Kubo linear response theory and the imaginary part of the dynamical excitonic susceptibility is found by adapting the random phase approximation. In the semimetal state, one always finds a sharp peak in the optical conductivity spectrum indicating the stability of the excitonic condensation in the BCS type if the correlation between electrons and phonons becomes significant. In contrast, the peak is smeared out on the semiconducting side indicating the stability of the BEC-type excitonic condensate. In this semiconducting side, the sharp peak signature appears and the system turns to the BCS-type excitonic condensation state by increasing the electron-phonon correlations. In either the semimetal or the semiconducting normal state, increasing the electron-phonon correlations always reinforces a low-energy sharp peak in the dynamical excitonic susceptibility spectrum, indicating the existence of the tightly bound excitonic excitations before the condensation state. Specifically, on the semiconducting side, the ``halo'' phase with the preformed excitons exiting outside of the BEC-excitonic condensation state has been specified. The halo phase becomes more recognizable by raising the electron-phonon correlations.

Topological Nodal Surface and Quadratic Dirac Semimetal States and van Hove Singularities in ScH3 and LuH3 Superconductors.

The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH3 and LuH3, at both ambient and high pressures. Our studies show that both ScH3 and LuH3 have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin-orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin-orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH3 and LuH3 are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.

Experimental progress of topological exciton insulators

Under Coulomb interactions, electrons and holes have a phase transition from a semi-metal state into an excitonic ground state, with a gap spontaneously opening at the Fermi level. The excitonic ground state is called excitonic insulator. The excitonic insulator has attracted extensive attention in condensed matter physics, but the experimental evidence of such a quantum state is still under search. Until recent years, optical spectral and transport evidence of the excitonic insulator has first been observed in shallowly inverted InAs/GaSb quantum wells, which confirms the existence of the exciton insulator in a two-dimensional system. Surprisingly, one-dimensional helical-like topological edge states, which are not sensitive to temperature nor magnetic field, have been observed in the excitonic insulator state by transport measurements. This new quantum phase cannot be well explained by existing single-particle theories, which is called a topological excitonic insulator. In this paper, we systematically review the experimental studies on the topological excitonic insulator in the InAs quantum well and GaAs quantum well, including magneto transport, terahertz transmission, capacitance, and Coulomb drag measurements. These experimental results comprehensively characterize the bulk properties and edge properties of the topological excitonic insulator. Furthermore, as a ground state consisting of bosons, the topological excitonic insulator is expected to have a quantum phase transition into Bose-Einstein condensate with macroscopic coherence under extreme conditions, which provides a new platform for studying the quantum phenomena of Coulomb interactions in low dimensions.

Dirac semimetallic Janus Ni-trihalide monolayer with strain-tunable magnetic anisotropy and electronic properties.

Two-dimensional (2D) ferromagnetic (FM) semiconductors have been paid much attention due to the potential applications in spintronics. Here, the electronic and magnetic properties of 2D Janus Ni-trihalide monolayer Ni2X3Y3 (X, Y = I, Br, Cl; X ≠ Y) are investigated by first-principle calculations. The properties of Ni2X3Y3 (X, Y = I, Br, Cl; X ≠ Y) monolayers are compared by selecting the NiCl3 monolayer as the reference material. Ni2X3Y3 monolayers have two distinct magnetic ground states of ferromagnetic (FM) and antiferromagnetic (AFM). In the Ni2X3Y3 monolayer, two different orbital splits were observed, one semiconductor state and the other semimetal state. The semimetal state of Ni2X3Y3 can be tuned to semiconductor or metallic state when biaxial strain is applied. The magnetic anisotropy energy (MAE) of the Ni2X3Y3 monolayer can display variations compared to that of the NiCl3 monolayer, with the direction of easy magnetization being influenced by the specific halogen elements present. The easy magnetization direction of Ni2X3Y3 can also be changed by applying biaxial strain. The Tc of Ni2X3Y3 is predicted to be about 100 K according to the calculation of the EAFM-EFM model. The design of the Janus Ni2X3Y3 structure has expanded the range of 2D magnetic materials, a significant contribution has been made to the advancement of spintronics and its applications.

Non-centrosymmetric Weyl semimetal state and strain effect in the twisted-brick phase transition metal monochalcogenides.

Weyl semimetals are a class of gapless electronic excitation topological quantum materials upon breaking time-reversal or inversion symmetry. Here, we demonstrate the existence of the Weyl semimetal state in the non-centrosymmetric twisted-brick phase MoTe theoretically. The topological properties and strain effects of MoTe have been systematically studied based on first-principles calculations and the Wannier-based tight-binding method. In the absence of spin-orbit coupling (SOC), MoTe exhibits gapless nodal loop states related to the mirror reflection symmetry. When the SOC is turned on, the two nodal loops split into 22 pairs of Weyl points (WPs) with opposite chirality. When the effect of uniaxial (εz) strain is taken into account, the Weyl semimetal phase of MoTe shows great robustness and striking tunable topological strength. In particular, the total number of WPs changes significantly under strain. MoTe under +4% and +8% uniaxial strains have only four pairs of WPs with a relatively large separation in momentum space. These results show that MoTe under weak strain is a promising partly ideal type I Weyl semimetal candidate, while the isolog structure WTe both opens a direct gap with and without SOC, showing a compensated semimetal state.

Investigation of the electronic and thermoelectric properties of nitrogen chains doping SWCNT: ab initio study

In this work, we have investigated the electronic and thermoelectric properties of CN, C2N2 and C4N2 nanotubes resulting from doping of nitrogen atoms, three and two N-zigzag chains on small (3,3) single walled carbon nanotube (SWCNT) respectivelly. All calculations were performed via DFT theory using WIEN2K code. The electronic structure calculations were done using GGA with TB-mBJ exchange potential, while the thermoelectric calculations were done using semi-classical Boltzmann transport theory. The results show that all structures are energetically stable. The electronic behaviour of (3,3) SWCNT transforms from semiconductor to metal in CN nanotube and to topological Weyl semimetal (WSM) state for C2N2 and C4N2 nanotubes. The calculations of thermoelectric properties, including electrical conductivity, Seebeck coefficient and power factor, reaveal that the N-doping enhances the thermoelectric properties of pristine nanotube. SWCNT with nitrogen doping has promising electronic and thermoelectric capabilities that make it a potential for electronic and thermoelectric devices.

Spin-dependent scattering induced by surface states in spin-degenerate nodal-line semimetal

The topological nodal-line semimetal is characterized by the conduction band and valence band of electrons crossing along a one-dimensional line or closed loop in reciprocal space, with each nodal line carrying Π Berry phase. According to bulk-boundary correspondence, there exist drumheadlike surface states with weak dispersion at the boundary of system, surrounded by the projection of nodal loops onto the surface Brillouin zone. In most of nodal-line semimetals, the spin orbit coupling effect is weak, leading to the absence of a spin configuration for surface states under the single-particle picture. However, the featured weak dispersion of drumheadlike surface states enhances the electron-electron interaction effect, which triggers out ferromagnetic instability and causes spin splitting in the surface state. In this work, spin-dependent scattering caused by ferromagnetic surface states in spin-degenerate nodal-line semimetals is considered. It is found that both spin-splitting drumheadlike surface states can lead to resonant spin-flipped reflection. This physical process is reflected in a double-peak structure in the spin conductance spectrum. Specifically, we deal with the scattering problem induced by surface states in normal metal and nodal-line semimetal heterojunctions by using the scattering matrix and the Green’s functions theory, respectively, and obtain consistent conclusions. The result points out that spin-degenerate nodal-line semimetal surface states can still lead to spin-dependent transport, which provides a new perspective for the detection and potential application of spintronics in nodal-line semimetals.

Two-dimensional quadratic double Weyl semimetal

Unconventional Weyl semimetals have attracted intensive research interest in condensed-matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and first-principles electronic structure calculations, we predict that the Si/Bi van der Waals heterostructure is a two-dimensional unconventional quadratic double Weyl semimetal with strong spin-orbit coupling (SOC). Although unprotected by the ${C}_{3v}$ double group symmetry of the heterostructure, the two-dimensional quadratic double Weyl semimetal is stable for compressive strains up to 6.64%. The system transforms into a trivial semimetal with further increasing strain, where the phase boundary is a two-dimensional triply degenerate semimetal state. Furthermore, the Kane-Mele tight-binding model calculations show that the quadratic double Weyl phase is derived from the competition between the Rashba SOC and the proximity-effect-enhanced intrinsic SOC. On the other hand, by breaking mirror symmetry, the quadratic double Weyl semimetal transforms into a quantum spin Hall insulator as well as a quantum valley Hall insulator phase. Thus, the Si/Bi heterostructure is an excellent platform for studying the exotic physics of the two-dimensional double Weyl semimetal and other novel topological phases.

Interaction-driven topological phase transition in monolayer CrCl2 (pyrazine) 2

The quadratic band crossing points (QBCPs) at the Fermi level in two dimensions have been proposed to be unstable under electron-electron interactions. The possible interaction-driven states include the quantum anomalous Hall (QAH) state and various nematic ordered states. In this paper, motivated by the discovery of ferromagnetic van der Waals layered metal-organic framework ${\mathrm{CrCl}}_{2}{(\mathrm{pyrazine})}_{2}$, we theoretically propose that a single layer of ${\mathrm{CrCl}}_{2}{(\mathrm{pyrazine})}_{2}$ might realize one or some of these interaction-driven states based on the QBCP protected by ${C}_{4}$ symmetry. By introducing short-range density-density type repulsion interactions into this system, we have found the phase diagram depending on different interaction ranges and strengths. The exotic phases include the staggered chiral flux state manifesting the QAH effect, the site-nematic insulator, and the site-nematic Dirac semimetal state. The QAH state is robust against perturbations breaking the QBCP but it is weakened by increasing temperature. The metal-organic framework is tunable by changing the transition-metal elements, which might improve the gap size and stability of this interaction-induced QAH state.

Tunable topological phases in monolayer Pt2HgSe3 with exchange fields

We investigate topological phases of monolayer jacutingaite (${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$) that arise when considering the competing effects of spin-orbit coupling (SOC), magnetic exchange interactions, and staggered sublattice potential $V$. The interplay between the staggered potential and exchange field offers the possibility of attaining different topological phases. By analyzing the Berry curvatures and computing the Chern numbers and Hall conductivities, we demonstrate that the system is time-reversal-symmetry-broken quantum spin Hall insulator when ${m}_{b}<{\ensuremath{\lambda}}_{\mathrm{so}}$, where ${m}_{b}$ is the exchange field operating on the bottom Hg sublattice and ${\ensuremath{\lambda}}_{\mathrm{so}}$ is the intrinsic SOC. For ${m}_{b}>{\ensuremath{\lambda}}_{\mathrm{so}}$ and in the presence of Rashba SOC, we find that the band gap at valley $K({K}^{\ensuremath{'}})$ is topologically trivial (nontrivial) with Chern number $\mathcal{C}=1$ and valley Chern number ${\mathcal{C}}_{v}=\ensuremath{-}1$, indicating that the system is valley-polarized quantum anomalous Hall insulator. We show that the topology of each valley is swapped (the Chern number becomes $\mathcal{C}=\ensuremath{-}1$) by reversing the sign of the exchange field. The system transitions to a valley-polarized metal and quantum valley Hall phase as $V$ increases. Along the phase boundaries, we observe a single Dirac-cone semimetal states. These findings shed more light on the possibility of realizing and controlling topological phases in spintronics and valleytronics devices.

Single pair of multi-Weyl points in nonmagnetic crystals

Topological semimetal states having the minimal number, i.e., only a single pair, of Weyl points are desirable for the study of effects associated with chiral topological charges. So far, the search for such states is focused on magnetic spinful systems. Here, we find that nonmagnetic spinless systems can host a class of single-pair-Weyl-point (SP-WP) states, where the two Weyl points are located at two high-symmetry time-reversal-invariant momenta. We identify 32 candidate space groups that host such states, and we show that the chiral charge of each Weyl point in the SP-WP state must be an even integer. Besides achieving the minimal number, Weyl points in SP-WP states are far separated in momentum space, making the physics of each individual point better exposed. The large separation combined with the even topological charge lead to extended surface Fermi loops with a non-contractible winding topology on the surface Brillouin zone torus, distinct from conventional Weyl semimetals. We confirm our proposal in the phonon spectra of two concrete materials TlBO$_2$ and KNiIO$_6$. Our finding applies to a wide range of systems, including electronic, phononic, and various artificial systems. It offers a new direction for the search of ideal platforms to study chiral particles.

Monomer Mott Insulator (BEDT-TTF)Cu[N(CN)2]2 as a Potential Nodal Line System

We report the band structure calculations and the experimental results of resistivity and magnetic susceptibility in a spin-1/2 (BEDT-TTF)$^{\bullet +}$ monomer Mott insulator (BEDT-TTF)Cu[N(CN)$_2$]$_2$. The band calculations indicate a Dirac semimetal state with nodal lines at the Fermi level. The resistivity and the magnetic susceptibility as functions of temperature are well interpreted in terms of the monomer Mott insulating state instead of the expected semimetal state probably owing to strong electron correlation. In addition, we find that an Arrhenius-type steep reduction of the paramagnetic susceptibility appears below approximately 25 K, which indicates a spin-singlet ground state.

Evolution of the optical response of the magnetic topological insulators Mn( Bi1−xSbx)2Te4 with Sb content

MnBi$_2$Te$_4$ is a promising representative of intrinsic antiferromagnetic topological insulators, which could enable rare quantum mechanical effects like the quantum anomalous Hall effect. Especially at low temperatures, numerous studies have been reported, demonstrating the great potential of this compound in the magnetically ordered state below $T_{\mathrm{N}}$. Among recent findings, the alloy compound Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$ has been suggested to be an interesting candidate for the realization of an ideal Weyl semimetal state. By exchanging Bi by Sb, the electronic structure is influenced in terms of a shift of the Fermi energy, and a decrease in the energy gap has been predicted. In this work, we investigate and compare the optical conductivity of Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$ single crystals with various Sb doping levels $x$ by infrared reflectivity measurements. We observe a big impact of the Sb content on the low-energy excitations characterizing the metallic state of our samples. Different $x$=0.26 crystals show significant differences in their optical response and also a strong position dependence. The findings are compared to the recently reported optical conductivity spectrum of the pure compound MnBi$_2$Te$_4$.

Giant Dampinglike-Torque Efficiency in Naturally Oxidized Polycrystalline TaAs Thin Films

We report the measurement of efficient charge-to-spin conversion at room temperature in Weyl semimetal/ferromagnet heterostructures with both oxidized and pristine interfaces. Polycrystalline films of the Weyl semimetal, TaAs, are grown by molecular beam epitaxy on (001) GaAs and interfaced with a metallic ferromagnet (Ni$_{0.8}$Fe$_{0.2}$). Spin torque ferromagnetic resonance (ST-FMR) measurements in samples with an oxidized interface yield a spin torque efficiency as large as $\xi_{\mathrm{FMR}}=0.45\pm 0.25$ for a 8 nm Ni$_{0.8}$Fe$_{0.2}$ layer thickness. By studying ST-FMR in these samples with varying Ni$_{0.8}$Fe$_{0.2}$ layer thickness, we extract a damping-like torque efficiency as high as $\xi_{\mathrm{DL}}=1.36\pm 0.66$. In samples with a pristine (unoxidized) interface, the spin torque efficiency has opposite sign to that observed in oxidized samples ($\xi_{\mathrm{FMR}}=-0.27\pm 0.14$ for a 5 nm Ni$_{0.8}$Fe$_{0.2}$ layer thickness). We also find a lower bound on the spin Hall conductivity ($424 \pm 110 \frac{\hbar}{e}$ S/cm) which is surprisingly consistent with theoretical predictions for the single crystal Weyl semimetal state of TaAs.

Emergent topological states via digital (001) oxide superlattices

Oxide heterostructures exhibit many intriguing properties. Here we provide design principles for inducing multiple topological states in (001) (AMO3)1/(AM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AM^{\\prime}$$\\end{document}O3)1 oxide superlattices. Aided by first-principles calculations and model analysis, we show that a (SrMO3)1/(SrM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document}O3)1 superlattice (M = Nb, Ta and M′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document} = Rh, Ir) is a strong topological insulator with Z2 index (1;001). More remarkably, a (SrMoO3)1/(SrIrO3)1 superlattice exhibits multiple coexisting topological insulator (TI) and topological Dirac semi-metal (TDS) states. The TDS state has a pair of type-II Dirac points near the Fermi level and symmetry-protected Dirac node lines. The surface TDS Dirac cone is sandwiched by two surface TI Dirac cones in the energy-momentum space. The non-trivial topological properties arise from the band inversion between d orbitals of two dissimilar transition metal atoms and a particular parity property of (001) superlattice geometry. Our work demonstrates how to induce non-trivial topological states in (001) perovskite oxide heterostructures by rational design.

Critical topology and pressure-induced superconductivity in the van der Waals compound AuTe2Br

The study on quantum spin Hall effect and topological insulators formed the prologue to the surge of research activities in topological materials in the past decade. Compared to intricately engineered quantum wells, three-dimensional weak topological insulators provide a natural route to the quantum spin Hall effect, due to the adiabatic connection between them and a stack of quantum spin Hall insulators, and the convenience in exfoliation of samples associated with their van der Waals-type structure. Despite these advantages, both theoretical prediction and experimental identification of weak topological insulators remain scarce. Here, based on first-principles calculations, we show that AuTe2Br locates at the boundary between a strong and a weak topological semimetal state. We identify the key structural parameter that dictates the traversal of the topological transition, which can be easily realized in experiments. More interestingly, the critical topology of AuTe2Br persists up to an applied pressure of ~15.4 GPa before a structural phase transition accompanied by a change of electronic topology and the onset of superconductivity. Our results establish AuTe2Br as a new candidate for an effective tuning between weak and strong topological phases in a single material, with the potential to realize various other topological phases of matter.

Two-dimensional semimetal states in transition metal trichlorides: A first-principles study

The two-dimensional (2D) transition metal trihalide (TMX3, X = Cl, Br, I) family has attracted considerable attention in recent years due to the realization of CrCl3, CrBr3, and CrI3 monolayers. Up to now, the main focus of the theoretically predicted TMX3 monolayers has been on the Chern insulator states, which can realize the quantum anomalous Hall effect. Here, using first-principles calculations, we theoretically demonstrate that the stable OsCl3 monolayer has a ferromagnetic ground state and a spin-polarized Dirac point without spin–orbit coupling (SOC), which disappears in the band structure of a Janus OsBr1.5Cl1.5 monolayer. We find that OsCl3 exhibits in-plane magnetization when SOC is included. By manipulating the magnetization direction along the C2 symmetry axis of the OsCl3 structure, a gapless half-Dirac semimetal state with SOC can be achieved, which is different from the gapped Chern insulator state. Both semimetal states of OsCl3 monolayer without and with SOC exhibit a linear half-Dirac point (twofold degenerate) with high Fermi velocities. The achievement of the 2D semimetal state with SOC is expected to be found in other TMX3 monolayers, and we confirm it in a TiCl3 monolayer. This provides a different perspective to study the band structure with SOC of the 2D TMX3 family.

Periodic Clifford symmetry algebras on flux lattices

Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the $d$-dimensional spinless rectangular lattices with $\pi$ flux per plaquette. Due to the $T$-invariant flux configuration, real Clifford algebras are realized as projective symmetry algebras of lattice symmetries. Remarkably, $d$ mod $8$ exactly corresponds to the eight Morita equivalence classes of real Clifford algebras with eightfold Bott periodicity, resembling the eight real Altland-Zirnbauer classes. The representation theory of Clifford algebras determines the degree of degeneracy of band structures, both at generic $k$ points and at high-symmetry points of the Brillouin zone. Particularly, we demonstrate that the large degeneracy at high-symmetry points offers a rich resource for forming novel topological states by various dimerization patterns, including a $3$D higher-order semimetal state with double-charged bulk nodal loops and hinge modes, a $4$D nodal surface semimetal with $3$D surface solid-ball zero modes, and $4$D M\"{o}bius topological insulators with a eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable $\mathbb{Z}_2$ gauge fields and capability to simulate higher dimensional systems.

Manipulation of intrinsic quantum anomalous Hall effect in two-dimensional MoYN2CSCl MXene

Quantum anomalous Hall effect (QAHE) is an innovative topological spintronic phenomenon with dissipationless chiral edge states and attracts rapidly increasing attention. However, it has only been observed in few materials in experiments. Here, according to the first-principles calculations, we report that the MXene MoYN2CSCl shows a topologically nontrivial band gap of 37.3 meV, possessing QAHE with a Chern number of C = 1, which is induced by band inversion between d xz and d yz orbitals. Also, the topological phase transition for the MoYN2CSCl can be realized via strain or by turning the magnetization direction. Remarkably, MoYN2CSCl shows the nodal-line semimetal state dependent on the electron correlation U. Our findings add an experimentally accessible and tunable member to the QAHE family, which stands a chance of enriching the applications in spintronics.

Topological states and topological phase transition in Cu2SnS3 and Cu2SnSe3

Based on the first-principles calculations and model analysis, we propose that the isostructural compounds ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ and ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ are both the simplest nodal-line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The inclusion of SOC drives ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for a WSM with time-reversal symmetry. In contrast, SOC leads ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ to a strong topological insulator (STI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a STI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of the mirror plane, and the ${Z}_{2}$ indices protected by time-reversal symmetry, has been demonstrated by the calculation of ${\mathrm{Cu}}_{2}\mathrm{Sn}{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ within virtual crystal approximation and an effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling the TPT and the evolution of Weyl nodes will stimulate further efforts to explore them.