Crystalline Insulator Research Articles

Twisted nodal wires and three-dimensional quantum spin Hall effect in distorted square-net compounds

Recently, square-net materials have attracted lots of attention for the Dirac semimetal phase with negligible spin-orbit coupling (SOC) gap, e.g., ZrSiS/LaSbTe and ${\mathrm{CaMnSb}}_{2}$. In this paper, we demonstrate that the Jahn-Teller effect enlarges the nontrivial SOC gap in the distorted structure, e.g., LaAsS and ${\mathrm{SrZnSb}}_{2}$. Its distorted $X$ square-net layer ($X=$ P, As, Sb, Bi) resembles a quantum spin Hall (QSH) insulator. Since these QSH layers are simply stacked in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ direction and weakly coupled, three-dimensional QSH effect can be expected in these distorted materials, such as insulating compounds ${\mathrm{CeAs}}_{1+x}{\mathrm{Se}}_{1\ensuremath{-}y}$ and ${\mathrm{EuCdSb}}_{2}$. Our detailed calculations show that it hosts two twisted nodal wires without SOC [each consists of two noncontractible time-reversal symmetry- and inversion symmetry-protected nodal lines touching at a fourfold degenerate point], while with SOC it becomes a topological crystalline insulator with symmetry indicators $(000;2)$ and mirror Chern numbers $(0,0)$. The nontrivial band topology is characterized by a generalized spin Chern number ${C}_{s+}=2$ when there is a gap between two sets of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{s}}_{x}$ eigenvalues. The nontrivial topology of these materials can be well reproduced by our tight-binding model and the calculated spin Hall conductivity is quantized to ${\ensuremath{\sigma}}_{yz}^{x}=(\frac{\ensuremath{\hbar}}{e})\frac{{G}_{x}{e}^{2}}{\ensuremath{\pi}h}$ with ${G}_{x}$ a reciprocal lattice vector.

Angular momentum invoked band inversions in mirror symmetry protected topological states

The notion of a band inversion provides an intuitive physical paradigm for understanding the electronic band topology. Here we study the general band inversion mechanism, which exploits local atomic orbitals and lattice symmetry, in mirror protected topological crystalline insulators (TCIs). Based on low-energy effective theory analysis, we find that for these mirror protected TCIs, the topological invariant (i.e., the mirror Chern number ${\mathcal{C}}_{M}$) is determined by the difference of total magnetic quantum numbers ${m}_{j}$ of orbitals involved in the band inversion: $|{\mathcal{C}}_{M}|=|\mathrm{\ensuremath{\Delta}}{m}_{j}|$. This angular-momentum criterion is further verified by the atomic tight-binding model calculations in two-dimensional (2D) crystalline, quasicrystalline, and disordered lattices. Moreover, such an angular momentum invoked band inversion (AMBI) is also extendable to 3D lattices and gives rise to topological semimetals with Dirac points in the bulk and double Fermi arcs on surfaces. As a concrete material example, we further predict that the Ba monolayer is an AMBI-induced TCI by first-principles calculations. In addition, we also show that a large number of previously proposed TCI materials satisfy the AMBI mechanism. Our findings not only provide an alternative understanding of mirror protected band topology but also offer useful guidance for designing or engineering mirror protected TCI materials.

Switchable quantum anomalous Hall effect in a ferromagnetic topological crystalline insulating NpSb monolayer

The combination of band topology and magnetic order provides an exciting platform for exploring prominent topological quantum effects, such as the quantum anomalous Hall (QAH) effect, which is well known to emerge when the ferromagnetic (FM) order is introduced in two-dimensional (2D) topological (crystalline) insulators. However, a topological phase transition between QAH insulators and magnetic topological (crystalline) insulators in 2D intrinsic magnets is seldom reported. Here, in contrast to previous magnetic doping, we predict that a switchable topological phase transition between a QAH insulator and a 2D topological crystalline insulator can emerge in an intrinsic FM NpSb monolayer via strain engineering. With the spin-up and spin-down manifolds being oppositely tunable, the calculated mirror Chern number, Chern number, and nontrivial edge states clearly confirm the topological phase transition as well as the QAH effect. Moreover, we reveal the feasibility of attaining the QAH effect while strain is introduced by an appropriate substrate. These results are of great scientific interest for exploring and understanding nontrivial topology in 2D magnets.

Obstructed Surface States as the Descriptor for Predicting Catalytic Active Sites in Inorganic Crystalline Materials.

The discovery of new catalysts that are efficient and sustainable is a major research endeavor for many industrial chemical processes. This requires an understanding and determination of the catalytic origins, which remains a challenge. Here, a novel method to identify the position of active sites based on searching for crystalline symmetry-protected obstructed atomic insulators (OAIs) that have metallic surface states is described. The obstructed Wannier charge centers (OWCCs) in OAIs are pinned by symmetries at some empty Wyckoff positions so that surfaces that accommodate these sites are guaranteed to have metallic obstructed surface states (OSSs). It is proposed and confirmed that the OSSs are the catalytic activity origins for crystalline materials. The theory on 2H-MoTe2 , 1T'-MoTe2 , and NiPS3 bulk single crystals is verified, whose active sites are consistent with the calculations. Most importantly, several high-efficiency catalysts are successfully identified just by considering the number of OWCCs and the symmetry. Using the real-space-invariant theory applied to a database of 34 013 topologically trivial insulators, 1788 unique OAIs are identified, of which 465 are potential high-performance catalysts. The new methodology will facilitate and accelerate the discovery of new catalysts for a wide range of heterogeneous redox reactions.

Magnetically tunable Dirac and Weyl fermions in the Zintl materials family

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ is a dual topological insulator with ${Z}_{2}=(1;000)$ and mirror Chern number ${C}_{M}=\ensuremath{-}1$. Its isostructural and isovalent antiferromagnetic cousin ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$ is found to be an axion insulator with ${Z}_{4}=2$. The broken time-reversal symmetry via Eu doping in ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{\mathrm{As}}_{2}$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic ${\mathrm{EuIn}}_{2}{\mathrm{P}}_{2}$ is a trivial insulator with ${Z}_{4}=0$, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with ${Z}_{4}=1$ with applied magnetic field. Our study identifies ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{(\text{As},\mathrm{P})}_{2}$ as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.

Robust dual topological insulator phase in NaZnBi

Topological insulators are characterized by {Bbb Z}_2 indices, and their metallic surface states are protected by time-reversal symmetry. In topological crystalline insulators, on the other hand, crystal symmetry plays a key role in protecting surface states. Therefore, perturbation breaking time-reversal or crystal symmetry induces a phase transition to a conventional band insulator. In dual topological insulators (DTIs), in which time-reversal and crystal symmetries coexist, the topological character is more robust against perturbation. Here, we propose that NaZnBi is a new DTI with {Bbb Z}_2 invariants (nu _0;nu _1nu _2nu _3) = (1;000) and odd mirror Chern numbers ±1. We find that the characteristic Dirac cone is preserved even if either time-reversal or mirror symmetry is broken, verifying the robustness of the DTI phase. Given that gapless surface states can be experimentally observable even under perturbations that break any lattice symmetry or time-reversal, NaZnBi can be a good candidate material for future device applications.

Evolution of magnetoresistance with temperature in the insulating van der Waals compound Ta2Pd3Te5

Ta2Pd3Te5 has been recently identified as a van der Waals topological crystalline insulator candidate, but its magnetotransport properties are not reported. Here, we study electrical transport properties of Ta2Pd3Te5 single crystals. Ta2Pd3Te5 shows an insulating behavior with a trend of saturation below 20 K. The activity energy determined from the fits to polaron hopping model is Ea ∼ 36.1 meV, close to the value of 42 meV determined from previous scanning tunneling microscopy measurement. The linear Hall resistivity with a negative slope suggests an n-type conductivity for bulk Ta2Pd3Te5. The magnetoresistance (MR) is positive at 2 K, and the dip-like feature at low magnetic fields is attributed to the weak antilocalization effect. On the other hand, a negative low-field MR develops in the temperature range between 5 and 30 K, which is identified as a fingerprint of the weak localization effect. Such a transition from weak antilocalization to weak localization with increasing temperature reveals that the spin–orbit interaction plays an important role in Ta2Pd3Te5. Our results reveal highly enriched physical properties in Ta2Pd3Te5 single crystals, and they can be exploited in future magnetoresistance device design.

Exploring temperature dependent electron–electron interaction of rocksalt SnS and SnSe within Matsubara-time domain

Both experimental and theoretical studies show non-trivial topological behaviour in native rocksalt phase for SnS and SnSe and categorize these materials in topological crystalline insulators. Here, the detailed electronic structures studies of SnS and SnSe in the rocksalt phase are carried out using many-body GW based theory and density functional theory both for ground states and temperature dependent excited states. The estimated values of fundamental direct bandgaps around L-point using G 0 W 0 (mBJ) are ∼0.27 (∼0.13) eV and ∼0.37 (∼0.17) eV for SnS and SnSe, respectively. The strength of hybridization between Sn 5p and S 3p (Se 4p) orbitals for SnS (SnSe) shows strong k-dependence. The behaviour of (ω), which is the averaged value of diagonal matrix elements of fully screened Coulomb interaction, suggests to use full-GW method for exploring the excited states because the correlation effects within these two materials are relatively weak. The temperature dependent electronic structure calculations for SnS and SnSe provide linearly decreasing behaviour of bandgaps with rise in temperatures. The existence of collective excitation of quasiparticles in form of plasmon is predicted for these compounds, where the estimated values of plasmon frequency are ∼9.5 eV and ∼9.3 eV for SnS and SnSe, respectively. The imaginary part of self-energy and mass renormalization factor (Z k (ω)) due to electron–electron interaction (EEI) are also calculated along W–L–Γ direction for both the materials, where the estimated ranges of Z k (ω) are 0.70 to 0.79 and 0.71 to 0.78 for SnS and SnSe, respectively, along this k-direction. The present comparative study reveals that the behaviour of temperature dependent EEI for SnS and SnSe are the almost same and EEI is important for high temperature transport properties.

Optical N -insulators: Topological obstructions to optical Wannier functions in the atomistic susceptibility tensor

A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational symmetry in both directions. Similarly, Wannier functions that respect time-reversal symmetry cannot be formed in quantum spin Hall insulators. This molecular orbital interpretation of topology has been enlightening and was recently extended to topological crystalline insulators which include obstructions tied to space group symmetries. In this article, we introduce a new class of two-dimensional topological materials known as optical $N$-insulators that possess obstructions to constructing localized molecular polarizabilities. The optical $N$-invariant $N\in\mathbb{Z}$ is the winding number of the atomistic susceptibility tensor $\chi$ and counts the number of singularities in the electromagnetic linear response theory. We decipher these singularities by analyzing the optical band structure of the material -- the eigenvectors of the susceptibility tensor -- which constitutes the collection of optical Bloch functions. The localized basis of these eigenvectors are optical Wannier functions which represent the molecular polarizabilities at different lattice sites. We prove that in a nontrivial optical phase $N\neq 0$, such a localized polarization basis is impossible to construct. Utilizing the mathematical machinery of $K$-theory, these optical $N$-phases are refined further to account for the underlying crystalline symmetries of the material, generating a classification of the topological electromagnetic phase of matter.

One–One Correspondence between n-Type SnTe Thermoelectric and Topological Phase Transition

A lot of thermoelectric materials (TE) have been proved as topological crystalline insulators (TCIs), like SnTe, although the internal connection of thermoelectric and topological states has remained unclear. Herein, we deeply and experimentally verified the one–one correspondence between the n-type SnTe thermoelectric and topological phase transition. The challenging n-type SnTe could only be realized after the topological phase transition from topologically nontrivial phase to topologically trivial phase, induced by Pb alloying via tuning the L6+ and L6− states in the band edge at the L point in the Brillouin zone, followed by donor doping via Br, pushing the Fermi level into the conduction band. Outstanding ZTmax of ∼0.7 and ∼0.8 at 573 K and excellent ZTave of ∼0.42 and ∼0.58 at 300–823 K are achieved for the n-type Sn0.6Pb0.4Te0.9875Br0.0125 polycrystal and the SnTe–Pb–Br crystal, respectively. Our work explored the significant n-type SnTe from the combined bulk and surface states aspects and experimentally revealed that the thermoelectric, especially the conductivity, behavior is directly and profoundly influenced by the topological phase transition in the SnTe TE/TCI system, which will inspire further researches on other TE/TCI materials and thermoelectric devices with p- and n-type SnTe legs.

Prediction of topological Dirac semimetal in Ca-based Zintl layered compounds CaM2X2 (M\u2009=\u2009Zn or Cd; X\u2009=\u2009N, P, As, Sb, or Bi)

Topological Dirac materials are attracting a lot of attention because they offer exotic physical phenomena. An exhaustive search coupled with first-principles calculations was implemented to investigate 10 Zintl compounds with a chemical formula of CaM2X2 (M = Zn or Cd, X = N, P, As, Sb, or Bi) under three crystal structures: CaAl2Si2-, ThCr2Si2-, and BaCu2S2-type crystal phases. All of the materials were found to energetically prefer the CaAl2Si2-type structure based on total ground state energy calculations. Symmetry-based indicators are used to evaluate their topological properties. Interestingly, we found that CaM2Bi2 (M = Zn or Cd) are topological crystalline insulators. Further calculations under the hybrid functional approach and analysis using k · p model reveal that they exhibit topological Dirac semimetal (TDSM) states, where the four-fold degenerate Dirac points are located along the high symmetry line in-between Г to A points. These findings are verified through Green's function surface state calculations under HSE06. Finally, phonon spectra calculations revealed that CaCd2Bi2 is thermodynamically stable. The Zintl phase of AM2X2 compounds have not been identified in any topological material databases, thus can be a new playground in the search for new topological materials.

Acoustic Möbius Insulators from Projective Symmetry

In the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here, we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.

Growth and characterization of high-quality single-crystalline SnTe retaining cubic symmetry down to the lowest temperature studied

SnTe, an archetypical topological crystalline insulator, often shows a transition from a highly symmetric cubic phase to a rhombohedral structure at low temperatures. In order to achieve the cubic phase at low temperatures, we have grown SnTe employing the modified Bridgman method and studied its properties in detail. Analysis of the crystal structure using Laue diffraction and rocking curve measurements shows a high degree of single crystallinity and mosaicity of the sample. The magnetic susceptibility shows diamagnetic behavior, and the specific heat data match phonon contributions typical of a bulk insulator. Resistivity data exhibit metallic conduction similar to two-dimensional systems, and the signature of the structural transition has not been observed down to the lowest temperature studied. Detailed powder x-ray diffraction measurements show a cubic structure in the entire temperature range studied. This is supported by the angle-resolved photoemission data at low temperatures exhibiting a Dirac cone typical of a topological material. These results demonstrate that the ground state structure of SnTe can be stabilized in the cubic phase, providing a promising platform for quantum applications.

Two-Dimensional Weak Antilocalization Signatures Due to Quantum Coherent Transport in Nanocrystalline SnTe.

Nanostructured topological crystalline insulators (TCIs) in the presence of exotic surface states with spin momentum locking reported in individual nanostructures are predicted to hold a great promise for spintronics and quantum computing applications. However, practical application demands a strategy with large-scale production and integration for device applications. In this work, we demonstrate through prominent signatures of weak antilocalization (WAL), arising predominantly from destructive quantum interference on robust surface states, that a correlated TCI phase is possible in the nanobulk assembly of carefully nanostructured quasi-two-dimensional SnTe (edge-to-edge length ∼ 382 nm) synthesized by a simple, rapid, and scalable microwave-assisted solvothermal method. Hikami-Larkin-Nagaoka analysis (T-0.71), as well as the temperature dependence of resistivity, illustrates an interplay of both conductions from 2D channels and 3D EEI effects as the precursor for the observed WAL at low temperatures (2-6 K). Interestingly, the enhanced thermoelectric power of the sample of ∼45 μV/K, with a p-type carrier concentration of ∼1018/cm3 at 300 K, makes this SnTe nanocrystalline assembly more attractive as a multifunctional material for large-scale technological applications.

Optical-Pump Terahertz-Probe Spectroscopy of the Topological Crystalline Insulator Pb1–xSnxSe through the Topological Phase Transition

Topological crystalline insulators -- topological insulators whose properties are guaranteed by crystalline symmetry -- can potentially provide a promising platform for terahertz optoelectronic devices, as their properties can be tuned on demand when layered in heterostructures. We perform the first optical-pump terahertz-probe spectroscopy of topological crystalline insulators, using them to study the dynamics of Pb1-xSnxSe as a function of temperature. At low temperatures, excitation of Dirac fermions leads to an increase in terahertz transmission; from this negative photoconductivity, the intrasubband relaxation rate of 6 ps is extracted. At high temperatures where only massive fermions exist, the free-carrier losses induced by the pump reduce the terahertz transmission for the duration of the 27 ps interband lifetime. Both effects are present at temperatures near the topological-to-trivial transition. Our experimental observations provide critical details for potential applications of Pb1-xSnxSe and provide a direct measurement of the topological character of Pb1-xSnxSe heterostructures.

Interaction between interface and massive states in multivalley topological heterostructures

Topological interface states (TISs) in multivalley systems are studied to unravel their valley sensitivity. For this purpose, multivalley IV--VI topological crystalline insulator (TCI) heterostructures are explored using magnetooptical Landau level spectroscopy up to 34 teslas. We characterize the TISs emerging from the distinct $L$ valleys in ${\mathrm{Pb}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}\mathrm{Se}$ multiquantum wells grown along the [111] direction. It is shown that the shape of the two-dimensional (2D) Fermi surfaces of TISs residing at the TCI-trivial insulator interfaces are strongly affected by the valley anisotropy of topologically trivial ${\mathrm{Pb}}_{1\ensuremath{-}y}{\mathrm{Eu}}_{y}\mathrm{Se}$ barriers. This phenomenon is shown to be due to the deep penetration of the TISs into the barriers. For the valleys tilted with respect to the confinement direction, a significant interaction between topological states and the conventional massive quantum well states is observed, evidenced by the resulting large anticrossings between Landau levels. These are theoretically well described by a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model that considers tilt and anisotropy of the valleys in 2D. Therefore, in this paper, we provide a precise characterization of the TIS valley splitting as well as an accurate determination of the anisotropy of their Dirac cone dispersion.

Properties of topological crystalline insulator Pb0.5Sn0.5Te epitaxial films doped with bismuth

We report here on the properties of topological crystalline insulator Pb0.5Sn0.5Te epitaxial films doped with bismuth at levels from 0% (undoped) to 0.15%. The undoped film exhibits a p-type character due to metal vacancies. As the doping level rises, the hole concentration reduces. At a level of 0.06%, the electrical character inverts to n-type and the electron density continues to increase for rising doping level up to 0.15%. This result demonstrates an effective extrinsic n-type doping of Pb0.5Sn0.5Te crystal with bismuth due to substitutional Bi atoms in metal sites. High-resolution x-ray diffraction and reciprocal space mapping show that fully relaxed high-quality films are obtained. A pristine (111) film surface is revealed after removal of the Te cover layer using a method combining Ar+ sputtering and thermal desorption. Angle-resolved photoemission spectroscopy (ARPES) data acquired at 30 K near the Γ¯ point of the undoped film surface show a parabolic-like dispersion of the bulk valence band close to the Fermi level. Now, the ARPES data for a sample doped with 0.1% of Bi reveal that the chemical potential is shifted by 40 meV upwards in the direction of the conduction band. The ARPES results also indicate that there might be a discrepancy between surface and bulk chemical potential in the doped sample. This divergence suggests that Te atoms diffuse into the surface during the thermal process to desorb the protective layer, inverting the surface to p-type.

Electronic Quantum Materials Simulated with Artificial Model Lattices.

The band structure and electronic properties of a material are defined by the sort of elements, the atomic registry in the crystal, the dimensions, the presence of spin–orbit coupling, and the electronic interactions. In natural crystals, the interplay of these factors is difficult to unravel, since it is usually not possible to vary one of these factors in an independent way, keeping the others constant. In other words, a complete understanding of complex electronic materials remains challenging to date. The geometry of two- and one-dimensional crystals can be mimicked in artificial lattices. Moreover, geometries that do not exist in nature can be created for the sake of further insight. Such engineered artificial lattices can be better controlled and fine-tuned than natural crystals. This makes it easier to vary the lattice geometry, dimensions, spin–orbit coupling, and interactions independently from each other. Thus, engineering and characterization of artificial lattices can provide unique insights. In this Review, we focus on artificial lattices that are built atom-by-atom on atomically flat metals, using atomic manipulation in a scanning tunneling microscope. Cryogenic scanning tunneling microscopy allows for consecutive creation, microscopic characterization, and band-structure analysis by tunneling spectroscopy, amounting in the analogue quantum simulation of a given lattice type. We first review the physical elements of this method. We then discuss the creation and characterization of artificial atoms and molecules. For the lattices, we review works on honeycomb and Lieb lattices and lattices that result in crystalline topological insulators, such as the Kekulé and “breathing” kagome lattice. Geometric but nonperiodic structures such as electronic quasi-crystals and fractals are discussed as well. Finally, we consider the option to transfer the knowledge gained back to real materials, engineered by geometric patterning of semiconductor quantum wells.

Edge states in a non-Hermitian topological crystalline insulator

Breaking Hermiticity in topological systems gives rise to intriguing phenomena, such as the exceptional topology and the non-Hermitian skin effect. In this work, we study a non-Hermitian topological crystalline insulator sitting on the Kekul\'{e}-modulated honeycomb lattice with balanced gain and loss. We find that the gaplessness of the topological edge states in the non-Hermitian system is insensitive to edge geometries under moderate strength of gain and loss, unlike the cases of Hermitian topological crystalline insulators that depend on edge geometries crucially. We focus on two types of gain and loss configurations, which are $PT$-symmetric and $PT$-asymmetric, respectively. For the $PT$-symmetric configuration, the Dirac point of the topological edge states in the Hermitian molecular-zigzag-terminated ribbons splits into a pair of exceptional points. The edge gap in the Hermitian armchair-terminated ribbons vanishes and a Dirac point forms as far as moderate gain and loss is induced. The band gaps of edge and bulk states in the Hermitian armchair-terminated ribbons close simultaneously for the $PT$-asymmetric configuration.

Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd_{3}As_{2}.

We show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd_{3}As_{2} is a promising platform for BCL Floquet engineering. Without strain, BCL irradiation induces a transition to a noncentrosymmetric magnetic Weyl semimetal phase with tunable energy separation between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topological crystalline insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2^{'}) and can be controlled by light.