Nonsymmorphic Crystal Symmetry Research Articles

Tunable quantum transport in topological semimetal candidates LaxSr1-xMnSb2

The magnetic semimetal SrMnSb2 contains a nonsymmorphic crystal symmetry that could protect Dirac crossings, offering the coexistence of a quasi-two-dimensional characteristic, magnetic order and nontrivial topology in bulk single crystals. Here, we report the evolution of Fermi surfaces by probing quantum oscillations in the La x Sr1-x MnSb2 single crystals. Hall measurements reveal that the conduction process changes from a hole-dominated multiband nature to a single hole-band nature after La doping. Compared with parent-SrMnSb2, the Fermi surface corresponding to F α is slightly enlarged and the small Fermi surface corresponding to F γ appears with a tunable feature in La-doped crystals. The topological semimetal candidates La x Sr1-x MnSb2 provide a fine-tuning platform for potential applications in the future.

Coexistence of the hourglass and nodal-line dispersions in Nb3SiTe6 revealed by ARPES

SummaryThe non-symmorphic crystal symmetry protection in the layered topological semimetal Nb3SiTe6 can generate exotic band crossings. Herein, high-quality Nb3SiTe6 single crystal was synthesized via chemical vapor transport. The lattice structure of Nb3SiTe6 was characterized by scanning transmission electron microscopy, X-ray diffraction, core-level photoemission, and Raman spectroscopies. Angle-resolved photoemission spectroscopy was used to reveal its topological properties by presenting band structures along different high-symmetry directions. Our data show that nontrivial band features coexist in Nb3SiTe6, including an hourglass-type dispersion formed by two bands along the S-R high-symmetry line, two node lines along the S-X path and the S-R-U path, respectively. These results provide a context for the understanding and exploration of the exotic topological properties of Nb3SiTe6.

Observation of symmetry-protected Dirac states in nonsymmorphic α -antimonene

Two-dimensional (2D) Dirac states with linear band dispersion have attracted enormous interest since the discovery of graphene. However, to date, 2D Dirac semimetals are still very rare due to the fact that 2D Dirac states are generally fragile against perturbations such as spin-orbit couplings. Nonsymmorphic crystal symmetries can enforce the formation of Dirac nodes, providing a new route to establishing symmetry-protected Dirac states in 2D materials. Here we report the symmetry-protected Dirac states in nonsymmorphic alpha-antimonene. The antimonene was synthesized by the method of molecular beam epitaxy. Two Dirac cones with large anisotropy were observed by angle-resolved photoemission spectroscopy. The Dirac state in alpha-antimonene is of spin-orbit type in contrast to the spinless Dirac states in graphene. The result extends the 'graphene' physics into a new family of 2D materials where spin-orbit coupling is present.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor.

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk. In this work, a highly anomalous behavior of surface superconductivity in topologically nontrivial 3D superconductor In2 Bi, where the surface states result from its nontrivial band structure, itself a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling, is reported. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field, Hc2 , as seen in conventional superconductors, a near-perfect, Meissner-like screening of low-frequency magnetic fields well above Hc2 is observed. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity, Hc3 . Using theoretical modeling, the anomalous screening is shown to be consistent with modification of surface superconductivity by the topological surface states. The possibility of detecting signatures of the surface states using macroscopic magnetization provides a new tool for the discovery and identification of topological superconductors.

Topologically driven linear magnetoresistance in helimagnetic FeP

The helimagnet FeP is part of a family of binary pnictide materials with the MnP-type structure, which share a nonsymmorphic crystal symmetry that preserves generic band structure characteristics through changes in elemental composition. It shows many similarities, including in its magnetic order, to isostructural CrAs and MnP, two compounds that are driven to superconductivity under applied pressure. Here we present a series of high magnetic field experiments on high-quality single crystals of FeP, showing that the resistance not only increases without saturation by up to several hundred times its zero-field value by 35 T, but that it also exhibits an anomalously linear field dependence over the entire range when the field is aligned precisely along the crystallographic c-axis. A close comparison of quantum oscillation frequencies to electronic structure calculations links this orientation to a semi-Dirac point in the band structure, which disperses linearly in a single direction in the plane perpendicular to field, a symmetry-protected feature of this entire material family. We show that the two striking features of magnetoresistance—large amplitude and linear field dependence—arise separately in this system, with the latter likely due to a combination of ordered magnetism and topological band structure.

New Classification Theory for Topological Gapless Superconducting Nodes

A new classification theory on topological superconducting gap nodes predicts two new gap structures emerging from a nonsymmorphic crystal symmetry and angular momentum.

Nonsymmorphic nodal-line metals in the two-dimensional rare earth monochalcogenides MX (M = Sc, Y; X = S, Se, Te)

We predict a new family of two-dimensional (2D) rare earth monochalcogenide materials MX (M = Sc, Y; X = S, Se, Te). Based on first-principles calculations, we confirm their stability and systematically investigate their mechanical properties. We find that these materials are metallic and interestingly, they possess nodal lines in the low-energy band structure surrounding the whole Brillouin zone, protected by nonsymmorphic crystal symmetries in the absence of spin-orbit coupling (SOC). SOC opens small energy gaps at the nodal line, except for two high-symmetry points, at which fourfold degenerate 2D spin-orbit Dirac points are obtained. We show that these topological band features are robust under uniaxial and biaxial strains, but can be lifted by the shear strain. We also investigate the optical conductivities of these materials, and show that the transformation of the band structure under strain can be inferred from the optical absorption spectrum. Our work reveals a new family of 2D topological metal materials with interesting mechanical and electronic properties, which will facilitate the study of nonsymmorphic symmetry enabled nodal features in 2D.

Symmetry-enforced Weyl phonons

In spinful electronic systems, time-reversal symmetry makes that all Kramers pairs at the time-reversal-invariant momenta are Weyl points (WPs) in chiral crystals. Here, we find that such symmetry-enforced WPs can also emerge in bosonic systems (e.g. phonons and photons) due to nonsymmorphic symmetries. We demonstrate that for some nonsymmorphic chiral space groups, several high-symmetry k-points can host only WPs in the phononic systems, dubbed symmetry-enforced Weyl phonons (SEWPs). The SEWPs, enumerated in Table 1, are pinned at the boundary of the three-dimensional (3D) Brillouin zone (BZ) and protected by nonsymmorphic crystal symmetries. By performing first-principles calculations and symmetry analysis, we propose that as an example of SEWPs, the twofold degeneracies at P are monopole WPs in K2Sn2O3 with space group 199. The two WPs of the same chirality at two nonequivalent P points are related by time-reversal symmetry. In particular, at ~17.5 THz, a spin-1 Weyl phonon is also found at H, since two Weyl phonons at P carrying a non-zero net Chern number cannot exist alone in the 3D BZ. The significant separation between P and H points makes the surface arcs long and clearly visible. Our findings not only present an effective way to search for WPs in bosonic systems, but also offer some promising candidates for studying monopole Weyl and spin-1 Weyl phonons in realistic materials.

Strong spin-orbit coupling and Dirac nodal lines in the three-dimensional electronic structure of metallic rutile IrO2

Using high-resolution angle-resolved photoemission spectroscopy and ab initio calculation, we have studied the bulk and surface electronic structure of metallic rutile $5d$ transition metal oxide ${\mathrm{IrO}}_{2}$ that harbors both edge and corner sharing Ir-O octahedrons. We observe strong modulation of the band structure by spin-orbit coupling (SOC). The measured band structure is well reproduced by our ab initio calculation without band renormalization, suggesting the absence of the SOC-enhanced correlation effect in ${\mathrm{IrO}}_{2}$. In accordance with the calculation, we visualize two types of Dirac nodal lines (DNLs) protected by mirror symmetry and nonsymmorphic crystal symmetry, respectively. SOC gaps the first type of DNLs, which may contribute largely to the strong spin Hall effect. The second type of DNLs at the edges of Brillouin zone, however, remain intact against SOC. Our results not only provide important insights into the exotic transport properties of ${\mathrm{IrO}}_{2}$, but also shed light on the understanding of the role of SOC in the iridate family.

Topological bulk band structures of the hourglass and Dirac nodal-loop types in Ce Kondo systems: CeNiSn, CeRhAs, and CeRhSb

We have investigated the electronic structures of Ce Kondo systems, CeNiSn, CeRhAs, and CeRhSb, which have attracted recent attention as promising candidates of ``M\obius Kondo insulators.'' In the conventional density functional theory calculations, all three systems are obtained to be semimetallic, while only CeRhAs opens a full gap in the band calculation incorporating the more elaborate (modified Becke-Jones) exchange-correlation potential. Intriguingly, for all three systems, we have obtained the hourglass-type bulk band crossings around $\mathbf{k}=S$, which produce Dirac nodal-loop structures enclosing S in the [100] Brillouin zone boundary. Such topologically protected hourglass-type band structures arise from the spin-orbit coupling on top of the nonsymmorphic crystal symmetry $(Pnma)$ of these systems. Our finding suggests that Ce Kondo insulators would display temperature $(T)$ -dependent topological phase transitions from a potential M\obius Kondo insulator at low $T$ to a Dirac nodal-loop semimetal at high $T$.

Observation of band crossings protected by nonsymmorphic symmetry in the layered ternary telluride Ta3SiTe6

We have performed angle-resolved photoemission spectroscopy of layered ternary telluride Ta3SiTe6 which is predicted to host nodal lines associated with nonsymmorphic crystal symmetry. We found that the energy bands in the valence-band region show Dirac-like dispersions which present a band degeneracy at the R point of the bulk orthorhombic Brillouin zone. This band degeneracy extends one-dimensionally along the whole SR high-symmetry line, forming the nodal lines protected by the glide mirror symmetry of the crystal. We also observed a small band splitting near EF which supports the existence of hourglass-type dispersions predicted by the calculation. The present results provide an excellent opportunity to investigate the interplay between exotic nodal fermions and nonsymmorphic crystal symmetry.

Electronic structure of the candidate 2D Dirac semimetal SrMnSb2: a combined experimental and theoretical study

SrMnSb_22 is suggested to be a magnetic topological semimetal. It contains square, 2D Sb planes with non-symmorphic crystal symmetries that could protect band crossings, offering the possibility of a quasi-2D, robust Dirac semi-metal in the form of a stable, bulk (3D) crystal. Here, we report a combined and comprehensive experimental and theoretical investigation of the electronic structure of SrMnSb_22, including the first ARPES data on this compound. SrMnSb_22 possesses a small Fermi surface originating from highly 2D, sharp and linearly dispersing bands (the ‘Y-states’) around the (0,/a)-point in kk-space. The ARPES Fermi surface agrees perfectly with that from bulk-sensitive Shubnikov de Haas data from the same crystals, proving the Y-states to be responsible for electrical conductivity in SrMnSb_22. DFT and tight binding (TB) methods are used to model the electronic states, and both show good agreement with the ARPES data. Despite the great promise of the latter, both theory approaches show the Y-states to be gapped above E_FF, suggesting trivial topology. Subsequent analysis within both theory approaches shows the Berry phase to be zero, indicating the non-topological character of the transport in SrMnSb_22, a conclusion backed up by the analysis of the quantum oscillation data from our crystals.

Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt3

We study the emergence of odd-frequency superconducting pairing in UPt$_3$. Starting from a tight-binding model accounting for the nonsymmorphic crystal symmetry of UPt$_3$ and assuming an order parameter in the $E_{2u}$ representation, we demonstrate that odd-frequency pairing arises very generally, as soon as inter-sublattice hopping or spin-orbit coupling is present. We also show that in the low temperature superconducting $B$ phase, the presence of a chiral order parameter together with spin-orbit coupling, leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$ phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase is only present if odd-$\omega$ pairing also exists.

Quasilinear quantum magnetoresistance in pressure-induced nonsymmorphic superconductor chromium arsenide

In conventional metals, modification of electron trajectories under magnetic field gives rise to a magnetoresistance that varies quadratically at low field, followed by a saturation at high field for closed orbits on the Fermi surface. Deviations from the conventional behaviour, for example, the observation of a linear magnetoresistance, or a non-saturating magnetoresistance, have been attributed to exotic electron scattering mechanisms. Recently, linear magnetoresistance has been observed in many Dirac materials, in which the electron–electron correlation is relatively weak. The strongly correlated helimagnet CrAs undergoes a quantum phase transition to a nonmagnetic superconductor under pressure. Here we observe, near the magnetic instability, a large and non-saturating quasilinear magnetoresistance from the upper critical field to 14 T at low temperatures. We show that the quasilinear magnetoresistance may arise from an intricate interplay between a nontrivial band crossing protected by nonsymmorphic crystal symmetry and strong magnetic fluctuations.

Möbius Kondo insulators

Heavy fermion materials have recently attracted attention for their potential to combine topological protection with strongly correlated electron physics. To date, the ideas of topological protection have been restricted to the heavy fermion or "Kondo" insulators with the simplest point-group symmetries. Here we argue that the presence of nonsymmorphic crystal symmetries in many heavy fermion materials opens up a new family of topologically protected heavy electron systems. Re-examination of archival resistivity measurements in nonsymmorphic heavy fermion insulators Ce$_3$Bi$_4$Pt$_3$ and CeNiSn reveals the presence of low temperature conductivity plateau, making them candidate members of the new class of material. We illustrate our ideas with a specific model for CeNiSn, showing how glide symmetries generate surface states with a novel Mobius braiding that can be detected by ARPES or non-local conductivity measurements. One of the interesting effects of strong correlation, is the development of partially localization or "Kondo breakdown" on the surfaces, which transforms Mobius surface states into quasi-one dimensional conductors, with the potential for novel electronic phase transitions.

Electric Control of Dirac Quasiparticles by Spin-Orbit Torque in an Antiferromagnet.

Spin orbitronics and Dirac quasiparticles are two fields of condensed matter physics initiated independently about a decade ago. Here we predict that Dirac quasiparticles can be controlled by the spin-orbit torque reorientation of the Néel vector in an antiferromagnet. Using CuMnAs as an example, we formulate symmetry criteria allowing for the coexistence of topological Dirac quasiparticles and Néel spin-orbit torques. We identify the nonsymmorphic crystal symmetry protection of Dirac band crossings whose on and off switching is mediated by the Néel vector reorientation. We predict that this concept verified by minimal model and density functional calculations in the CuMnAs semimetal antiferromagnet can lead to a topological metal-insulator transition driven by the Néel vector and to the topological anisotropic magnetoresistance.

Nodal lines and nodal loops in nonsymmorphic odd-parity superconductors

We discuss the nodal structure of odd-parity superconductors in the presence of non-symmorphic crystal symmetries, both with and without spin-orbit coupling, and with and without time reversal symmetry. We comment on the relation of our work to previous work in the literature, and also the implications for unconventional superconductors such as UPt$_3$.

Electric-field tunable Dirac semimetal state in phosphorene thin films

We study the electric-field tunable electronic properties of phosphorene thin films, using the framework of density functional theory. We show that phosphorene thin films offer a versatile material platform to study two dimensional Dirac fermions on application of a transverse electric field. Increasing the strength of the transverse electric field beyond a certain critical value in phosphorene leads to the formation of two symmetry protected gapless Dirac fermions states with anisotropic energy dispersion. The spin-orbit coupling splits each of these Dirac state into two spin- polarized Dirac cones which are also protected by non-symmorphic crystal symmetries. Our study shows that the position as well as the carrier velocity of the spin polarized Dirac cone states can be controlled by the strength of the external electric field.

Nonsymmorphic Weyl superconductivity inUPt3based onE2urepresentation

We show that a heavy fermion superconductor UPt_3 is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the E_2u representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc node protected by the nonsymmorphic crystal symmetry on the Brillouin zone face.

Node-surface and node-line fermions from nonsymmorphic lattice symmetries

We propose a kind of novel topological quantum state of semimetals in a quasi-one-dimensional (1D) crystals BaMX$_3$ (M = V, Nb or Ta; X = S or Se) family by using symmetry analysis and first principles calculation. We find that in BaVS$_3$ the valence and conduction bands are degenerate in the $k_z=\pi/c$ plane ($c$ is the lattice constant along $\hat{z}$ axis) of the Brillouin Zone (BZ). These nodal points form a node-surface and they are protected by a nonsymmorphic crystal symmetry consisting of a two-fold rotation about the $\hat{z}$ axis and a half-translation along the same $\hat{z}$ axis. The band degeneracy in the node-surface is lifted in BaTaS$_3$ by including strong spin-orbit coupling (SOC) of Ta. The node-surface is reduced into 1D node-lines along the high-symmetry paths $k_x=0$ and $k_x$ = $\pm{\sqrt{3}}k_y$ on the $k_z=\pi/c$ plane. These node-lines are robust against SOC and guaranteed by the symmetries of $P6_3/mmc$ space group. These node-line states are entirely different from previous proposals which are based on the accidental band touchings. We also propose a useful material design for realizing topological node-surface and node-line semimetals.