Intersecting topological nodal ring and nodal wall states in superhard superconductor FeB4

Abstract

Novel materials with both topological nontrivial states and superconductivity have attracted considerable attention in recent years. Single-crystal FeB4 was recently synthesized and demonstrated to exhibit superconductivity at temperatures lower than 2.9 K, and its nanoindentation hardness was measured to be 65 GPa. In this study, based on first-principles calculation and the low-energy k • p effective Hamiltonian, we found that this Pnnm-type superhard FeB4 superconductor hosts topological behaviors with intersecting nodal rings (INRs) in the 𝑘𝑘 𝑥𝑥 = 0 and 𝑘𝑘 𝑧𝑧 = 0 planes and nodal wall states in the 𝑘𝑘 𝑦𝑦 = 𝜋𝜋 and 𝑘𝑘 𝑧𝑧 = 𝜋𝜋 planes. The observed surface drumhead-like (D-H-L) states on the [100] and [001] surfaces confirmed the presence of INR states in this system. According to our investigation results, FeB4, with its superconductivity, superior mechanical behaviors, one-dimensional (1D) and twodimensional topological elements, and D-H-L surface states, is an existing single-phase target material that can be used to realize the topological superconducting state in the near future.

Electride pure α-Zr: interstitial electrons induced type-II nodal line

“…Therefore, compared with traditional materials, the approximately non-nuclear bound interstitial electrons in electrides are easier to occur band inversion near the Fermi level [18]. Then, these crossing points near the Fermi level form different types of topological fermions under multiple symmetric operations, such as Weyl/Dirac points (WP/DPs) [19][20][21], nodal lines (NLs) [22][23][24], nodal surfaces (NSs) [25][26][27], etc. Subsequently, a series of studies have confirmed that electrides are excellent carriers for exploring topological fermions, such as 0D electride C12A7:4e − with six-fold excited state [28], 1D electride Sr 3 CrN 3 with two-fold NS [29], 2D electrides Gd/Y 2 C with NLs [30,31], etc.…”

Scanning Intrinsic Superconductivity and the Spin Hall Effect in Niobium Borides

“…The possible explanations of TMBs’ exotic mechanical properties can be attributed to the complicated localized interactions including boron–boron, metal–metal, and metal–boron bonds. Moreover, the strong covalent bonds of B–B and the light mass of boron in TMBs, which may result in high vibrational frequencies, also make it to be considered as a pre-eminent platform to generate superconducting excitations. ,,, For instance, among TMBs with MgB 2 -type, MgB 2 owns a high superconducting transition temperature ( T C ) of 39 K, while 9.4 K for NbB 2 . More intriguingly, some superconducting borides also display nontrivial topological electronic states.…”

“…For instance, FeB 4 , unveiled as a superhard iron superconductor, was predicted to be a topological nodal line semimetal and hold nodal wall states. 12 Moreover, TaB 2 and NbB 2 were also predicted to hold Dirac surface states. 9 These findings indicate that superconducting and topological TMBs are a promising platform to investigate exotic electronic excitations and to explore the possible topological superconducting states for the construction of fault-tolerant quantum computations.…”

“…More intriguingly, some superconducting borides also display nontrivial topological electronic states. For instance, FeB 4 , unveiled as a superhard iron superconductor, was predicted to be a topological nodal line semimetal and hold nodal wall states . Moreover, TaB 2 and NbB 2 were also predicted to hold Dirac surface states .…”