Topological nodal line states and a potential catalyst of hydrogen evolution in the TiSi family

TL;DR

This paper introduces a new topological nodal line semimetal in the TiSi family that shows promise as a catalyst for hydrogen evolution, leveraging its surface states and topological properties for efficient water splitting.

Contribution

It reports the discovery of a TiSi-type topological nodal line semimetal with near-zero hydrogen adsorption free energy, proposing it as a novel quantum catalyst for HER based on topological surface states.

Findings

TiSi family exhibits a closed Dirac nodal line in the bulk.

Hydrogen adsorption on TiSi surfaces yields near-zero ΔG_{H*}.

Topological charge participates in the HER process.

Abstract

Topological nodal line (DNL) semimetals, formed by a closed loop of the inverted bands in the bulk, result in the nearly flat drumhead-like surface states with a high electronic density near the Fermi level. The high catalytic active sites associated with the high electronic densities, the good carrier mobility, and the proper thermodynamic stabilities with $\Delta G_{H^*}$$\approx$0 are currently the prerequisites to seek the alternative candidates to precious platinum for catalyzing electrochemical hydrogen (HER) production from water. Within this context, it is natural to consider whether or not the DNLs are a good candidate for the HER because its non-trivial surface states provide a robust platform to activate possibly chemical reactions. Here, through first-principles calculations we reported on a new DNL TiSi-type family with a closed Dirac nodal line consisting of the linear band crossings in the $k_y$ = 0 plane. The hydrogen adsorption on the (010) and (110) surfaces yields the $\Delta G_{H^*}$ to be almost zero. The topological charge carries have been revealed to participate in this HER. The results are highlighting that TiSi not only is a promising catalyst for the HER but also paves a new routine to design topological quantum catalyst utilizing the topological DNL-induced surface bands as active sites, rather than edge sites-, vacancy-, dopant-, strain-, or heterostructure-created active sites.

Full text

Topological semimetalsTSM , which have been classified into topological Dirac semimetal (TDs)TD ; na3bi1 ; na3bi2 ; na3bi3 ; na3bi4 ; cdas1 ; cdas2 ; cdas3 , topological Weyl semimetals (TWs)TW ; taas1 ; taas2 ; taas3 ; taas4 ; taas5 ; ta3s2 ; tairte4 ; wte2 ; wte3 ; cts ; hgte ; zrte , and topological nodal line semimetals (DNLs)Fang2016 ; TL-1 ; TL-2 ; TL-3 ; Li2016 ; dnl1 ; dnl2 ; dnl3 ; dnl4 ; dnl5 ; dnl6 ; dnl7 and beyond TBS , have currently attracting extensively interest in condensed matter physics and materials science. In difference from both TDs and TWs which exhibit isolated Dirac cones and Weyl nodes in its bulk phase, the class of DNLs Li2016 ; dnl1 ; dnl2 ; dnl3 ; dnl4 ; dnl5 ; dnl6 ; dnl7 ; dnl8 ; dnl9 ; dnl10 shows a fully closed line nearly at the Fermi level in its bulk phase. The projection of the DNLs into a certain surface would result in a closed ring in which the topological surface states (usually flat bands) occur due to the non-trivial topological property of its bulk phase. This kind of exotic band structures exhibit various novel properties, such as giant surface Friedel oscillation in beryllium Li2016 , flat Landau level Landau2015 and long-range Coulomb interaction Moon2016 . Currently, only the DNL-induced topological surface bands has been directly confirmed in beryllium Li2016 and the DNLs have been, partially or indirectly, observed in several bulk materials, such as PtSn4 6 ,TlTaSe28 and PbTaSe27 and ZrSiS9 ; 10 ; 11 as well as in a two-dimensional DNL monolayer of Cu2Si 12 .

Most recently, TWs (NbP, TaP, NbAs and TaAs) have been considered to serve as excellent candidates of catalysts because of the remarkable performance of the hydrogen evolution reaction (HER)TWs-HRE9 . This key concept of TWs as catalysts is extremely nice by alternatively providing a way to create the active sites with topological surface states, rather than by traditionally increasing the active edge sites or vacancies HER00 ; HER01 ; HRE3 ; HRE4 ; HRE5 ; HRE10 ; HRE11 . The possible bottleneck of TWs as catalyst may be its much lower carrier density around the Fermi level (Fig. 1a), because that the strength of electrostatic screening in TWs is much weaker than the normal metal (e.g., Pt). However, a DNL material shows two distinguishing features from both TDs and TWs TWs-HRE9 . In its bulk phase, a DNL results in a certain carrier density around the Fermi level (Fig. 1b) and its topologically protected nearly flat drumhead-like non-trivial surface states provide an unusually high electronic density around the Fermi level (Fig. 1b), as seen in pure metal beryllium Li2016 . Besides these advantages, in similarity to both TDs and TWs the DNL-induced surface states certainly provides sufficient active plane (Fig. 1b) and the carrier mobilities are, in principle, high, because the DNL is formed by the continuously linear crossings of energy bands around the Fermi level (Fig. 1b). Therefore, DNLs would fit better catalyst for the HER due to three combined advantages: (i) non-trivial drumhead-like surface states as robust active sites, (ii) good mobilities of carriers, (iii) a certain density of carriers around the Fermi level. In addition, the crucial thermodynamic descriptor HER00 ; HER01 ; HRE1 ; HRE3 ; HRE4 ; HRE5 ; HRE6 ; HRE7 ; HRE8 ; HRE10 ; HRE11 of $\Delta G_{H^{*}}$ as good catalysts should be zero as close as possible, which can be screened well through first-principles calculations.

Within this context, through first-principles calculations (details refer to Ref. online, ) we report a new DNL family of the TiSi-type materials $MX$ ($M$ = Ti, Zr, Hf; $X$ = Si, Ge, Sn). The DNL exists in the $k_{y}$ = 0 plane of the bulk Brillouin zone (BZ) and induces the nearly flat drumhead-like topological non-trivial surface states, thereby resulting in a highly high localized electronic density around the Fermi level on the surface. Interestingly, on the two (010) and (110) surfaces of TiSi the hydrogen adsorption free energies $\Delta G_{H^{*}}$ are derived to be almost zero, being much more closer to zero than those values of all known catalysts for the HERHRE1 ; HRE3 ; HRE4 ; HRE5 ; HRE6 ; HRE7 ; HRE8 including the most extensively used precious platinum (Pt).

The TiSi samples were first prepared by the arc melted method and then annealed in vacuum for 48 hours at 1200 oC. The X-ray diffraction demonstrate that TiSi crystallizes in the orthorhombic lattice (Fig. 2a) with the space group of Pnma (No. 62) and the refinement reveals that Si occupies the Wyckoff 4$c$ site (0.0362, 0.2500, 0.1103) and Ti at another Wyckoff 4$c$ site (0.1820, 0.2500, 0.6250). Our current experimental findings are supported by our theoretical lattice constants $a$ = 6.529 Å , $b$ = 3.645 Å  and $c$ = 5.004 Å , also in good accord with the previous experimental data expt1 ; expt2 ; expt3 ; expt4 (supplementary Table S1). In addition, the derived phonon dispersion does not show any imaginary frequencies and is dynamically stable (Fig. 2b).

In standard DFT calculations, as shown in Fig. 3a the bands near the Fermi energy are mainly contributed from the Ti d-like orbitals. Without the SOC inclusion, there are the two nearly linear band crossings, A and B points, as marked in Fig. 3a. The one (A) locates at 0.1 eV above the Fermi level in the X-$\Gamma$ direction and the other one (B) lies about 0.18 eV below the Fermi level along the $\Gamma$-Z direction. They are physically induced by the band inversion. At the centre of the Brillouin zone (BZ, Fig. 1b), $\Gamma$, the $d_{yz}$ $\rightarrow$ $d_{z^{2}}$ band inversion (Fig. S1 online ) occurs between the two bands No. 1 and No. 2, as marked in Fig. 3a. Strikingly, the band crossings not only appear at these two points, but also form a circle-like closed line around the $\Gamma$ point in the ky=0 plane (Fig. 3d). This is the apparent sign of the DNL appearance. The band crossings between No.1 and No.2 bands do not occur at the same energy level, but show a wave-like closed curve upon the $k$ vectors around the centered $\Gamma$ point. Certainly, this DNL stability is highly robust, protected by the inversion and time-reversal symmetry without the spin-orbit coupling (SOC) effect. Because of the light masses of Ti and Si, its SOC effect is rather weak; therefore, it does not affect the electronic band structure, apparently (Fig. S2online ). Furthermore, the non-trivial topology order of TiSi is confirmed by the non-Abelian Berry connection method Waner2011 ; Waner20112 ; Sun2016 , as shown in Fig. 3(b) and 3(c). In the $k_{y}$ = 0 plane in which the DNL locates, the loop of the Wannier center evolution change partners from $k_{x}$ = 0 to $k_{x}$ = $\pi$. However, In the $k_{y}$ = $\pi$ plane, no partner changes. Hence, the evolution loop of the Wannier center cuts the reference line odd times in the $k_{y}$ = 0 plane, whereas the crossing between Wannier center evolution loop and the reference line zero or even times in the $k_{y}$ = $\pi$ plane.

We have also considered the isoelectronic and isostructural TiGe, TiSn, HfSi, HfGe, HfSn and ZrSi, ZrGe and ZrSn. As shown in supplementary Table S1 and Fig. S1-S6 online , the electronic band structures of ZrSi and GeSi are qualitatively the same physics as TiSi does (see Fig. 3(e and f)).

To inspect the topological surface bands for TiSi, we have calculated the electronic structures of the (010) surface by varying the thickness of the slabs (Fig. S7online ). As expected, the robust surface electronic bands (topological SF-band 1 in Fig. 4a) appear, when the slab’s thickness is above eight atomic layers along the b-axis. From Fig. 4a, outside the Dirac nodal ring on the (010) surface projected by the DNL of its bulk phase, the two-fold degenerated topological SF-band 1 clearly separates: one goes to the unoccupied conduction bands integrating with the projection of the electronic bands of bulk phase and the other one emerges into the valence bands overlapping with the projected bulk bands. With other words, these separated surface bands outside the projected Dirac nodal ring are the topologically trivial states and not correlated with the bulk DNL states. These separated trivial surface bands mainly originates from the Ti $d_{xz}$-, $d_{xy}$- and $d_{x^{2}-y^{2}}$-like states. This means that the topological non-trivial surface bands SF-band 1 only occur within the DNL-projected Dirac nodal ring on the (010) surface. The topologically protected SF-band 1 around the $\bar{\Gamma}$ point are mainly comprised with the $d_{yz}$ and $d_{z^{2}}$-like electronic states from the topmost atomic layer, reflecting well the $d_{yz}$ $\rightarrow$ $d_{z^{2}}$ band inversion in its bulk phase (Fig. 2a). This SF-band 1 is two-fold degenerated, half-filled when the surface is electrically neutral, in similarity to the case of Be Li2016 .

Importantly, the three main features of the DNLs in TiSi motivates us to consider its activities as catalysts, as conceptually shown in Fig. 5a. Firstly, the nearly flat drumhead-like non-trivial topological surface states (SF-band 1 in Fig. 4a) on the (010) surface disperses parabolically and its lowest-energy part exactly cuts the Fermi level of 0 eV at $\bar{\Gamma}$, suggesting the possibility of robust active planes for catalysis against defects, impurities, and other surface modifications. Secondly, from Fig. 3a the Dirac nodal points on the NDLs around the Fermi level are expected to exhibit high mobility because the linear band crossing. In similarity to TDs and TWs, it will be favorable for the free and quick diffusion of electrons. Thirdly, the topology carrier density is not low due to the DNL presence around the Fermi level.

Following the theoretical suggestions HER00 ; HER01 ; HRE1 ; HRE3 ; HRE4 ; HRE5 ; HRE6 ; HRE7 ; HRE8 ; HRE10 ; HRE11 , we evaluate the HER activities of the two (010) and (110) planes, where the hydrogen adsorption free energy $\Delta G_{H^{*}}$ was determined by varying different adsorption sites on the specified surface (see methodonline ). Theoretically, $\Delta G_{H^{*}}$ is known to scale with activation energies and has been successfully used as a descriptor for correlating theoretical predictions with experimental measurements of catalytic activity for various systemsHER00 ; HER01 ; HRE1 ; HRE3 ; HRE4 ; HRE5 ; HRE6 ; HRE7 ; HRE8 ; HRE10 ; HRE11 . The previous theoretical suggestions that for the best activity the optimal value of $\Delta G_{H^{*}}$ should be 0 eV, where hydrogen is bound neither too strongly nor weakly with active sites on the surface HRE1 . Surprisingly, our calculated results demonstrate that $\Delta G_{H^{*}}$ of HER on different TiSi surfaces are very close to zero. It shows us that on the (010) surface $\Delta G_{H^{*}}$ = -0.03 eV when hydrogen bridges two nearest neighboring Ti atoms (Fig. 5c) and -0.05 eV with hydrogen bridging Ti and Si on the topmost atomic layer. The (110) surface even yields, $\Delta G_{H^{*}}$ = -0.005 eV, of an almost zero value. In comparison with some typical catalysts (MoS2, Pt and hydrogenase) in Fig. 5e, the HER activities on the TiSi surfaces are highly attractive. It can be seen that the values of $\Delta G_{H^{*}}$ of TiSi show a much closer value to zero than both the typical catalysts of Pt ($\Delta G_{H^{*}}$ = -0.09 eV)HER01 and the edge states ($\Delta G_{H^{*}}$ = 0.082 eV)HER01 of MoS2. Furthermore, we have plot the Volcano curves for the HER of TiSi in comparison with some data known. Remarkably, among all known data TiSi exhibits a $\Delta G_{H^{*}}$ most close to zero. In particular, in comparison with these TWsTWs-HRE9 in Fig. 5e, TiSi possibly shows a more excellent HER performance, because their $\Delta G_{H^{*}}$ values of TiSi are almost at the top of the Volcano curve. However, the $\Delta G_{H^{*}}$ of both NbP and TaP are much lower than that of Pt, and their asenides even have the corresponding values as negative as -0.75 eV and -1.0 eV, respectively.

Mechanically, the calculations demonstrate that, after the hydrogen adsorption on the (010) surface, the topological SF-band 1 (Fig. 4b) becomes unoccupied above the Fermi level. The hydrogen atom will obtain the charges and disperse in the deep energy region below the Fermi level. This process can be made more clear by visualizing the local charges in Fig. 5(b,c and d). On the clean (010) surface, the charges of the topological SF-band 1 are clearly localized at two nearest neighboring Ti atoms with the $d_{yz}$ orbitals (Fig. 5b). After the hydrogen adsorption, the topological charges are indeed transferred to the hydrogen. As evidenced in Fig. 5c, a lone-pair s-like orbital appears in terms of the charge accumulations. Correspondingly, the charge depletion of the two nearest neighboring Ti atoms are highly visualized in Fig. 5d, which also refers to the position of the localized topological charges on the H-free adsorption (010) surface in Fig. 5b. This fact indicates that the topology carrier on the SF-band 1 states are fully transferred into hydrogen $s$-like orbitals, indicating that the bulk DNLs play an important role in the HER as a potential catalyst.

Summarizing, we have reported on the new DNLs’ family (TiSi, TiGe and ZrSi) and theoretically demonstrate that they have the promising potential as excellent catalyst for the HER performance because of the active sites provided by the robust nearly flat drumhead-like non-trivial surface states, a stable supply of itinerant electrons from the certain carrier density and the high mobilities related with the DNLs, and the most suitable $\Delta G_{H^{*}}\approx$ 0 for the HER.

Acknowledgments Work was supported by the “Hundred Talents Project” of the Chinese Academy of Sciences and by the National Natural Science Foundation of China (Grant Nos. 51671193 and 51474202) and by the Science Challenging Project No. JCKY2016212A504. All calculations have been performed on the high-performance computational cluster in the Shenyang National University Science and Technology Park and the National Supercomputing Center in Guangzhou (TH-2 system)

‡ These authors contributed equally to this work.