Plasmonic high-entropy carbides

Discovering multifunctional materials with tunable plasmonic properties, capable of surviving harsh environments is critical for advanced optical and telecommunication applications. We chose high-entropy transition-metal carbides because of their exceptional thermal, chemical stability, and mechanical properties. By integrating computational thermodynamic disorder modeling and time-dependent density functional theory characterization, we discovered a crossover energy in the infrared and visible range, corresponding to a metal-to-dielectric transition, exploitable for plasmonics. It was also found that the optical response of high-entropy carbides can be largely tuned from the near-IR to visible when changing the transition metal components and their concentration. By monitoring the electronic structures, we suggest rules for optimizing optical properties and designing tailored high-entropy ceramics. Experiments performed on the archetype carbide HfTa4C5 yielded plasmonic properties from room temperature to 1500K. Here we propose plasmonic transition-metal high-entropy carbides as a class of multifunctional materials. Their combination of plasmonic activity, high-hardness, and extraordinary thermal stability will result in yet unexplored applications.


Supplementary Note 2. Simulation of optical properties using POCC
Here we test the capability of the POCC method in simulating the optical spectra of disordered systems. We consider the case of the disordered AuAg solid-solution, compared to the Au and Ag fcc constituents, all well-known plasmonic systems. AuAg is simulated by using 44 POCC structures with 8 atoms per cell. The imaginary part i of the dielectric function of the three systems is shown in Supplementary Figure 3(a), along with the corresponding experimental counterpart (inset), extracted from Ref. [1]. The disordered alloy has a distinct character, with spectral features not directly ascribable to the ordered crystalline phases of the single elements. The excellent agreement with the experimental findings confirms the accuracy of the present approach in including the effect of disorder into the description of the optical properties.
The excitation of plasmons is a purely electronic effect, i.e., intraband electron-electron excitations. The excitation of the electron gas is an ultrafast process (on the femtosecond scale) that does not involve the interaction with phonons. The ionic temperature has an indirect and minor effect of the plasmon excitation energies, mostly ascribable to the thermal expansion of the lattice and thus to the average modifications of the bond lengths. Supplementary Figure 3(b) shows the simulated EELS spectra of disordered AuAg solid-solution at different configurational temperatures. The results match well with the measured redshift of the plasmonic band (see gray dashed line) of AuAg as the temperature is increased [2]. This effect, usually of the order of 0.1 eV, has been observed also for Ag bulk systems and it is associated to thermal structural expansion [3]. As shown in Supplementary Figure 1(b), this effect is reproduced by POCC, which describes the spatial distribution of the atoms in the disordered system. Beyond a certain temperature (system dependent), structural instabilities and/or phase transitions (e.g., melting), will change the morphology of the system, yet affecting optical properties. This is not considered in the article because it focuses on thermodynamically homogeneous systems. Therefore, we can conclude that away from critical temperatures, temperature has a secondary effect on the plasmonic excitation energy and that our approach well describes this process.
The stability (i.e., lifetime) and of the de-excitation of the plasmonic resonance follows a different scenario [4,5]. Here, the interaction with the lattice, and thus with the ionic temperature, is critical. After the initial ultrafast thermalization of the hot-electron gas through electron-electron scattering, the energy is transferred to the lattice via phonon emission (electron-phonon coupling) on the nanosecond scale. Finally, thermal energy is radiated (heat-diffusion) towards the external environment through phonon-phonon scattering on the micro-to-millisecond scale. While increasing temperature may favor the plasmon extinction through destructive electron-phonon interaction, it does not directly affect the energy position of the plasmon resonance and/or of the crossover energy (beyond considerations about thermal expansion). Therefore, we can conclude that below the critical melting point, temperature has a minor effect on the plasmonic excitation energy and that the POCC method well characterizes the phenomenon.

Supplementary Note 3. Chemical modifications in HfTa4C5
Starting from optimized HfTa 4 C 5 , we calculated the optical properties of derived materials. Simulations on these derived materials have been done on a single POCC structure and without further atomic relaxation. Supplementary Figure 4 shows the EELS spectra for Hf x Ta 5−x C 5 model, by varying the amount of Hf in the cell, with x = [0 − 5]. The cases x = 0 and x = 5 correspond to TaC and HfC, respectively. Supplementary Figure 5 shows the EELS spectra for M Ta 4 C 5 model, with M =Ti, Zr, Hf, V, Nb, Cr, Mo, and W.

Supplementary Note 4. Plasmonic High-Entropy Carbides
Simulated reflectivity spectra for selected PHECs.  [6], and with the single particle (SP) approach based on the Drude-Lorentz in the limit for transferred momentum q → 0. Both approaches are implemented in the Quantum ESPRESSO distribution [7]. For both systems, the two spectra are identical, within the numerical errors.
Supplementary Figure 8. Comparison between the optical complex dielectric functionˆ (E) ≡ ( r + i i) calculated with the Liouville-Lanczos TD-DFPT approach and the Drude-Lorentz single particle (SP) approach, as implemented in the Quantum ESPRESSO suite of codes for (a) fcc TaC rocksalt crystal, and (b) 3-HfNbTaTiZrC5 high entropy carbide (single pocc). r , i, and E0 identify the real, (imaginary) part of the dielectric function and the crossover energy, respectively. Source data are provided as a Source Data file.

Supplementary Note 6. Experimental measurements
Electron transparent lamellae were prepared for EELS analysis from the center of a cross-sectioned HfTa 4 C 5 pellet in a Thermofisher Scientific Helios NanoLab 660 Dual Beam focused ion beam (FIB)-scanning electron microscope (SEM) using a 30 keV Ga ion beam. A sacrificial carbon protective layer was deposited on top of the HfTa 4 C 5 prior to milling to limit excess ion implantation as the cross section was thinned to electron transparency, after which each face of the lamellae was polished using a 5 keV Ga ion beam to remove resputtered material and reduce the thickness of any amorphous implantation layer produced during milling at high accelerating voltages. Once thinned, the sections were lifted and transported to a Protochip Fusion Select Heating E-chip and micro-welded to the chip using localized 5 keV ion assisted deposition of carbon. Supplementary Figure 9 shows the thinned and polished cross section after transport to the heating chip. Panel (b) shows a monochromated STEM image of the HfTa 4 C 5 lamellae, which indicates the region where all EELS spectra were collected as a function of temperature.

a) b)
Supplementary Figure 9. (a) Ion milled electron transparent cross-section of sintered HfTa4C5 pellet fixed to Protochip Fusion Select Heating E-chip. The center of the cross-section was thinned to electron transparency and polished using a Ga ion beam prior to transfer to the E-chip, where the section was micro-welded to the chip using Ga ion assisted deposition of carbon as indicated on the left of the figure. (b) Monochromated STEM micrograph of the HfTa4C5 cross-section, which indicates the region where all EELS spectra were collected. Source data are provided as a Source Data file.