## Introduction

The CO2 electroreduction reaction (CO2RR) to valuable fuels and feedstocks, powered using renewable electricity, offers a sustainable approach to store intermittent renewable energy1. Prior CO2RR studies have reported the generation of C1 to C3 chemicals such as CO, methane, formate, ethylene, ethanol, and n-propanol2,3,4,5,6,7,8,9,10. Among these products, carbon-neutral methane produced from CO2RR is desired due to well-established natural gas infrastructure11.

Practical CO2RR systems need to produce a desired product with high selectivity, conversion rate, and energy efficiency (EE)12,13. In prior reports, most advances in improving the selectivity to methane in CO2RR operate at current densities below 50 mA cm−2 (ref. 14,15,16,17,18). Techno-economic analyses suggest that compelling CO2RR systems require current densities above 100 mA cm−2 (ref. 19), which prompted us to concentrate on improving the performance of CO2RR to methane in high current density regimes (>100 mA cm−2).

In CO2RR, *CO protonation to *CHO is the potential-determining step for methane formation, and it competes with C–C coupling toward C2 products20,21. In addition, *CO protonation competes with the hydrogen evolution reaction (HER), since both need *H (ref. 22). The simultaneous suppression of both HER and C–C coupling will improve methane selectivity.

Early studies by Hori et al.2 showed that Cu is the transition metal catalyst that generates methane and C2+ products; but that it did so with low product selectivity. Introducing a second metal into Cu has been shown to be a promising route to tune the product selectivity in CO2RR (refs. 23,24,25,26,27,28,29,30). Prior studies report that Au–Cu bimetallic catalysts of varying structures exhibit good selectivity to CO or alcohols, albeit with pure CO2 feeds (refs. 31,32,33,34). Here we present a strategy wherein we regulate *CO availability on Au–Cu catalysts, enabling selectivity to methane at high production rates in CO2RR. Density functional theory (DFT) calculations indicate that the introduction of Au in Cu not only steers the selectivity from C–C coupling to *CO protonation under low *CO coverage, but also tends to suppress HER relative to Cu. By implementing this concept experimentally, we achieve an FE of (56 ± 2)% to methane. The methane:H2 selectivity ratio is improved 1.6× compared with prior reports having a total current density above 100 mA cm−2 (Supplementary Table 1) (refs. 35,36,37,38,39).

## Results

### DFT calculations

In a previous study, we found that lowering the *CO coverage on a Cu surface improved the selectivity to methane in CO2RR while still suffering from prominent HER (ref. 35). Introducing a second element to Cu, such as Ag, has been shown to suppress HER (refs. 21,28). Au—like Ag—has a greater free energy of hydrogen adsorption than Cu, suggesting that it is also a poor HER catalyst40. We thus use Au–Cu as a representative example to assess methane selectivity on catalysts with HER-suppressing dopants under different *CO coverages. In addition, we note that selecting an element that is on the same side of the hydrogen adsorption volcano curve as Cu avoids any synergistic effects that may optimize the *H binding energy leading to better HER, such as with Cu–Ni or Cu–Pt (refs. 41,42,43).

Computationally, we built three Au–Cu surfaces by replacing one, two, or three surface Cu atoms of a (3 × 3 × 4) Cu(111) supercell with Au atoms, denoted Au1Cu35, Au2Cu34, and Au3Cu33, respectively. With DFT, we first calculated the reaction free energies of *CO to *CHO (∆G*CHO) for methane formation and C–C coupling (∆G*OCCOH) for C2 products on these Au–Cu surfaces under different *CO coverages (Fig. 1a, Supplementary Figs. 14, and Supplementary Tables 2 and 3). ∆G*CHO–∆G*OCCOH is used as a descriptor of the propensity for *CO protonation vs. C–C coupling. We found that the values of ∆G*CHO–∆G*OCCOH on Au–Cu surfaces decrease when one reduces *CO coverage from 4/9 to 2/9 monolayer (ML) (Fig. 1b), a trend similar to that on Cu. Thus lowering *CO coverage on Au–Cu surfaces is predicted to favor methane vs. C2 products, as previously shown on Cu (ref. 35). In addition, DFT calculation results show that the values of ∆G*CHO–∆G*OCCOH on Au–Cu surfaces are not always lower than the values of ∆G*CHO–∆G*OCCOH on Cu at different *CO coverages (Fig. 1b), suggesting that only under low *CO coverage do some Au–Cu surfaces show a higher ratio of methane to C2 products compared to Cu.

To compare the HER activities on Cu and Au–Cu surfaces, we calculated the reaction free energies of *H intermediate formation (∆G*H) (Fig. 1c and Supplementary Fig. 5). The results suggest that Au–Cu surfaces tend to suppress HER compared to Cu under high *H coverages (Fig. 1c).

Taken together, these DFT studies suggest that Au–Cu tends to promote methane selectivity with low *CO coverage, since this will suppress C–C coupling; and that Au–Cu will further advance CO2RR over HER compared to pure Cu.

### Preparation and characterization of catalysts

To achieve the goal of high selectivity to methane in CO2RR with high current densities, we sought to fabricate Au–Cu catalysts. We used a galvanic replacement approach enabled by the differing reduction potentials of Au and Cu (ref. 44). Firstly, we prepared a 100 nm thick layer of Cu catalysts on the surface of polytetrafluoroethylene (PTFE) nanofibers via sputter deposition (Supplementary Figs. 6 and 7). We then immersed the Cu/PTFE in an N2-saturated HAuCl4 aqueous solution at 65 °C for 15 min to prepare the Au–Cu catalysts on PTFE as the electrodes (Fig. 2a–d) via the galvanic replacement between Cu and AuCl4—this approach allows us to directly tune the ratio of Au and Cu on PTFE substrates.

Low-magnification scanning electron microscope (SEM) images and energy-dispersive X-ray spectroscopy (EDX) elemental mapping show a uniform distribution of elemental Cu and Au on PTFE nanofibers, accompanied by loosely distributed Au nanoparticles also on the nanofibers (Fig. 2a, b). The bright-field scanning transmission electron microscope (STEM) image with higher magnification and corresponding EDX elemental mapping further confirms that Au and Cu are distributed evenly on the PTFE nanofibers (Fig. 2d). High-resolution X-ray photoelectron spectroscopy (XPS) characterization of Au–Cu electrodes shows the presence of Au0 and Cu which has been partially oxidized to Cu+ in the air (Fig. 2e, f and Supplementary Figs. 8 and 9)45. The atomic percentage of Au in the catalyst surface is approximately 7% determined by XPS (denoted 7% Au–Cu), which is lower than previously reported Au–Cu alloy catalysts studied in CO2RR (refs. 31,32,33).

### Investigation of CO2 electroreduction

The CO2RR experiments were performed in a flow cell reactor with a three-electrode configuration (Supplementary Figs. 10 and 11) using CO2-saturated 1 M KHCO3 aqueous solution as the electrolyte. Previous studies show that, in CO2RR, both reaction rate—determined by current density—and CO2 concentration affect the concentration of *CO on the catalyst surface35. We thus evaluated the CO2RR performance of 7% Au–Cu electrodes by supplying gas streams consisting of different volume ratios of CO2 to N2 (Fig. 3, Supplementary Figs. 12 and 13, and Supplementary Table 4).

Figure 3a, b shows FEs of methane and ethylene on 7% Au–Cu catalysts in the current density range of 100–250 mA cm−2 at various CO2 concentrations (25% CO2, 50% CO2, 75% CO2, 84% CO2, 92% CO2, and pure CO2). At low current densities (≤150 mA cm−2), 7% Au–Cu delivers appreciable ethylene FEs under pure CO2 and CO2–N2 mixed streams (Fig. 3b). However, at high current densities (200–250 mA cm−2), relative to pure CO2, the methane FEs on 7% Au–Cu catalysts increase sharply in CO2–N2 mixed streams while the ethylene FEs decrease dramatically, which we ascribe to the low *CO coverage on catalyst surfaces as a result of the reduced CO2 concentration and high reaction rate. We note that, once they reach their peaks in these mixed streams, the methane FEs start to decrease with further increase in current density (Fig. 3a), a finding we attribute to the lack of *CO for the *CO protonation step of methane formation46. In particular, at 84% CO2, we achieve the highest CH4 FE of (56 ± 2)% on 7% Au–Cu catalysts with a CH4 production rate of (112 ± 4) mA cm−2. We calculated the CH4 cathodic EEs at different current densities under different CO2 concentrations (Fig. 3c): the highest CH4 cathodic EE of (24 ± 1)% was achieved at 200 mA cm−2 under 84% CO2.

To evaluate experimentally the selectivity between *CO protonation and C−C coupling reaction steps, we further calculated the ratios of methane FE to total C2+ FE ($${{\rm{FE}}}_{{{{\rm{CH}}}}_{4}}/{{\rm{FE}}}_{{\rm{C}}_{2+}}$$) on 7% Au–Cu catalysts at various CO2 concentrations (Fig. 3d). With low reaction rates (≤150 mA cm−2), the C2+ selectivity is higher than the methane selectivity regardless of the CO2 concentration. Under high current densities (200–250 mA cm−2), the $${\rm{FE}}_{{\rm{CH}}_{4}}/{\rm{FE}}_{{\rm{C}}_{2+}}$$ ratio on 7% Au–Cu catalysts in CO2–N2 mixed streams is much greater than that in pure CO2, suggesting that low *CO coverage on the surface of Au–Cu catalysts—as a consequence of a reduced CO2 concentration and high current density—promotes the *CO protonation step for methane production, consistent with our DFT calculations.

To explore the effect of Au concentration on CO2RR performance under CO2–N2 co-feeds, we also prepared 3% Au–Cu and 10% Au–Cu catalysts on PTFE through a similar galvanic replacement approach (Supplementary Figs. 7 and 1419) and measured CO2RR performance of the 3% Au–Cu, 10% Au–Cu, and Cu catalysts at 84% CO2 for comparison (Fig. 4a–c, Supplementary Figs. 20 and 21, and Supplementary Table 5). At low reaction rates (≤150 mA cm−2), the methane FEs on 3% Au–Cu, 7% Au–Cu, 10% Au–Cu, and Cu catalysts are below 11% (Fig. 4a), while ethylene and ethanol are the main CO2RR products on these catalysts (Supplementary Fig. 20c and Supplementary Table 5). At high reaction rates (200–250 mA cm−2), methane becomes the main CO2RR product while ethylene FEs are below 12% on the 3% Au–Cu, 10% Au–Cu, and Cu catalysts; methane FEs on 3% Au–Cu, 10% Au–Cu, and Cu catalysts give peak values at 200 mA cm−2 and then decrease along with the increase in current density (Fig. 4a). These trends are similar to that observed on the 7% Au–Cu catalysts. By comparing the highest methane FEs on different catalysts, we note that, among the catalysts studied, only 7% Au–Cu catalysts deliver higher methane FE vs. Cu catalysts (Fig. 4b), suggesting the significance of controlling Au concentration in Au–Cu catalysts for promoting methane selectivity. The 7% Au–Cu delivers—compared to 3% Au–Cu and 10% Au–Cu—higher methane FE at 200 mA cm−2. We associate this with improved suppression of HER on 7% Au–Cu (Supplementary Fig. 20a) and note that both HER and *CO coverage impact methane FE. We also calculated the $${\rm{FE}}_{{\rm{CH}}_{4}}/{\rm{FE}}_{{\rm{C}}_{2+}}$$ ratios on Cu and three Au–Cu catalysts at 84% CO2: only at high current density—low *CO coverage—do some of Au–Cu catalysts show higher $${{\rm{FE}}}_{{{{\rm{CH}}}}_{4}}/{{\rm{FE}}}_{{\rm{C}}_{2+}}$$ ratios compared to Cu, in agreement with DFT calculations.

At high current densities (200–250 mA cm−2) with high methane selectivity, the H2 FEs on 3% Au–Cu, 7% Au–Cu, and 10% Au–Cu catalysts are lower than that on the Cu catalysts (Supplementary Fig. 20a), suggesting that the introduction of Au in Cu tends to suppress HER when using dilute CO2 feeds. We further calculated the ratio of methane FE to H2 FE ($${\rm{FE}}_{{\rm{CH}}_{4}}/{\rm{FE}}_{{\rm{H}}_{2}}$$) on catalysts in high current density regimes (Fig. 4c): compared with Cu catalysts, 3% Au–Cu, 7% Au–Cu, and 10% Au–Cu catalysts exhibit higher $${\rm{FE}}_{{\rm{CH}}_{4}}/{\rm{FE}}_{{\rm{H}}_{2}}$$ ratios—with the highest value of 2.7 on 7% Au–Cu catalysts— indicating that the Au–Cu catalysts shifted the reaction from undesired HER toward *CO protonation for methane production.

To investigate the chemical state of Cu in the catalysts during CO2RR, we carried out operando X-ray absorption spectroscopy (XAS) at the Cu K-edge at a constant current density of 200 mA cm−2 with an 84% CO2 feed (Fig. 4d). The average valence states of Cu in 3% Au–Cu, 7% Au–Cu, 10% Au–Cu, and Cu catalysts are zero during CO2RR, demonstrating that the difference in product selectivity among these catalysts is associated with the metallic state of Cu in lieu of copper oxides5,47.

## Discussion

This work demonstrates that the introduction of Au in Cu facilitates *CO protonation for methane formation using CO2–N2 co-feeds and suppresses HER at high current densities. DFT results show that a decrease in *CO coverage on Au–Cu surfaces favors *CO protonation vs. C–C coupling; compared with Cu, Au–Cu suppresses HER, enabling methane selectivity improvements under dilute CO2 streams. Experimentally, we fabricated Au–Cu catalysts and regulated *CO availability by controlling the CO2 concentration and current density, wherein the selectivity ratio of methane to H2 exhibited the highest value of 2.7. We report a CO2-to-methane conversion with a high methane FE of (56 ± 2)% at a partial current density of (112 ± 4) mA cm−2 with a CO2–N2 co-feed. These findings suggest a promising strategy to convert CO2 to carbon-neutral methane with a combination of high selectivity, high conversion rate, and high cathodic EE through catalyst design and tuning local *CO coverage.

## Methods

### DFT calculations

In the Vienna ab initio simulation package, the generalized gradient approximation and the Perdew–Burke–Ernzerhof exchange-correlation functional was implemented for all DFT calculations48,49,50,51,52. The projector-augmented wave (PAW) method was used to treat the electron–ion interactions53,54 with an energy cut-off of 450 eV for the plane-wave basis set. The force and energy convergence for all DFT calculations were set to 0.01 eV Å−1 and 10−5 eV, respectively. A (3 × 3 × 4) Cu(111) supercell with the bottom two layers fixed was used to simulate the exposed Cu surface with a 15 Å vacuum gap. One, two, or three surface Cu atoms were substituted by Au atoms in the Au1Cu35, Au2Cu34, and Au3Cu33, respectively. A (3 × 3 × 1) Monkhorst–Pack k-points grid was used to optimize all the surface structures. In DFT calculations, we did not consider the isolated arrangement of Au dopants in Cu as the XAS characterization of the Au–Cu catalysts showed that Au atoms were not atomically dispersed in Cu (Supplementary Fig. 22 and Supplementary Table 6).

Surface *CO coverages of 2/9 ML, 3/9 ML, and 4/9 ML were studied, where 2/9 ML corresponds to two single-carbon adsorbed species or one double-carbon species on the surface of the supercell. To systematically determine the most stable geometry of each reaction intermediate in CO2RR and HER under different *CO coverages (2/9, 3/9, and 4/9 ML) on different surfaces (Cu36, Au1Cu35, Au2Cu34, and Au3Cu33), we considered different possibilities of *CO adsorption, protonation, and C–C coupling, as well as different directions of *OCCO protonation (more details of our computational workflow in Supplementary Fig. 23). We note that the models reported in this study include a charged water layer, i.e., an ML of six water molecules, one of which is a hydronium or charged water (H3O+) molecule, to consider both field and solvation effects55. The water structure was determined by ab initio molecular dynamics and adopted from a previous study56. The two competing CO2RR reaction steps as listed below57,58,59,60,61 were simulated for the three *CO coverages while *H adsorption was simulated for equivalent *H coverages

$$\ast {\rm{CO}}+{\rm{H}}_{2}{\rm{O}}+{\rm{e}}^{-}\to \ast {\rm{CHO}}+{\rm{OH}}^{-}$$
(1)
$$\ast {\rm{CO}}+\ast {\rm{CO}}+{{\rm{H}}}_{2}{\rm{O}}+{{\rm{e}}}^{-}\to \ast {\rm{OCCOH}}+{{\rm{OH}}}^{-}$$
(2)
$${{\rm{H}}}^{+}+{{\rm{e}}}^{-}+\ast \to \ast {\rm{H}}$$
(3)

The Gibbs free energy changes (∆G) for *CO protonation, C–C coupling, and *H adsorption were calculated without dipole corrections based on the computational hydrogen electrode (CHE) model62. The Gibbs free energy of adsorbed and non-adsorbed species (G) is calculated as

$$G=E+{\rm{ZPE}}+\smallint C{p}{\rm{d}}T-TS$$
(4)

where E, ZPE, Cp, and S are the electronic energy directly obtained from DFT calculations, zero-point energy, heat capacity, and entropy, respectively (see Supplementary Table 2 for more details). T is set to room temperature (298.15 K) for a better comparison with the experimental measurements.

### Electrode preparation

All chemicals were used as received without further purification. All aqueous solutions were prepared using deionized water with a resistivity of 18.2 MΩ cm. The Cu/PTFE cathodes were prepared by sputtering 100 nm thickness of Cu catalysts (Cu target, 99.999%, Kurt J. Lesker company) on PTFE membranes (pore size: 450 nm, Beijing Zhongxingweiye Instrument Co., Ltd.) using a magnetron sputtering system. In the cathode, a porous PTFE membrane functions as a stable hydrophobic gas diffusion layer and prevents flooding during operation7. 3% Au–Cu, 7% Au–Cu, and 10% Au–Cu cathodes were prepared by immersing the Cu/PTFE electrodes in N2-saturated HAuCl4 aqueous solution (5 μmol L−1) at 40 °C for 30 min, 65 °C for 15 min, and 65 °C for 30 min, respectively. Ag/AgCl reference electrode (3 M KCl, BASi) and Ni foam (1.6 mm thickness, MTI Corporation) was used as the reference electrode and anode, respectively. Ni foam was used as an OER electrode in the anode due to its commercial availability and good stability35,63.

Material characterization. SEM images and the corresponding EDX elemental mapping were taken using the Hitachi FE-SEM SU5000 microscope. HAADF-STEM and bright-field STEM images, and the corresponding EDX elemental mapping were taken using a Hitachi HF-3300 microscope at 300 kV. XRD was recorded on Rigaku SmartLab X-ray diffractometer with Cu-Kα radiation. The surface compositions of electrodes were determined by XPS (Thermo Scientific K-Alpha) using a monochromatic aluminum X-ray source. Operando Cu K-edge XAS spectra recorded in fluorescence yield were performed at the SuperXAS beamline at the Swiss Light Source. Ex situ XAS measurements were carried out at the Advanced Photon Source (Argonne National Laboratory). XAS data were processed by Athena and Artemis software included in a standard IFEFFIT package64.

### Electrochemical measurements

The electrochemical measurements were conducted in an electrochemical flow cell setup configuration with the three-electrode system at an electrochemical station (AUT50783). The geometric area of the cathode in the flow cell is 1 cm2, which is used for all current density calculations. 30 mL of CO2-saturated 1 M KHCO3 aqueous solution was introduced into the cathode chamber and the anode chamber at the rate of 10 mL min−1 by two pumps, respectively. An anion exchange membrane (Fumasep FAB-PK-130, Fuel Cell Store) was used to separate the cathode chamber and anode chamber. Pure CO2 gas (Linde, 99.99%) or N2-diluted CO2 gas with different CO2 concentrations (75% and 84%) was continuously supplied to the gas chamber of the flow cell at a flow rate of 90 mL min−1. The CO2RR performance was tested using constant-current electrolysis while purging CO2 into the catholyte during the whole electrochemical test. The potentials vs. Ag/AgCl reference electrode were converted to values vs. reversible hydrogen electrode using the equation

$${E}_{\rm{RHE}}={E}_{{\rm{Ag}}/{\rm{AgCl}}}+0.210\,{\rm{V}}+0.0591\times {\rm{pH}}$$
(5)

The ohmic loss between the working and reference electrodes was evaluated by electrochemical impedance spectroscopy technique and 80% iR compensation was applied to correct the potentials manually.

Gas products were analyzed using a gas chromatograph (PerkinElmer Clarus 600) equipped with thermal conductivity and flame ionization detectors. Liquid products were analyzed by nuclear magnetic resonance spectrometer (Agilent DD2 600 MHz) and dimethylsulfoxide was used as an internal standard.

We calculated the methane cathodic EE based on the equation as follows7:

$${\rm{Cathodic}}\,EE=\frac{(1.23+(-{E}_{{\rm{methane}}}))\times F{E}_{{\rm{methane}}}}{(1.23+(-{E}_{{\rm{applied}}}))},$$
(6)

where the overpotential of oxygen evolution is assumed to be 0, Eapplied is the potential used in the experiment, FEmethane is the measured Faradaic efficiency of methane in percentage, and Emethane = 0.17 VRHE for CO2RR (ref. 65).