S1. -COHP of Na-O (O from Na-O-TM) (TM=Co, Cu, V, Cr, Ni, Fe, Mn, Zn, Ti) in doped β-NaMnO₂

1. Screening of doped atoms in β-NaMnO₂(a) Schematic crystal structure of β-NaMnO₂ doped by 3d transition metal atoms; (b) -ICOHP of Na-O and TM-O (TM=Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn); (c) -COHP of Na-O and Cu-O in Cu doped β-NaMnO₂; (d) -COHP of Na-O and Ti-O in Ti doped β-NaMnO₂. Colorful figures are available on website

2. Structure and morphology of β-MTC811(a) Crystal structure modeling of β-MTC811 that obtained by calculation; (b) Comparison of calculated and experimental XRD patterns of β-MTC811; (c) SEM image of β-MTC811; (d) EDS mappings of β-MTC811; (e) TEM image of β-MTC811; (f) Enlarged image of zig-zag layered structure in (e)

S2. -COHP of TM-O (TM=Mn, Zn, Ti, V, Cr, Fe, Co, Ni, Cu) in doped β-NaMnO₂

S3. XRD patterns of β-MTC811, β-MTC721 and β-MTC712

3. Electrochemical performance of β-MTC811 cathode(a-c) Charge/discharge curves of (a) β-MTC811, (b) β-MTC721 and (c) β-MTC712 at 0.2C; (d) Cycling performance, (e) rate performance and (f) dQ/dV curves of β-MTC811Colorful figures are available on website

S4. Crystal-structure modelings of (a, b) β-MTC712 and (c, d) β-MTC721

4. Electrochemical reaction mechanisms(a) Mn2p and (b) Cu2p XPS spectra of β-MTC811 in different charging and discharging states. Colorful figures are available on website

5. First-principles calculations of β-MTC811 cathode(a) Schematic diagram of desodiation process; (b) Lattice constant c/a during desodiation; (c) Calculated and fitted voltage plateaus, and experimental voltage curve; (d) Bader charge of Mn and Cu; (e-g) pDOS of Mn3d and Cu3d during different desodiation processesColorful figures are available on website

S5. Electrochemical performance of (a-c) β-MTC721 and (d-f) β-MTC712 cathodes(a, d) Cycling performance during 50 cycles; (b, e) rate performance; (c, f) dQ/dV curves

S6. CV curves of β-MTC811