Fig. 4: Interface charge tuning and theoretical results.

a Schematic of the MnO₂⁽⁻¹⁾-terminated structure (top) and LaO⁽⁺¹⁾-terminated structure (bottom) obtained by inserting a 2-unit-cell LaMnO₃ layer between HZO and LSMO layers. The resulting termination is MnO₂⁽⁻¹⁾ with a negative ionic charge or LaO⁽⁺¹⁾ with a positive ionic charge for A- and B-type heterostructures, respectively. b XRD data for the MnO₂⁽⁻¹⁾-terminated structure (blue curve) and the LaO⁽⁺¹⁾-terminated structure (red curve). c Calculated work functions of o-HZO, MnO₂-terminated LSMO (MnO₂-LSMO), LaSrO-terminated LSMO (LaSrO-LSMO), and LaO-terminated LSMO (LaO-LSMO). MnO₂-terminated LSMO donates holes to HZO, while LaSrO- and LaO-terminated LSMO donates electrons. d Relative stability of orthorhombic (green circles) and monoclinic (blue circles) HfO₂ phases as a function of hole doping density. The lowest energy phase is used as the reference, and its energy is set to zero. The energy of the other phase is given with respect to the most stable one.