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Prediction of a native ferroelectric metal

Over 50 years ago, Anderson and Blount discussed symmetry-allowed polar distortions in metals, spawning the idea that a material might be simultaneously metallic and ferroelectric. While many studies have ever since considered such or similar situations, actual ferroelectricity—that is, the existence of a switchable intrinsic electric polarization—has not yet been attained in a metal, and is in fact generally deemed incompatible with the screening by mobile conduction charges. Here we refute this common wisdom and show, by means of first-principles simulations, that native metallicity and ferroelectricity coexist in the layered perovskite Bi5Ti5O17. We show that, despite being a metal, Bi5Ti5O17 can sustain a sizable potential drop along the polar direction, as needed to reverse its polarization by an external bias. We also reveal striking behaviours, as the self-screening mechanism at work in thin Bi5Ti5O17 layers, emerging from the interplay between polar distortions and carriers in this compound.

we report some structural and energetic details of the various structures in the two materials.

Supplementary Note 2
Figure 2d of the main text shows that the resistivity is anisotropic and metal-like. Resistivity experiments 1 for La-5517 (nearly isostructural to our newly designed Bi-5517, and the closest existing material in many respects 2 ) suggest that the resistivity components are insulator-like over significant temperature intervals. The resistivity is activated, with several different small activation energies at play, indicating that the upturn is probably due to defects of some kind. This situation can be described theoretically considering an effective-mass two-band model including a light-mass (0.7 m e ) t 2g band edge and a single localized state lying 40 meV lower, contributing to current by thermal activated hopping. The calculated resistivities along the crystal axes, shown in Supplementary Figure 2, are anisotropic and have an insulating upturn quite similarly to experimental ones. This corroborates the attribution of the insulator-like resistivity upturn in such low-density, flat Fermi-surface metals to low-activation-energy defects.

Supplementary Discussion
In the following we further discuss depolarizing fields in our investigated materials, commenting on similarities and differences with regular ferroelectrics.
Depolarizing field: geometry and confinement. The main issue in the assessment of the depolarizing field in Bi-5517 is the termination of the finite system. We checked that a slab of a normal insulating ferroelectric (PbTiO 3 in the (001) direction) in vacuum has the same depolarizing field with symmetric or asymmetric surface terminations. This need not apply to Bi-5517, given the presence of free charge. The symmetric BiO surface-terminated slab, obtained adding vacuum above and below the primitive cell, has essentialy zero residual field, i.e no macroscopic dipole; this is due to the conduction charge being almost entirely located at surface states, and therefore screening the polarization charge very effectively. The asymmetric termination with a TiO 2 layer on one side and a BiO on the other leads to a large field: however, this results again from conduction charge bound into surface states on the Ti-terminated surface, rather than from screened polarization. This is also confirmed by calculations in another asymmetric surface termination, whereby we find a large field opposite to that expected from polarization.
This motivates us to extract the properties of a finite Bi-5517 system using a Bi-5517/insulator superlattice. We choose Bi 2 Zr 2 O 7 (BZO-227) as our cladding insulator. This material is nonpolar in the configuration we impose on it, although it turns out to be ferroelectric with polarization along the c axis when relaxed as stand-alone bulk. BZO is also BTO-stoichiometric on the A site, thus virtually eliminating the possibility of interface-state related fields.
BZO-227 provides a good confinement of the conduction electrons within Bi-5517, which is desirable in the present case. Examining the locally-projected density of states (DOS), we find that at the BTO/BZO interface there is essentially zero valence band offset, but a sizable conduction band offset. As shown in Supplementary Figure 3, the centroid of the d DOS of the Zr adjacent to the interface is about 2 eV higher than the d DOS of the Ti just opposite to it across the interface. (We consider the d DOS since the conduction band is mostly of d character of the octahedrally coordinated cation.) There is a tail of Zr DOS overlapping Ti's DOS, due to a single orbital presumably involved in bonding across the interface. Thus, it seems fair to extract the conduction offset by a linear extrapolation of the two DOS to zero following the slope on the low energy side of the main peaks. This gives an offset of about 2.0 to 2.2 eV. In Fig. 4c of the main paper this offset is not directly visible as it cancels out in the potential difference, but is indirectly visible in the confinement of the conduction charge inside Bi-5517 shown in Fig. 4a.
Depolarizing field vs density of mobile charge. Any reduction of the conduction charge (2 electrons per cell in Bi-5517) should cause an increase of the depolarizing field. This reduction may be produced by doping or field-effect injection; for example, Ca substitution of Bi at the 10% level (i.e. two Bi-5517 units become CaBi 9 Ti 10 O 34 ) will reduce the conduction charge in the unit cell to 1 electron. Since doping is difficult to simulate and may lead to unintended consequences (such as modifying the polarization, etc.), we study the effect of conduction charge removal for the same superlattice as before, simply subtracting by hand a certain amount of charge ΔQ. (The ions are kept clamped for simplicity; as mentioned in the paper, the polar distortion is unaffected by relaxation.) The charge is effectively removed from within Bi-5517, and neutrality is maintained by a uniform compensating background that spreads over the whole cell. The spurious potential thus induced is eliminated automatically by taking the difference of the potentials of non-CS and CS superlattices. We can thus compare the filtered averages of the potential for various values of ΔQ all the way up to 2 electrons, i.e. to zero conduction charge remaining, and extract the field in the superlattice as a function of removed charge.
In Supplementary Figures 4a-b we report the potential difference between non-CS and CS superlattices for various values of ΔQ, for both the filters mentioned in the previous Section, in the two top panels. The [d,2d] filter, in particular, highlights the local screening within each block of Bi-5517. In Supplementary Figure 4c we show the fields extracted from the total potential drop across the gray-shaded regions for both filters. Clearly, the values are quite similar in both cases. In the limiting case of 2 electrons removed, the field is limited by the gap to about 0.5 GV/m. The valence electron screening brings it down further to about 0.1 GV/m, for an effective valence dielectric constant of 5.
Ferroelectricity in a finite field. It is known 3 that the energy associated with the depolarizing field may destroy ferroelectricity in a finite system. We checked that is the case for a PbTiO 3 slab containing four Ti units. The unscreened bulk polarization charge (0.8 C/m 2 ) would generate a field of 90 GV/m and a corresponding energy of 100 eV in the simulation cell. With ions clamped in the ferroelectric configuration, the purely electronic response reduces the field to 5 GV/m, i.e. a 0.3 eV field energy. Since the ferroelectric well depth of PbTiO 3 is about 0.08 eV per Ti, this field energy is sufficient to remove ferroelectricity. Indeed relaxing the ions we recover the paraelectric geometry. This is not an issue for Bi-5517. The bare ΔP field is 37 GV/m (field energy 51 eV in the SL cell), but the screened field is 0.02 GV/m, and hence the field energy becomes negligible and the system is comfortably on the ferroelectric-stable side.