Abstract
Over 50 years ago, Anderson and Blount discussed symmetryallowed 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 firstprinciples simulations, that native metallicity and ferroelectricity coexist in the layered perovskite Bi_{5}Ti_{5}O_{17}. We show that, despite being a metal, Bi_{5}Ti_{5}O_{17} 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 selfscreening mechanism at work in thin Bi_{5}Ti_{5}O_{17} layers, emerging from the interplay between polar distortions and carriers in this compound.
Introduction
The possibility that metals may exhibit ferroelectricity is an intriguing open issue. Anderson and Blount^{1} showed that certain martensitic transitions involve inversion symmetry breaking and, formally, the existence of a polar axis. Metallic ferroelectric behaviour has thus been claimed for metals undergoing a centrosymmetric (CS) to nonCS structural transformation, such as^{2,3} Cd_{2}ReO_{7} and LiOsO_{3}, or being natively nonCS, such as^{4} (Sr,Ca)Ru_{2}O_{6}. The same label has been attached to ferroelectric insulators whose polar distortion survives moderate metallicity induced by doping or proximity^{5,6,7}. However, it seems fair to say that none of these systems, nor any other to our knowledge, embodies a truly ferroelectric metal with native switchable polarization and native metallicity coexisting in a single phase.
Here we report a theoretical prediction of such a material. By firstprinciples calculations, we show that the layered perovskite Bi_{5}Ti_{5}O_{17} has a nonzero density of states (DOSs) at the Fermi level and metallike conductivity, as well as a spontaneous polarization in zero field. Further, we predict that the polarization of Bi_{5}Ti_{5}O_{17} is switchable both in principle (the material complies with the sufficient symmetry requirements) and in practice (in spite of being a metal, Bi_{5}Ti_{5}O_{17} can sustain a sizable potential drop along the polar direction, as needed to revert its polarization by application of an electric bias). Beyond their conceptual importance, our results reveal striking behaviours—such as a selfscreening mechanism at work in thin Bi_{5}Ti_{5}O_{17} layers—emerging from the intimate interplay between polar distortions and free carriers. Our results thus challenge the common wisdom regarding the possibilities to control charges and fields at the nanoscale, with exciting potential implications in areas ranging from photovoltaics to electronics.
Results
NonCS metallic ground state in Bi_{5}Ti_{5}O_{17}
We focus on layered perovskite titanates A_{n}Ti_{n}O_{3n+2} (refs 8, 9), whose structure foreshadowing lowdimensional behaviour combines with their tunable conduction charge: assuming fixed ionic charges for A^{3+} and O^{2−}, Ti has nominal oxidation state of (3+4/n), that is, between 4+ for n=4 (for example, the band insulator, hightemperature ferroelectric La_{2}Ti_{2}O_{7}) and 3+ in the n→∞ limit (for example, the Mottinsulating Ti3d^{1} perovskite LaTiO_{3}). The metallic n>4 phases are not nearly as studied as the end compounds^{10,11,12}. Motivated by experimental reports of possible nonCS structures in the n=5 compound La_{5}Ti_{5}O_{17} (La5517 hereafter)^{13}, here we discuss this material as well as the alternative composition Bi_{5}Ti_{5}O_{17} (Bi5517).
The n=5 layered titanate can be viewed as a stack of slabs containing 5 [011]oriented perovskitelike planes and AO terminated. (See Fig. 1, as well as Supplementary Fig. 1 and Supplementary Note 1, for details. Directions are given in the pseudocubic setting of the perovskite structure.) The crystal axes are b=[011], which will be shown to coincide with the polar axis, and a=[100] and c=[0–11], which define the plane where the conduction charge is largely confined. Our simulation supercell comprises two fivelayer blocks along b and is compatible with all structures of interest here. To identify the ground state, we start from the highsymmetry structure (Immm space group, Fig. 1a) and condense all its unstable distortions as obtained from a Hessian analysis. (See the Methods for details of the firstprinciples simulations.) For La5517, the ground state is CS Pmnn (Fig. 1b), barring the existence of polarization. We also simulate the experimentally proposed structure of ref. 13, but find it to be a highenergy unstable configuration.
Inspired by the observation that perovskites where Bi^{3+} replaces La^{3+} tend to be ferroelectric due to Bi^{3+}’s tendency to form lowcoordination complexes with neighbouring oxygens^{14,15}, we explore symmetry breaking in Bi5517, obtained by replacing all La atoms with Bi’s. As in La5517, the Immm phase is a highenergy saddle point. However, at variance with La5517, the Pmnn structure is also a saddle point for Bi5517. We then condense the unstable distortions of this phase, and identify as lowestenergy solution a structure with the nonCS Pm2_{1}n space group (Fig. 1c). We computed the Hessian for this Pm2_{1}n structure and confirmed it to be a minimum of the energy. The symmetry breaking distortion in the Pm2_{1}n phase can be appreciated by looking at the Bi’s in the central layer (Bi_{c} in Fig. 1): although they remain at highsymmetry CS positions in both Immm and Pmnn, they move offcentre in Pm2_{1}n, thus breaking the (011) mirror plane and yielding a symmetrywise ferroelectric structure.
As regards the electronic structure, Bi5517’s Pm2_{1}n phase is clearly metallic, as can be seen in Fig. 2a–e from the atom and orbitalresolved DOS. We have two conduction electrons per primitive cell (that is, a density of 3 × 10^{21} cm^{−3}), with E_{F} crossing the Ti 3dt_{2g} band manifold ∼0.4 eV above the conduction band bottom (CBB). The nearCBB DOS highlights a marked twodimensional character, with 40% of the conduction charge confined within the central Ti layer of each block, 25% in each of the two intermediate layers and only 5% in each of the edge Ti’s. The t_{2g} CBB is split into d_{yz} (laying orthogonally to the stacking plane, rising in energy due to reduced hopping along the stacking direction) and d_{xy}/d_{xz} states (the hopping along x being unaffected by the stacking). d_{xy} and d_{xz} are also split: only d_{xy} has significant DOS below E_{F} in one of the fivelayer blocks, and only d_{xz} in the other, signalling orbital ordering. Figure 2f highlights the anisotropy of the conduction bands: the two occupied bands per block are doubled, there being two blocks in the supercell; yet, the splitting due to interblock coupling is negligible, confirming good confinement of the conduction electrons within each block. The inset of Fig. 2f shows that the bands are completely flat along the ΓY (stacking) direction, with no band crossing E_{F}. The system is thus gapped at Γ along this direction, although of course it may not be for a generic kpoint away from zone centre.
Figure 2g shows the Fermi surface (FS). The lowestenergy band S_{1} consists of two disconnected parallel sheets, and the higher S_{2} band contributes an elliptic tube. Along ΓY (b direction), the FS is very flat and resistivity is high, as shown in Fig. 2h. Along ΓX (a direction), the lightmass S_{2} contributes to mobility, while S_{1} is disconnected. Finally, along ΓZ (c direction), both sections contribute, but yield relatively high resistivity as the corresponding masses are much heavier than along ΓX. As a result, the predominant lowresistivity channel is largely onedimensional along a; nevertheless, the resistivity temperature dependence is that of a metal in all directions. The ordering of the resistivities is quite consistent with experiments^{9} for La5517, and the weak insulating upturn observed in La5517 can be reproduced by inserting small defectlike activation energies in the conductivity model (see Supplementary Fig. 2 and Supplementary Note 2 for details).
One might wonder whether the metallic Pm2_{1}n structure could experience additional symmetrybreaking distortions (for example, of the Peierls or JahnTeller type) that might open a gap within the conduction band and render an insulating solution. If they existed, such gapopening distortions would appear as (softmode) instabilities of the Pm2_{1}n phase, that is, they would have negative eigenvalues of the corresponding Hessian matrix associated to them. As mentioned above, we explicitly checked that no such soft mode exists, and that the Pm2_{1}n phase is a stable energy minimum. Hence, the metallic character of Bi5517’s nonCS ground state is robust.
Electric polarization and selfscreening in Bi_{5}Ti_{5}O_{17}
We now tackle the calculation of the ferroelectric polarization appearing in the Pm2_{1}n phase of Bi5517. Let us first note that the polarization—defined as the integrated current flowing along the stacking direction when we move from the CS phase (Immm) to the nonCS one (Pm2_{1}n)—can be split into contributions from ionic cores, valence electrons and conduction electrons. The first two dominate the effect and are trivial to compute by standard methods^{16,17}: we obtain P_{ion}=55.5 μC cm^{−2} and P_{val}=−14.6 μC cm^{−2}. In contrast, calculating P_{cond} is not standard. Nevertheless, we can take advantage of the localized character of conduction electrons within the Bi5517 blocks and implement two independent approaches to calculate P_{cond}. These approaches provide consistent results.
First, we compute P_{cond} from the dipole associated to conduction electrons within a fivelayer block in Bi5517. Figure 3 shows the planaraveraged conduction charge of the Pm2_{1}n phase, as well as that of a CS system with Pm2_{1}n cell parameters and Immm atomic positions. The Pm2_{1}n phase displays an evident inversion symmetry breaking; a dipole appears within each block and we obtain P_{cond}=−4.0 μC cm^{−2}. Note that, again, a significant twodimensional (2D) charge confinement is apparent in Fig. 3, and this strategy to compute P_{cond} would be exact if the conduction charge were strictly confined within the blocks.
Alternatively, we can compute P_{cond} using a modified version of the Berry phase formalism. As the occupied conduction bands are rather flat along the ΓY direction of the Brillouin zone (the reciprocalspace signature of confinement), we can generalize the usual formulation to allow for changing numbers of contributing bands at different kpoint strings (see the Methods for details). We eventually obtain P_{cond}=−7.5 μC cm^{−2}, which we deem in reasonable agreement with our estimate above.
Figure 3 also reveals a fascinating effect, namely, how the mobile carriers rearrange within each of the fivelayer blocks to screen the field created by the local dipoles resulting from the CSbreaking displacements of the central Bi cations (see the respective enhancement and decrease in electron density on the right and left sides of the Bi_{c} planes). Remarkably, the ferroelectric instability persists in spite of this selfscreening mechanism, contradicting the general notion that an abundance of mobile carriers should prevent any such polar distortion. This result highlights the difference between our material (whose ferroelectric phase has a local, chemical origin associated to the Bi–O bonding) and compounds such as BaTiO_{3} (where the ferroelectric instability relies on the action of dipole–dipole interactions^{18} that are strongly weakened by screening charges^{5}). Note that the difference in behaviour between chemically driven and dipole–dipoledriven ferroelectrics is well illustrated by the predicted response of prototypical compounds such as BiFeO_{3} (similar to Bi5517 in that BiO bonding dominates the ferroelectric distortion^{15,19,20}) and BaTiO_{3} to electron doping and the accompanying metallization: the doping is not detrimental to the polar distortion in the former^{21}, but annihilates it in the latter^{5}.
Hence, our calculations indicate that the Pm2_{1}n phase of Bi5517 has a spontaneous polarization of ∼35 μC cm^{−2}, which is in the same league as the most common ferroelectric perovskites (for example, 30 μC cm^{−2} for BaTiO_{3}). Ferroelectricity largely originates from Bi^{3+} cations moving offcentre in the perovskite framework. This displacement is invertible with respect to the (011) plane, so that switching between two equivalent polar states is possible symmetrywise. The computed ferroelectric well depth of 0.31 meV Å^{−3} suggests a critical temperature upward of 500 K.
Discussion
So far, we have shown that metallicity coexist with zerofield polarization in Bi5517. Is it possible to switch the polarization of this ferroelectric metal? Can a finite Bi5517 sample sustain a finite field, as would be required to switch its polarization? For Bi5517 in the usual capacitor configuration with metallic electrodes, one may expect the bias to induce a current rather than to act on the polar distortion. For Bi5517 cladded within insulating layers, current flow is precluded by construction (neglecting tunneling), but mobile carriers should screen an applied bias, and leave the CSbreaking distortion unaffected. It turns out that Bi5517 is quite at odds with this reasonable expectation. We show this by studying a superlattice (SL) of alternating Bi5517 (one primitive cell, ∼31 Å thick) and Bi_{2}Zr_{2}O_{7} (BZO227, n=4 of the same family; layer ∼26 Å thick) layers. BZO227 acts as a cladding insulator providing seamless stoichiometric continuity on the Acation site as well as effective confinement of the conduction electrons within Bi5517 (see Supplementary Fig. 3 and Supplementary Discussion for details). We compare a SL where Bi5517 is nonCS (starting from the Pm2_{1}n bulk phase) with a reference SL that is a suitable symmetrization of the nonCS one (which yields a Pmnnlike structure for the Bi5517 layer).
Figure 4 shows planar and filter averages^{7} (see the Methods) of the potentials and conduction densities of the two SLs, and their differences. The key result is the sizable depolarizing field E_{dep}∼20 MV m^{−1}=0.02 GV m^{−1}, which we estimate from the potential slope in the central region of Bi5517 (see Fig. 4, bottom, for details). Thus, the mobile charge dominates the screening process, but is unable to screen out entirely the polarizationinduced field. (This residual depolarizing field increases further if the number of mobile electrons is reduced by hole injection; see Supplementary Fig. 4 and Supplementary Discussion for details.) The difference between the nonCS and CS conduction densities (Fig. 4, top and centre panel) clearly shows, first, the local selfscreening within each fivelayer block already observed in the bulk case; and second, a net charge imbalance—with negative and positive carriers accumulating, respectively, at the right (Bi5517/BZO227) and left (BZO227/Bi5517) interfaces—that acts against the polarizationgenerated field. Although the overall selfscreening response is incomplete, it is still amply sufficient to stabilize the monodomain polar state even under such unfavourable electrical boundary conditions. (Owing to the ∇D=ρ_{free}=0 condition across the interface, the monodomain configuration of thin ferroelectric layers in a ferroelectric–dielectric SL is generally unstable; see Supplementary Discussion for details.) Indeed, explicitly relaxing the nonCS SL, we find that the Bi5517 layer is almost identical to the polar bulk phase, which confirms the stability of the monodomain configuration.
The switching of polarization, and more generally the response to an applied field, in Bi5517 is a nontrivial problem. However, our finite Bi5517 cladded layer is in an opencircuit configuration where, because of the insulating BZO227 layers, no current flows; in this case, a plausible argument can be made for the switching. Consider the situation shown in Fig. 4, where the polarization (mostly due to ions) points towards the right side of the layer. The layer screens the polarizationinduced field incompletely, so that there is a residual depolarizing field that points from right to left and acts against the polarization. The incomplete screening in itself implies that the layer is effectively a dielectric medium with finite lowfrequency, lowwavevector dielectric function. Hence, it is natural to conclude that, upon application of a field exceeding the finite screening ability of the Bi5517 layer, the polarization will switch. Pictorially, an external field pointing towards the left will push cations (oxygens) to the left (right), whereas valence electrons and mobile conduction electrons go to the right. Yet, the latter response is necessarily limited by the Bi5517 layer’s modest stock of mobile charges and the finiteness of the system, and hence the screening will be incomplete. Note that, in contrast, ferroelectric switching seems less likely in a bulk Bi5517 sample; in that case, the reservoir of mobile carriers is essentially unlimited, and the details of the dynamical response of electrons and lattice to the external bias will probably become critical to decide whether switching can be achieved or not.
As just shown, even a unit cell of singledomain Bi5517 is polarized and sustains a polarizationgenerated field. Bi5517 thus contradicts the natural assumption that, in the nanometricfilm limit^{6}, polarization can never survive its own depolarization field. Indeed, Bi5517 stands apart from any other known ferroelectric material because of the coexistence of a localized and strong polar instability (driven by the formation of Bi–O bonds) and a selfscreening mechanism that does not prevent the chemically driven polar distortion but does partly cancel the corresponding depolarizing field. In this context, Bi5517 is akin to socalled hyperferroelectrics^{22}, whereby soft LO phonons are associated to a large highfrequency dielectric constant and small Born dynamical charges (a feature generally barred by the large gaps and Born charges characteristic of prototypical ferroelectric perovskites). In this sense, Bi5517 behaves as a limiting case of hyperferroelectric, and might thus be considered an instance of selfscreened hyperferroelectric metal.
In conclusion, we have designed a Bibased layeredperovskite titanate that presents native metallicity—in the form of a conductive lowdimensional electron gas—and, simultaneously, complies with the requirements of a regular switchable ferroelectric. Besides its conceptual significance, and the fundamental interest of further characterizing the behaviour of Bi5517 and related materials, our finding opens interesting perspectives for innovative applications. Intriguing possibilities range from the fields of photovoltaics (as a metal, Bi5517 can be expected to be a good absorber that, simultaneously, features a builtin driving force to separate electrons and holes) to electronics (Bi5517 may be expected to behave as a heavily ndoped semiconductor strongly responsive to applied fields) or spintronics (there are obvious strategies to construct a spinpolarized, multiferroic version of our ferroelectric metal). We thus hope our work will motivate further investigations of this compound and related ones based on similar strategies to achieve the coexistence of ferroelectricity and metallicity.
Methods
Simulation details
Our calculations are performed at the firstprinciples level within the local density approximation^{23,24} to densityfunctional theory and the projectoraugmented wave scheme^{25} to treat the interaction between ionic cores and valence electrons, as implemented in the firstprinciples package VASP^{26,27,28,29}. The following electrons are explicitly considered in the simulations: Ti's 3s, 3p, 3d and 4s; La’s 5s, 5p, 5d and 6s; Bi's 5d, 6s and 6p; O's 2s and 2p. The electronic wave functions are represented in planewave basis truncated at 500 eV. For all selfconsistency and force calculations, Brillouin zone integrals are computed on the kpoint 6 × 1 × 5 grid, reflecting the elongated shape of the cells (a≈3.9 Å, b≈31.0–55 Å and c≈5.4 Å; details are given in Supplementary Table 1.)
For the analysis of the electronic structure, we also use the variational pseudoselfinteractioncorrected densityfunctional approach^{30,31}, which uses ultrasoft pseudopotentials^{32} with planewave cutoff of 476 eV. DOS calculations use 12 × 4 × 8 grids for Brillouin zone integration.
For transport, we use two approaches: first, the Bloch–Boltzmann transport theory^{33} as implemented in the BoltzTraP code^{34}, interpolating the band structure over a 30 × 14 × 22 ab initio calculated kpoint values; second, an effectivemass band model that allows an easy inclusion of localized states below the mobility edge. In both cases, the relaxation time needed by Bloch–Boltzmann is calculated by analytic modelling, including the most important scattering contributions (that is, electronphonon and impurity scattering). The model was previously applied to describe several lowdimensional systems involving titanates, with satisfactory results^{35,36,37,38}.
Polarization of metals with confined conduction charges
To compute the electronic polarization contribution from the conduction electrons, we use a modified Berry phase^{16,17,39} approach. In its standard version, this approach shows that polarization in crystals is the integrated current flowing through the system as atoms displace from the CS (λ=0) to the nonCS phase (λ=1):
where k_{⊥}spans the Brillouin zone section, of area A_{k}, orthogonal to the polarization direction, and ϕ is the Berry phase of the Bloch wavefunctions:
with
where the 's are periodic parts of the Bloch wavefunctions, v the number of bands, n=[1, v] and m=[1, v] band indexes, and k_{j} runs over a string of N discrete points from Γ to G_{}, that is the shortest Gvector in the direction parallel to the polarization.
In general, the above expressions cannot be applied to a metal, as the Berry phase is well defined (that is, gaugedependent by unitary rotation) as long as the bands that contribute to the matrix in the above equation are an isolated subgroup (typically the whole valence band manifold of an insulator). Clearly, for a metal, this condition does not hold, as v depends on k, that is, the number of occupied bands change with k. However, if the system has flat bands along a specific direction (this applies to Bi5517 since electrons are quite localized within each 5unit block along the b axis), then the number of occupied bands only changes with k_{⊥}, but not along the string, that is, no band crosses the Fermi level along the kspace string parallel to the insulating direction. It follows that is well defined for any k_{⊥}, while v can change with k_{⊥} with the constraint
on the total electron charge Q. In practice may fluctuate widely with k_{⊥} due to the change in the number of bands contributing to the string, and in turn the 2D average in the above equation may be slowly convergent. The considerable computing effort required to calculate the Berry phase in largesize systems (such as Bi5517) suggests adopting a strategy to minimize the contribution of the variablebandnumber part. In the specific case of Bi5517, the latter contribution is limited to a few conduction bands, well separated by a large band gap from the valence bands. We therefore first calculate separately the polarization due to valence bands, which typically converges rapidly over a limited set of k_{⊥} points. For the conduction bands, the polarization is then calculated as the 2D average of the renormalized phase
where Q_{cond} is the conduction charge and v_{cond} the number of occupied conduction bands at k_{⊥}. With this choice, each kstring contribution is renormalized to the same number of electrons, and fluctuates much less with k_{⊥}, reducing the effort needed to converge the calculation. Further, in this approximation, even partial band occupancies—as it would correspond to k_{⊥} points at the FS—can be handled by allowing fractional values.
Filters
To analyse the potential and charge density in the SLs, we apply wellknown averaging processes, described, for example, in refs 7, 40. The filter average features prominently in Fig. 4 of the paper, and is defined as
with n a function (for example, the charge density). It is a onedimensional squarewave filter of the planar average (implicitly defined by the second equality, and calculated over a sectional area A) over a window of fixed width L, which is its defining parameter. If L is the microscopic periodicity length (assuming such periodicity exists), all microscopic oscillations in the planar average are eliminated. This basically amounts to filtering away all the Fourier components corresponding to microscopic oscillations.
However, the typical potential or charge density in our system has a rather wide spectrum in wavevector space, and filtering all components would entail a complete loss of information. So, in practice, we choose filters such that microscopic oscillations are reduced significantly after a couple of passes at most. We find that applying the filter twice, with L=d and 2d, or with L=3d and 2d, gives the best results in terms of oscillation removal, d being the average interplanar distance.
Additional information
How to cite this article: Filippetti, A. et al. Prediction of a native ferroelectric metal. Nat. Commun. 7:11211 doi: 10.1038/ncomms11211 (2016).
References
 1
Anderson, P. W. & Blount, E. I. Symmetry considerations on Martensitic Transformations: “Ferroelectric” Metals? Phys. Rev. Lett. 14, 217–219 (1965).
 2
Sergienko, I. A. et al. Metallic “Ferroelectricity” in the pyrochlore Cd2Re2O7 . Phys. Rev. Lett. 92, 065501 (2004).
 3
Shi, Y. et al. A Ferroelectriclike structural transition in a metal. Nat. Mater. 12, 1024–1027 (2013).
 4
Puggioni, D. & Rondinelli, J. M. Designing a robustly metallic noncentrosymmetric ruthenate oxide with large thermopower anisotropy. Nat. Commun 5, 3432 (2014).
 5
Wang, Y. et al. Ferroelectric instability under screened coulomb interactions. Phys. Rev. Lett. 109, 247601 (2012).
 6
Junquera, J. & Ghosez, P. h. Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422, 506–509 (2003).
 7
Ricci, F., Filippetti, A. & Fiorentini, F. Giant electroresistance and tunable magnetoelectricity in a multiferroic junction. Phys. Rev. B 88, 235416 (2013).
 8
Lichtenberg, F., Herrnberger, A., Wiedenmann, K. & Mannhart, J. Synthesis of perovskiterelated layered AnBnO3n+2=ABOx type niobates and titanates and study of their structural, electric and magnetic properties. Prog. Sol. St. Chem. 29, 1–70 (2001).
 9
Lichtenberg, F., Herrnberger, A. & Wiedenmann, K. Synthesis, structural, magnetic and transport properties of layered perovskiterelated titanates, niobates and tantalates of the type AnBnO3n+2, A’Ak1BkO3k+1 and AmBm1O3m . Prog. Sol. St. Chem. 36, 253–387 (2008).
 10
LópezPérez, J. & Íñiguez, J. Ab initio study of proper topological ferroelectricity in layered perovskite La2Ti2O7 . Phys. Rev. B 84, 075121 (2011).
 11
Scarrozza, M., Filippetti, A. & Fiorentini, V. Ferromagnetism and orbital order in a topological ferroelectric. Phys. Rev. Lett. 109, 217202 (2012).
 12
Scarrozza, M., Filippetti, A. & Fiorentini, V. Multiferroiticity in vanadiumdoped La2Ti2O7: insights from first principles. Eur. Phys. J. B 86, 128 (2013).
 13
Williams, T. et al. On the crystal structures of La2Ti2O7 and La5Ti5O17: high resolution electron microscopy. J. Sol. St. Chem. 93, 534–548 (1991).
 14
Guennou, M., Viret, M. & Kreisel, J. Bismuth based perovskites as multiferroics. Comptes Rendus Physique 16, 182–192 (2015).
 15
Diéguez, O., GonzálezVázquez, O. E., Wojdeł, J. C. & Íñiguez, J. Firstprinciples predictions of lowenergy phases of multiferroic BiFeO3 . Phys. Rev. B 83, 094105 (2011).
 16
KingSmith, R. D. & Vanderbilt, D. Theory of polarization of crystalline solids. Phys. Rev. B 47, 1651–1654 (1993).
 17
Resta, R. Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Rev. Mod. Phys. 66, 899–915 (1994).
 18
Ghosez, P., Gonze, X. & Michenaud, J.P. Coulomb interaction and ferroelectric instability of BaTiO3 . Europhys. Lett. 33, 713–718 (1996).
 19
Ravindran, P. et al. Theoretical investigation of magnetoelectric behavior in BiFeO3 . Phys. Rev. B 74, 224412 (2006).
 20
Seshadri, R. & Hill, N. A. Visualizing the role of Bi 6s “lone pairs” in the offcenter distortion in ferromagnetic BiMnO3 . Chem. Mater. 13, 2892–2899 (2001).
 21
He, X. et al. Evolution of the electronic and lattice structure with carrier injection in BiFeO3, Preprint at http://arxiv.org/abs/1511.07128 (2015).
 22
Garrity, K. F., Rabe, K. M. & Vanderbilt, D. Hyperferroelectrics: proper ferroelectrics with persistent polarization. Phys. Rev. Lett. 112, 127601 (2014).
 23
Ceperley, D. & Alder, B. J. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569 (1980).
 24
Perdew, J. P. & Zunger, A. Selfinteraction correction to densityfunctional approximations for manyelectron systems. Phys. Rev. B 23, 5048–5079 (1981).
 25
Blöchl, P. E. Projector augmentedwave method. Phys. Rev. B 50, 17953–17979 (1994).
 26
Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).
 27
Kresse, G. & Furthmüller, J. Efficiency of abinitio total energy calculations for metals and semiconductors using a planewave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
 28
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186 (1996).
 29
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
 30
Filippetti, A. et al. Variational pseudoself interactioncorrected density functional approach to the ab initio description of correlated solids and molecules. Phys. Rev. B 84, 195127 (2011).
 31
Filippetti, A. & Fiorentini, V. A practical firstprinciples bandtheory approach to the study of correlated materials. Eur. Phys. J. B 71, 139–183 (2009).
 32
Vanderbilt, D. Soft selfconsistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895 (1990).
 33
Allen, P. B. in Quantum Theory of Real Materials (eds Chelikowsky J. R., Louie S. G. 219–250Kluwer (1996).
 34
Madsen, G. & Singh, D. BoltzTraP. A code for calculating bandstructure dependent quantities. Comput. Phys. Comm 175, 67–71 (2006).
 35
Filippetti, A. et al. Thermopower in oxide heterostructures: The im portance of being multipleband conductors. Phys. Rev. B 86, 195301 (2012).
 36
Delugas, P. et al. Dopinginduced dimensional crossover and thermopower burst in Nbdoped SrTiO3 superlattices. Phys. Rev. B 88, 045310 (2013).
 37
Delugas, P. et al. Large band offset as driving force of twodimensional electron confinement: The case of SrTiO3/SrZrO3 interface. Phys. Rev. B 88, 115304 (2013).
 38
Pallecchi, I. et al. Giant oscillating thermopower at oxide interfaces. Nat. Commun 6, 6678 (2015).
 39
Vanderbilt, D. & KingSmith, R. D. Electric polarization as a bulk quantity and its relation to surface charge. Phys. Rev. B 48, 4442–4455 (1993).
 40
Peressi, M., Binggeli, N. & Baldereschi, A. Band engineering at interfaces: theory and numerical experiments. J. Phys. D Appl. Phys. 31, 1273–1299 (1998).
Acknowledgements
Work supported in part by MIURPRIN 2010 project Oxide (A.F., V.F., P.D., F.R.), Fondazione Banco di Sardegna (A.F., V.F., P.D.), FNR Luxembourg Grant No. FNR/P12/4853155/Kreisel (J.I.), MINECOSpain Grant No. MAT201340581P (J.I.), CINECAISCRA grants (A.F., V.F., F.R., P.D.), CAR of UniCagliari (V.F.). J.I. ran calculations at the CESGA supercomputing center. A.F., V.F., P.D. and F.R. ran calculations at CINECA.
Author information
Affiliations
Contributions
A.F. and P.D. led the work to characterize the electric, electronic and transport properties of Bi_{5}Ti_{5}O_{17}. V.F. and F.R. led the work to characterize the behaviour of finite layers and slabs, and the effects of doping. J.Í. led the work to identify Bi_{5}Ti_{5}O_{17} as a candidate ferroelectric metal.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Figures 14, Supplementary Table 1, Supplementary Notes 12, Supplementary Discussion and Supplementary References (PDF 684 kb)
Rights and permissions
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Filippetti, A., Fiorentini, V., Ricci, F. et al. Prediction of a native ferroelectric metal. Nat Commun 7, 11211 (2016). https://doi.org/10.1038/ncomms11211
Received:
Accepted:
Published:
Further reading

Large family of twodimensional ferroelectric metals discovered via machine learning
Science Bulletin (2020)

Flexoinduced ferroelectricity in lowdimensional transition metal dichalcogenides
Physical Review B (2020)

Conductivity, charge transport, and ferroelectricity of Ladoped BaTiO3 epitaxial thin films
Journal of Physics D: Applied Physics (2020)

Review on ferroelectric/polar metals
Japanese Journal of Applied Physics (2020)

Recent Progress in Two‐Dimensional Ferroelectric Materials
Advanced Electronic Materials (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.