Anisotropic resistivity and superconducting instability in ferroelectric metals

Abstract

We propose a theoretical model of a ferroelectric metal where spontaneous electric polarization coexists with the conducting electrons. In our model we adopt a scenario when conducting electrons interact with two soft transverse optical phonons, generalize it to the case when there is a spontaneous ferroelectric polarization in the system, and show that a linear coupling to the phonons emerges as a result. We find that this coupling results in anisotropic electric transport which has a transverse to the current voltage drop. Importantly, the obtained transverse component of the resistivity has distinct linear dependence with temperature. Moreover, we show that the coupling enhances superconducting transition temperature of the ferroelectric metal. We argue that our results help to explain recent experiments on ferroelectric strontium titanate as well as provide new experimental signatures to look for.

Generalized Rashba Electron-Phonon Coupling and Superconductivity in Strontium Titanate

“…(b) Absolute value of the estimated electron-FE-mode Rashba couplings [Eq. (35)] for band n for three possible eigenvectors of the FE mode: a pure S1 mode, eigenvector from neutron data [Eq. (37)] and from Raman data [Eq.…”

“…where l = A, B, C. Equation (35) shows that the klinear Rashba coupling τ (α) n,l of mode α is a weighted sum of the Rashba couplings τ ( Si) n,l [shown in Fig. 4(a)] with the coefficients ϕ αi weighing the contribution of the Si modes to the normal mode α.…”

“…Eqs. ( 31)- (35) allow to compute the coupling to polar modes with arbitrary eigenvectors so they can be used to determine, for example, the coupling to the soft polar mode from better refined eigenvectors in future studies. In other words, we have separated the problem of determining the coupling to the soft mode from the problem of determining its eigenvector.…”

“…Proposed pairing theories include the dynamical screening of the Coulomb interaction due to longitudinal modes [16][17][18][19] recently challenged in Ref. [20], bipolaron formation [21], and diverse approaches to linear coupling [1,[22][23][24][25][26][27][28][29][30] or quadratic coupling to the FE mode [31][32][33][34][35]. The last two proposals have the advantage that, coupling electrons directly to the FE soft mode, provide a natural explanation to the sensitivity to the FE instability.…”

“…In the more general context of polar or nearly polar metals, the coupling between electrons and the soft FE modes has received attention only very recently [24,25,28,30,[35][36][37][38]. The reason probably being that, as already mentioned, the FE soft modes in these systems have a predominantly transverse polarization.…”