Discovery of robust yet reversibly switchable electric dipoles at reduced dimensions is critical in advancing nanoelectronics devices. Energy bands flat in momentum space generate robust localized states that are activated independently of each other. We determined flat bands exist and induce robust yet independently switchable dipoles exhibiting a unique ferroelectricity in HfO2. Flat polar phonon bands in HfO2 cause extreme localization of electric dipoles within its irreducible half-unit-cell-widths (~3 Å). Contrary to conventional ferroelectrics with spread dipoles, those intrinsically localized dipoles are stable against extrinsic effects such as domain walls, surface exposure, and even down-to-angstrom-scale miniaturization. Moreover, the sub-nm-scale dipoles are individually switchable without creating any domain-wall energy cost. This offers unexpected opportunities for ultimately-dense unit-cell-by-unit-cell ferroelectric switching devices directly integrable into silicon technology.

Emergent phenomena, including superconductivity and magnetism, found in the two-dimensional electron liquid (2-DEL) at the interface between the insulators lanthanum aluminate (LaAlO 3 ) and strontium titanate (SrTiO 3 ) distinguish this rich system from conventional 2D electron gases at compound semiconductor interfaces. The origin of this 2-DEL, however, is highly debated, with focus on the role of defects in the SrTiO 3 , while the LaAlO 3 has been assumed perfect. Here we demonstrate, through experiments and firstprinciple calculations, that the cation stoichiometry of the nominal LaAlO 3 layer is key to 2-DEL formation: only Al-rich LaAlO 3 results in a 2-DEL. Although extrinsic defects, including oxygen deficiency, are known to render LaAlO 3 /SrTiO 3 samples conducting, our results show that in the absence of such extrinsic defects an interface 2-DEL can form. Its origin is consistent with an intrinsic electronic reconstruction occurring to counteract a polarization catastrophe. This work provides insight for identifying other interfaces where emergent behaviours await discovery.

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We present the structural and magnetic properties of a new compound family, Mg2RE3Sb3O14 (RE = Gd, Dy, Er), with a hitherto unstudied frustrating lattice, the "tripod kagome" structure. Susceptibility (ac, dc) and specific heat exhibit features that are understood within a simple Luttinger-Tisza type theory. For RE = Gd, we found long ranged order (LRO) at 1.65 K, which is consistent with a 120• structure, demonstrating the importance of diople interactions for this 2D Heisenberg system. For RE = Dy, LRO at 0.37 K is related to the "kagome spin ice (KSI)" physics for a 2D system. This result shows that the tripod kagome structure accelerates the transition to LRO predicted for the related pyrochlore systems. For RE = Er, two transitions, at 80 mK and 2.1 K are observed, suggesting the importance of quantum fluctuations for this putative XY system. Introduction.-The two-dimensional (2D) kagome lattice magnet (KLM) has been a favorite in the theoretical condensed matter community since the experimental work on SCGO [1], due to the strong frustration associated with its network of corner-shared triangles. [15]. From a materials standpoint, however, these two systems are limited by (i) known defect prone structures [14,16], and (ii) the inability to substitute facilely on the magnetic site (e.g with non-Heisenberg spins) to realize states other than the QSL. Clearly then, finding new KLM-containing compounds with spin-type variability is a challenge of the highest order.Intriguingly, a 2D KLM is naturally contained in the frustrated 3D pyrochlore structure. In pyrochlores RE 2 X 2 O 7 (RE = rare earth element, X = transition metal element), both the RE 3+ and X 4+ sublattices form alternating kagome and triangular layers along the [111] axis as a result of corner-shared tetrahedrons ( Fig. 1(a)) [17]. However, the strong inter-layer interaction enforces three-dimensionality. An exception is found in studies of Dy 2 Ti 2 O 7 in a [111] magnetic field, which polarizes the triangular layer spins, effectively decoupling the kagome planes, leading to a KSI state [17].Obviously, if one can remove the magnetic moment of the triangular layers in the pyrochlore lattice, a RE-kagome-

We present a systematic study of the structural and magnetic properties of two branches of the rare earth Tripod Kagome Lattice (TKL) family A2RE3Sb3O14 (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb; here, we use abbreviation A-RE, as in MgPr for Mg2Pr3Sb3O14), which complements our previously reported work on MgDy, MgGd, and MgEr 15 . The present susceptibility (χ dc , χac) and specific heat measurements reveal various magnetic ground states, including the non-magnetic singlet state for MgPr, ZnPr; long range orderings (LROs) for MgGd, ZnGd, MgNd, ZnNd, and MgYb; a long range magnetic charge ordered state for MgDy, ZnDy, and potentially for MgHo; possible spin glass states for ZnEr, ZnHo; the absence of spin ordering down to 80 mK for MgEr, MgTb, ZnTb, and ZnYb compounds. The ground states observed here bear both similarities as well as striking differences from the states found in the parent pyrochlore systems. In particular, while the TKLs display a greater tendency towards LRO, the lack of LRO in MgHo, MgTb and ZnTb can be viewed from the standpoint of a balance among spin-spin interactions, anisotropies and non-Kramers nature of single ion state. While substituting Zn for Mg changes the chemical pressure, and subtly modifies the interaction energies for compounds with larger RE ions, this substitution introduces structural disorder and modifies the ground states for compounds with smaller RE ions (Ho, Er, Yb).

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