The lattice dynamics of potassium dihydrogen phosphate (KDP) and its deuterated analog DKDP was studied via first-principles DFT calculations. A thorough assessment of the quality of a wide range of functionals supplemented with the approximate inclusion of quantum nuclear effects indicated that the non-local van der Waals functional vdW-DF [M. Dion et al, Phys. Rev. Lett. 92, 246401 (2004); J. Klimeš et al, Phys. Rev. B 83, 195131 (2011)] produces the best agreement with structural data for both compounds. This enabled the calculation of full phonon dispersions in the ferroelectric phase, and hence the phonon density of states and specific heat, in excellent agreement with experimental data. Phonon bands and especially modes at the Γ-point of the Brillouin zone were classified according to their vibrational pattern. This allowed for the assignment of stretching and bending modes of the hydrogen bonds. Internal modes involving the phosphate units were identified at lower frequencies, while the lowest-lying modes were those involving the K + ion. These assignments were used to interpret infrared and Raman spectra along the c-axis, and in the perpendicular plane. Phonon modes calculated at the Γ-point showed two types of instabilities. One was a normal mode polarized along the c-axis of the crystal, while the other corresponded to a twofold degenerate mode polarized in the perpendicular plane. The former gives rise to a spontaneous polarization in the ferroelectric phase at low temperatures by coupling to an optical K +-PO − 4 stretching mode, consistently with a significant off-diagonal Born effective charge on the hydrogen atoms. A mode describing the opposite rotation of neighboring PO4 tetrahedra was also found to couple strongly to the ferroelectric mode, as this modulates the O-O distance, which determines the barrier for proton transfer. The present study suggests that a minimal model to describe isotope effects in KDP should involve at least three fully-coupled vibrational modes.
Spin-hosting graphene nanostructures are promising metal-free systems for elementary quantum spintronic devices. Conventionally, spins are protected from quenching by electronic band gaps, which also hinder electronic access to their quantum state. Here, we present a narrow graphene nanoribbon substitutionally doped with boron heteroatoms that combines a metallic character with the presence of localized spin 1/2 states in its interior. The ribbon was fabricated by onsurface synthesis on a Au(111) substrate. Transport measurements through ribbons suspended between the tip and the sample of a scanning tunneling microscope revealed their ballistic behavior, characteristic of metallic nanowires. Conductance spectra show fingerprints of localized spin states in the form of Kondo resonances and inelastic tunneling excitations. Density functional theory rationalizes the metallic character of the graphene nanoribbon due to the partial depopulation of the valence band induced by the boron atoms. The transferred charge builds localized magnetic moments around the boron atoms. The orthogonal symmetry of the spin-hosting state's and the valence band's wave functions protects them from mixing, maintaining the spin states localized. The combination of ballistic transport and spin localization into a single graphene nanoribbon offers the perspective of electronically addressing and controlling carbon spins in real device architectures.
Chiral graphene nanoribbons are extremely interesting structures due to their narrow band gaps and potential development of spin-polarized edge states. Here, we study their band structure on low work function silver surfaces. The use of a curved Ag single crystal provides, within the same sample, regions of disparate step structure and step density. Whereas the former leads to distinct azimuthal growth orientations of the graphene nanoribbons atop, the latter modulates the substrate’s work function and thereby the interface energy level alignment. In turn, we disclose the associated charge transfer from the substrate to the ribbon and assess its effect on the nanoribbon’s properties and the edge state magnetization.
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