Valence Skipping Research Articles

Valence-skipping and quasi-two-dimensionality of superconductivity in a van der Waals insulator

Valence fluctuation of interacting electrons plays a crucial role in emergent quantum phenomena in correlated electron systems. The theoretical rationale is that this effect can drive a band insulator into a superconductor through charge redistribution around the Fermi level. However, the root cause of such a fluctuating leap in the ionic valency remains elusive. Here, we demonstrate a valence-skipping-driven insulator-to-superconductor transition and realize quasi-two-dimensional superconductivity in a van der Waals insulator GeP under pressure. This is shown to result from valence skipping of the Ge cation, altering its average valency from 3+ to 4+, turning GeP from a layered compound to a three-dimensional covalent system with superconducting critical temperature reaching its maximum of 10 K. Such a valence-skipping-induced superconductivity with a quasi-two-dimensional nature in thin samples, showing a Berezinskii-Kosterlitz-Thouless-like character, is further confirmed by angle-dependent upper-critical-field measurements. These findings provide a model system to examine competing order parameters in valence-skipping systems.

Valence skipping, internal doping, and site-selective Mott transition in PbCoO3 under pressure

We present a computational study of PbCoO$_3$ at ambient and elevated pressure. We employ the static and dynamic treatment of local correlation in form of density functional theory + $U$ (DFT+$U$) and + dynamical mean-field theory (DFT+DMFT). Our results capture the experimentally observed crystal structures and identify the unsaturated Pb $6s$ - O $2p$ bonds as the driving force beyond the complex physics of PbCoO$_3$. We provide a geometrical analysis of the structural distortions and we discuss their implications, in particular, the internal doping, which triggers transition between phases with and without local moments and a site selective Mott transition in the low-pressure phase.

Extending the Gutzwiller approximation to intersite interactions

We develop an extension of the Gutzwiller approximation (GA) formalism that includes the effects of Coulomb interactions of arbitrary range (including density density, exchange, pair hopping, and Coulomb-assisted hopping terms). This formalism reduces to the ordinary GA formalism for the multiband Hubbard models in the presence of only local interactions. This is accomplished by combining the $1/z$ expansion---where $z$ is the coordination number, and only the leading-order terms contribute in the limit of infinite dimensions---with a ${P}_{R}^{\ifmmode\dagger\else\textdagger\fi{}}{P}_{R}\ensuremath{-}I$ expansion, where ${P}_{R}$ is the Gutzwiller projector on the site $R$. The method is conveniently formulated in terms of a Gutzwiller Lagrange function. We apply our theory to the extended single-band Hubbard model. Similarly to the usual Brinkman-Rice mechanism, we find a Mott transition. A valence skipping transition is observed, where the occupation of the empty and doubly occupied states for the Gutzwiller wave function is enhanced with respect to the uncorrelated Slater determinant wave function.

Unusual electronic state of Sn in AgSnSe2

${\mathrm{AgSnSe}}_{2}$, by formal electron count, should have Sn in a highly unusual $3+$ valence state and was therefore suggested to be a valence-skipping compound with potential for negative-$U$ centers and local electron pairing. It has been proposed that the latter may be the mechanism beyond seemingly conventional superconductivity in this compound. We report NMR measurements and first-principles calculations that agree with each other perfectly, and both indicate that valence skipping does not take place and the highly unusual ${\mathrm{Sn}}^{3+}$ state is realized instead, likely because of geometrical constraint prohibiting a breathing distortion that could screen the on-site Coulomb repulsion.

Colossal Negative Thermal Expansion Induced by Valence Skipping Elements―Stagehand into Main Player―

Colossal Negative Thermal Expansion Induced by Valence Skipping Elements―Stagehand into Main Player―

Phase transitions in the Hubbard model for the bismuth nickelate

We study low temperature properties of the Hubbard model for the bismuth nickelate, where degenerate orbitals in the nickel ions and a single orbital in the bismuth ions are taken into account, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We discuss the effect of the attractive interactions to mimic the valence skipping phenomenon in the bismuth ions. We demonstrate how the charge and magnetically ordered states are stable against thermal fluctuations. It is furthermore clarified that the ferromagnetically ordered and orbital ordered states are stabilized due to the presence of the orbital degeneracy at low temperatures. The crossover between metallic and insulating states is also discussed.

Theory of Valence Transition in BiNiO_{3}.

Motivated by the colossal negative thermal expansion recently found in BiNiO_{3}, the valence transition accompanied by the charge transfer between the Bi and Ni sites is theoretically studied. We introduce an effective model for Bi-6s and Ni-3d orbitals taking into account the valence skipping of Bi cations, and investigate the ground-state and finite-temperature phase diagrams within the mean-field approximation. We find that the valence transition is caused by commensurate locking of the electron filling in each orbital associated with charge and magnetic orderings, and the critical temperature and the nature of the transitions are strongly affected by the relative energy between the Bi and Ni levels and the effective electron-electron interaction in the Bi sites. The obtained phase diagram well explains the temperature- and pressure-driven valence transitions in BiNiO_{3} and the systematic variation of valence states for a series of Bi and Pb perovskite oxides.

Valence skipping driven superconductivity and charge Kondo effect

Valence skipping in metallic compounds can give rise to an unconventional superconductivity. Several elements in the periodic table show valence skipping (or valence missing), for example, Bi forms the compounds in valence states +3 and +5. The doping of valence skipping elements will induce superconductivity and this will lead to a possibility of high temperature superconductivity. We consider the Wolf model with negative-U impurities, and show a phase diagram including superconducting phase. The superconducting state is changed into a metallic state with a local singlet as the attractive interaction |U| increases. There is a high temperature region near the boundary.

Quantum criticality and first-order transitions in the extended periodic Anderson model

We investigate the behavior of the periodic Anderson model in the presence of $d$--$f$ Coulomb interaction (${U}_{df}$) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of ${U}_{df}$ and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of ${U}_{df}$, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of ${U}_{df}$. For even larger ${U}_{df}$ valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.

Theory of Charge Kondo Effect on Pair Hopping Mechanism

A new microscopic model of the charge Kondo effect is proposed and is studied on the basis of numerical renormalization group calculations. It is shown that the charge Kondo effect is caused by the pair hopping interaction between the conduction band and the localized band. It is found that the formation of a charge Kondo–Yosida singlet due to its mechanism corresponds to the appearance of a valence skipping phenomenon, and that the charge Kondo–Yosida singlet and the spin Kondo–Yosida singlet state coexist for a tuned parameter set, because the charge and spin degrees of freedom are separated in this model. It is also found that the Sommerfeld coefficient is enhanced by the competition between these two singlet states.

Microscopic observation of the spin-Singlet cluster in the frustrated spinel AlV2O4

The spinel oxide AlV2O4 exhibits a structural phase transition from cubic to rhombohedral lattice at Tc = 700 K, accompanied by V valence skipping. We have investigated the microscopic magnetic properties by the 51V and 27Al NMR measurements across Tc in a temperature range from 2 K to 850 K. The Knight shifts at the 51V and 27Al sites selectively monitor the local spin susceptibilities with different temperature dependence. We reveal that there are two V sites having a nonmagnetic ground state and a frustrated paramagnetic spin. The results are consistent with the spin-singlet heptamer formation consisting of seven vanadium atoms with 18 electrons. This transition uniquely releases the spin and charge frustration on the original V pyrochlore lattice with an aid of the orbital order and the structural distortion. The spin frustration is also highlighted in the anomalous magnetic correlations detected by the nuclear spin-lattice relaxation rate at the V and Al sites.

Valence-skipping compounds as positive-U electronic systems

We find that arguments favoring negative-U behavior of intra-atomic origin, based upon valence skipping for compounds of column III, IV, and V metals, do not stand up to closer examination. It is suggested that real negative-U behavior (disproportionation in compounds such as $\mathrm{Tl}{\mathrm{Br}}_{2}$, ${\mathrm{Pb}}_{2}{\mathrm{O}}_{3}$, and $\mathrm{Ba}\mathrm{Bi}{\mathrm{O}}_{3}$) can, and does, only arise through relaxation of neighbors associated with changes in bond populations. Even then, very high dielectric constants are required to reduce the positive-U contribution, and disproportionation is not expected with lighter metals. Analogous displacements of water molecules may produce disproportionation in aqueous solutions of $\mathrm{Tl}{\mathrm{Br}}_{2}$. We find that Tl impurities in PbTe also disproportionate, through atomic displacements with transfer of electrons between bonds, which could explain, as well as would an atomic-electronic origin, an apparent ``charge-Kondo effect'' behavior, and enhanced superconductivity, found by Matsushita, Blume, Geballe, and Fisher.

Spin Singlet State in Heptamers Emerging in Spinel Oxide AlV2O4

We present our theoretical results on the electronic state in vanadium spinel oxide AlV$_2$O$_4$. The material is a mixed-valent system with the average valence V$^{2.5+}$, and V cations constitute a frustrated pyrochlore structure. It shows a structural transition at $\sim 700$ K, leading to the formation of seven V-sites clusters -- heptamers. We study the electronic state of the heptamer by explicitly taking account of orbital degree of freedom as well as electron correlations. We show that the ground state of the heptamer for realistic parameters becomes spin-singlet because of strong $\sigma$-type bonding states of $t_{2g}$ orbitals. The temperature dependence of the magnetic susceptibility in experiments is naturally understood by this singlet formation in heptamers. Our results indicate that in AlV$_2$O$_4$ orbital physics is relevant to stabilize a cluster-type singlet state instead of a previously proposed charge-ordered state with valence skipping.

Electronic structure and exchange couplings in [formula omitted

We report results of LSDA and LSDA + U band structure calculations performed for high (HT) and low temperature (LT) phases of AlV 2 O 4 . By mapping the LSDA total energy onto a classical Heisenberg model the effective exchange coupling constants J are estimated. It is found that in the LT phase the exchange coupling between V ions on the Kagomé sublattice ( V k ) is much larger than the coupling between V ions on the triangular sublattice ( V t ) and the one between ions on different sublattices, i.e. V k – V t . LSDA + U calculations for the LT phase show no evidence for a solution with a valence skipping. Instead, a solution with a disproportionation of V t 2 g charges into 2.67 for V k and 2 for V t ions and a small hybridisation gap was obtained.

Use of an AX 3 close-packing description of layered perovskites in understanding the role of various A ions in cuprate superconductors

The layered perovskite oxide systems have been modelled on the basis of two types of AX 3 close-packing found, for example, in the Ll 2 and DO 22 structure types of Cu 3Au and TiAl 3, respectively. The former is known to give the ABX 3 perovskite structure. It is proposed that the latter gives the AX rock-salt structure upon the loss of XX rows for which the ionic radius ratio r A r X >0.73 . The lower limit of the tolerance factor is also justified in such a packing scheme based on this geometrical constraint of r A r X ≥0.73 or a minimum r Asim;1.02 Å. An admixture of the two kinds of packing yields the layered perovskite structure. The AX # 3 packing (X # includes the anion vacancy) may be modelled in terms of pseudo-spins in the axial next-nearest-neighbor-Ising (ANNNI) model. The pseudo-spins correspond to the two relative orientations of the AX # rows instead of the lengths of the domains as in the usual description of long period intermetallic superlattices using antiphase boundary (APB) structures. Just as the intermetallic compounds, the layered cuprate perovskites in general have the 〈 m, 1 n 〉 Fisher-Selke notation where m is the number of spins in “ferromagnetic” …AX #.B.X #X #.AX #… (perovskite) domains and n is the number of spins in the “antiferromagnetic” …AX #.X #X #.X #A… (or rock-salt) domains. Three sites for the A ions may then be distinguished. The 〈3, 1〉 notation has the sequence …A PX #.X #X #.B.A FX #.X #X #.B.A PX #.X #X #.X #A R.X #X #.A RX #.X # X #…, where A P are large cations such as La 3+, Ba 2+, Sr 2+ in nine-fold coordination; A F are cations with eight-fold coordinations such as Ca 2+ and Y 3+. TlBa 2CaCu 2O 7 is an example of such a notation. The A R ions with six-fold coordination are ions such as Tl, Bi, Pb etc. It is proposed that the constraints of the close-packing model require the average size of the A R ions to have an average radius of 1.02 Å. This is due to an admixture of various valence states in the A R ions such as Bi, Tl, Pb to provide epitaxial stabilization. The possible role of an admixture of the valence skipping states of the A R ions in enhancing the superconducting transition temperatures is discussed.