Origins of bad-metal conductivity and the insulator–metal transition in the rare-earth nickelates

Abstract

For most metals, increasing temperature (T) or disorder hastens electron scattering. The electronic conductivity (σ ) decreases as T rises because electrons are more rapidly scattered by lattice vibrations. The value of σ decreases as disorder increases because electrons are more rapidly scattered by imperfections in the material. This is the scattering rate hypothesis, which has guided our understanding of metal conductivity for over a century. However, for so-called bad metals with very low σ this hypothesis predicts scattering rates so high as to conflict with Heisenberg's uncertainty principle 1,2 . Bad-metal conductivity has remained a puzzle since its initial discovery in the 1980s in high-temperature superconductors. Here we introduce the rare-earth nickelates (RNiO 3 , R = rare-earth) as a class of bad metals. We study SmNiO 3 thin films using infrared spectroscopy while varying T and disorder. We show that the interaction between lattice distortions and Ni-O covalence explains bad-metal conductivity and the insulator-metal transition. This interaction shifts spectral weight over the large energy scale established by the Ni-O orbital interaction, thus enabling very low σ without violating the uncertainty principle.The Drude model describes the dependence of σ on the lifetime (τ ) between scattering events, the free carrier concentration (n), the carrier effective mass (m * ), and the elementary charge (q): σ = nq 2 τ /m * . For metals the electron-phonon scattering rate increases with T , producing a linear dependence σ∝ T at sufficiently high T . Elementary quantum theory dictates that this relationship cannot continue indefinitely. According to Heisenberg's uncertainty principle the uncertainty E of a particle's energy is inversely proportional to its lifetime: E = h/τ . Therefore there exists a minimum τ below which the concept of a welldefined quasiparticle energy becomes unphysical. This lower bound on τ implies a minimum metallic conductivity (σ MIR ), which is called the Mott-Ioffe-Regel (MIR) limit 1,2 . Most metals reach their melting temperature well before the MIR limit. There are some so-called 'saturating' metals for which σ (T ) approaches σ MIR and saturates, thus validating the MIR limit. However, in bad metals the relationship σ −1 ∝ T continues unabated through the MIR limit. According to the Drude model these metals have lifetimes so short that the quasiparticles should be unstable (that is, decohere), producing an insulating state, and yet the transport properties remain metallic. Bad-metal conductivity is often found in strongly correlated materials such as the high-T superconductors and the Mott insulator-metal transition (IMT) system VO 2 . The phenomenon of bad-metal conductivity is a central problem in condensed matter physics 1-3 .Here we study bad-metal conductivity and the insulator-metal transition in the nickelates. The nickelate phase diagram features an antiferromagnetic insulator at low T and a paramagnetic metal (PM) at high T . For R = Sm and heavier there is also an in...

Optical spectroscopy and the nature of the insulating state of rare-earth nickelates

“…18,19 The Drude spectral weight is redistributed up to at least 5 eV when the system becomes insulating, [18][19][20] which was interpeted as an indication of Mott physics 19 or effects of electron-phonon interaction. 20 However, a clear mechanism of the optical response of the insulating phase has thus far been lacking.…”

Colossal resistance switching and band gap modulation in a perovskite nickelate by electron doping

“…The doubling of unit cell and combination of Ni 2 þ t 6 2g e 2 g and Ni 4 þ t 6 2g e 0 g render a new band diagram with a Mott-Hubbard splitting involved. Though there is a debate about whether nickelates are Mott-Hubbard insulator 16 , charge-transfer insulator 17 , negative charge-transfer insulator 18 or even band insulator 6 , both theoretical and experimental evidence indicate such band gap of SNO's insulating state is quite small (a few hundred millivolts) because of the mixed character of Ni 2 þ and Ni 4 þ (or Ni (3-…”

Bad Metals from Fluctuating Density Waves

“…It is in fact observed that in a large number of bad metals the Drude peak in the optical conductivity moves away from ω = 0 as the temperature is increased, leading to a suppression of low frequency spectral weight. This phenomenon is seen in ruthenates [16,17], cobaltates [18,19], cuprates [20][21][22][23][24], vanadates [25,26], manganates [27,28], nickelates [29] and organic conductors [30,31]. The behavior is illustrated in figure 1 below.…”