Theory Of Metal-insulator Transition Research Articles

Theory of metal-insulator transitions in graphite under high magnetic field

Graphite under high magnetic field exhibits consecutive metal-insulator (MI) transitions as well as re-entrant insulator-metal (IM) transition in the quasi-quantum limit at low temperature. In this paper, we identify the low-$T$ insulating phases as excitonic insulators with spin nematic orderings. We first point out that graphite under the relevant field regime is in the charge neutrality region, where electron and hole densities compensate each other. Based on this observation, we introduce interacting electron models with electron pocket(s) and hole pocket(s) and enumerate possible umklapp scattering processes allowed under the charge neutrality. Employing effective boson theories for the electron models and renormalization group (RG) analyses for the boson theories, we show that there exist critical interaction strengths above which the umklapp processes become relevant and the system enter excitonic insulator phases with long-range order of spin superconducting phase fields ("spin nematic excitonic insulator"). We argue that, when a pair of electron and hole pockets get smaller in size, a quantum fluctuation of the spin superconducting phase becomes larger and destabilizes the excitonic insulator phases, resulting in the re-entrant IM transitions. We also show that an odd-parity excitonic pairing between the electron and hole pockets reconstruct surface chiral Fermi arc states of electron and hole into a 2-dimensional helical surface state with a gapless Dirac cone. We discuss field- and temperature-dependences of in-plane resistance by surface transports via these surface states.

Theory of metal-insulator transition in the family of perovskite iridium oxides

We investigate the metal-insulator transition in the layered Ruddelsden Popper series of strontium iridates Srn+1IrnO3n+1. Tight-binding models of t2g orbitals for n = 1, 2, and infinity are constructed, and changes in band dispersion due to dimensionality and spin-orbit coupling are presented. Identifying the states near the Fermi level to be predominantly Jeff = 1/2, we use an effective Hubbard model to study the effect of correlations. Transitions from a metallic state to various magnetically ordered states at different critical interactions are obtained. A canted antiferromagnetic insulator is found for Sr2IrO4, a c-axis collinear antiferromagnetic insulator for Sr3Ir2O7, and non-coplanar canted antiferromagnetic insulator via magnetic metal for SrIrO3. We derive the strong-coupling spin-model and compare the magnetic ordering patterns obtained in the weak and strong coupling limits. We find that they are identical, indicating that magnetic ordering is not sufficient to justify Mott physics in this series of iridates.

Comment on “Theory of Metal-Insulator Transitions in Gated Semiconductors”

In a recent Letter, Altshuler and Maslov propose a model which attributes the anomalous temperature and field dependence of the resistivity of two-dimensional electron (or hole) systems to the charging and discharging of traps in the oxide (spacer), rather than to intrinsic behavior of interacting particles associated with a conductor-insulator transition in two dimensions. We argue against this model based on existing experimental evidence.

Theory of Metal-Insulator Transitions in Gated Semiconductors

It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the oxide layer. The gate voltage changes the number of charged traps which results in a sharp change in the resistivity. The observed exponential temperature dependence of the resistivity in the metallic phase of the transition follows from the temperature dependence of the trap occupation number. The model naturally describes the experimentally observed scaling properties of the transition and effects of magnetic and electric fields.

Theory of many-fermion systems

A general field-theoretical description of many-fermion systems, both with and without quenched disorder, is developed. Starting from the basic Grassmannian action for interacting fermions, we first bosonize the theory by introducing composite matrix variables that correspond to two-fermion excitations and integrating out the fermion degrees of freedom. The saddle-point solution of the resulting matrix field theory reproduces a disordered Hartree-Fock approximation, and an expansion to Gaussian order about the saddle point corresponds to a disordered random-phase approximation (RPA)-like theory. In the clean limit they reduce to the ordinary Hartree-Fock and random-phase approximations. We first concentrate on disordered systems, and perform a symmetry analysis that allows for a systematic separation of the massless modes from the massive ones. By treating the massive modes in a simple approximation, one obtains a technically satisfactory derivation of the generalized nonlinear $\ensuremath{\sigma}$ model that has been used in the theory of metal-insulator transitions. The theory also allows for the treatment of other phase transitions in the disordered Fermi liquid. We further use renormalization group techniques to establish the existence of a disordered Fermi-liquid fixed point, and show that it is stable for all dimensions $d>2$. The so-called weak-localization effects can be understood as corrections to scaling near this fixed point. The general theory also allows for studying the clean limit. For that case we develop a loop expansion that corresponds to an expansion in powers of the screened Coulomb interaction, and that represents a systematic improvement over RPA. We corroborate the existence of a Fermi-liquid fixed point that is stable for all dimensions $d>1$, in agreement with other recent field-theoretical treatments of clean Fermi liquids.

Theory of metal-insulator transition in (DCNQI) 2 Cu

Theoretical studies on the metal-insulator transition in an organic conductor, (DCNQI) 2Cu, are briefly reviewed. It has been stressed that this transition, which is first order with very large hystrisis, is unique since this can be viewed as a cooperative phase transition between Peierls transition and Mott transition.

Theory of metal insulator transition in strongly correlated electron systems

Abstract A comprehensive theory of the correlation driven metal insulator transition in 1D and 2D strongly correlated electron systems is given. In both the 1D and 2D Hubbard model the metal insulator transition encountered close to half filling is of Pokrovsky-Talapov type. An important consequence of this in the 2D Hubbard model is the break down of the Fermi liquid theory. We also describe in detail the properties of the Pokrovsky-Talapov transition in 2D ferroelectrics.

Theory of metal insulator transition of DCNQI-Cu

We investigate the metal insulator transition of quasi-one dimensional organic conductors (DCNQI) 2Cu by slave boson method. Within mean field approximation, we find that three interactions are needed for these organic conductors getting into insulator phase. These are an on-site Coulomb repulsion on Cu ions, an interaction between conduction electrons and phonons, and Jahn-Teller effect of d-electrons of Cu ions. Also we find that temperature dependence of the free energies of metal state and insulator state agrees with the assumption of our phenomenological theory.

Renormalization Group Theory of Metal-Insulator Transition in Doped Silicon

Assuming that the scattering of electrons by localized moments is strong, we show that the effect of Coulomb interaction on the metal-insulator transition is not important in many-valley semiconductors. We investigate the behavior of the conductivity and the dielectric constant applying renormalization group theory to non-interacting electrons, and we show that they behave like σ 0 | n / n c -1| s and χ 0 | n / n c -1| -2 s with s =0.5 near the transition, n being the donor concentration. The relation \( \sigma _{0}\sqrt{\chi _{0}}=e^{3}\sqrt{\nu}/\sqrt{3}\pi^{3/2}\hbar \) is derived with ν the density of states, and it agrees with the experiments within a factor 1.5.

Metal-insulator transition and local moments in a narrow band: A simple thermodynamic theory

A theory of metal-insulator transition (MIT) and of the localized moments in a narrow band is given both at temperature $T=0$ and $T\ensuremath{\ne}0$. In this approach the ratio $\ensuremath{\eta}$ of doubly occupied sites is expanded in a power-expansion parameter of the ground-state energy. The coefficients of the expansion are determined from known expressions for the energy and $\ensuremath{\eta}$ in certain limiting situations, while the optimal value of $\ensuremath{\eta}$ is found by minimizing the energy (at $T=0$) or the free energy ($T\ensuremath{\ne}0$). At $T=0$ the present theory reproduces the results for $\ensuremath{\eta}$ and the energy obtained with the Gutzwiller method. Also, we decompose the system into localized moments and the Fermi liquid, and provide a precise meaning to the former. At $T\ensuremath{\ne}0$ a simple expression for the entropy is proposed which contains both fermionic and localized-moment parts, each with an appropriate weighting factor. The entropy reproduces correctly both the metallic and paramagnetic-insulator limits. The coefficient $\ensuremath{\gamma}$ of the linear electronic specific heat is found to be strongly enhanced close to the MIT. Additionally, we show that the insulating system (at $T=0$) behaves at $T\ensuremath{\ne}0$ as a semiconductor with a Mott-Hubbard band gap. Our theory is based on the single-site approximation; in this paper only the paramagnetic phase is analyzed.

Theory of Metal-Insulator Transition in Peierls Systems with Nearly Half-Filled Bands

It is shown that a metal-insulator transition takes place in a Peierls system with half-filled bands at a critical concentration, ${c}_{\mathrm{cr}}$, of excess electrons. At $cl{c}_{\mathrm{cr}}$ the electrons form pinned (chaotic) soliton states; at $cg{c}_{\mathrm{cr}}$ the solitons form an unpinned conducting lattice. We find ${c}_{\mathrm{cr}}=\frac{{a}^{2}}{{\ensuremath{\pi}}^{2}{{l}_{0}}^{2}}$, where ${l}_{0}$ is the width of the solitons. The theory may explain the metal-insulator transition observed in doped polyacetylene at ${c}_{\mathrm{cr}}\ensuremath{\sim}1$%.