We observe a complex change in the hopping exponent value from 1/2 to 1/3 as a function of disorder strength and electron density in a sodium-doped silicon MOSFET. The disorder was varied by applying a gate voltage and thermally drifting the ions to different positions in the oxide. The same gate was then used at low temperature to modify the carrier concentration. Magnetoconductivity measurements are compatible with a change in transport mechanisms when either the disorder or the electron density is modified suggesting a possible transition from a Mott insulator to an Anderson insulator in these systems.
The suppression by a magnetic field of the anomalous H=0 conducting phase in high-mobility silicon MOSFETs is independent of the angle between the field and the plane of the 2D electron system. In the presence of a parallel field large enough to fully quench the anomalous conducting phase, the behavior is similar to that of disordered GaAs/AlGaAs heterostructures: the system is insulating in zero (perpendicular) field and exhibits reentrant insulator-quantum Hall effect-insulator transitions as a function of perpendicular field. The results demonstrate that the suppression of the low-T phase i…
We report exact multielectronic ground-states dependent on electron concentration for quantum mechanical two-dimensional disordered two-band type many body models in the presence of disordered hoppings and disordered repulsive finite Hubbard interactions, in fixed lattice topology considered provided by Bravais lattices. The obtained ground-states loose their eigenfunction character for independent electron approximation, perturbatively are not connected to the non-interacting but disordered case, and describe a localization-delocalization transition driven by the electron concentration, being…
A brief review of metal-insulator transitions in three-dimensional doped semiconductors, with emphasis on the "critical exponent puzzle"; and new experimental findings that signal the possibility of an unexpected metal-insulator transition in dilute two-dimensional systems, such as silicon MOSFETs and GaAs/AlGaAs heterostructures.
We consider two-dimensional system of particles localized on randomly distributed sites of squared lattice with anisotropic transfer matrix elements between localized sites. By summing of "diffusion ladder" and "cooperon ladder" type vertices we calculated the conductivity for various sites and particles densities.
The effect of interchain hopping and interaction on Anderson localization has been investigated for two coupled chains of spinless fermions with nearest neighbor interaction. Using the renormalization group method, we find that interchain hopping plays a significant role when the correlation gap induced by the interplay of interchain hopping and intrachain interaction becomes larger than the Anderson localization energy scale induced by impurities. The strong competition between localization and delocalization is examined for attractive interaction.
By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca$_{2-x}$Sr$_x$RuO$_4$ near the metal-insulator transition. The hopping exponent $α$ shows a systematic evolution from a value of $α=1/2$ deeper in the insulator to the conventional Mott value $α=1/3$ closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induc…
We study quantum corrections to conductivity in a 2D system with a smooth random potential and strong spin-orbit splitting of the spectrum. We show that the interference correction is positive and down to the very low temperature can exceed the negative correction related to electron-electron interactions. We discuss this result in the context of the problem of the metal-insulator transition in Si-MOSFET structures.
We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the inverse participation ratio, level-statistics, entanglement entropy and number fluctuations in the subsystem along with quench and wave-packet dynamics. Finite systems show delocalized, quasi-localized and localized phases. The delocalized phase shows strong area-law violation whereas the (quasi)localized phase adheres to (for large subsystems) the strict area …
For $N$ interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the ``sites''. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected ``sites'' is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of th…
In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against ful…
Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our result…
The 5d-electron honeycomb compound H$_3$LiIr$_2$O$_3$ [K. Kitagawa $et$ $al.$, Nature 554, 341-345 (2018)] exhibits an apparent quantum spin liquid (QSL) state. In this intercalated spin-orbital compound, a remarkable pile up of low-energy states was experimentally observed in specific heat and nuclear magnetic (NMR) spin relaxation. We show that a bond disordered Kitaev model can naturally account for this phenomenon, suggesting that disorder plays an essential role in its theoretical description. In the exactly soluble Kitaev model, we obtain, via spin fractionalization, a random bipartite h…
We study the ground state phase diagram of the Anderson-Hubbard model with correlated hopping at half filling in one-dimension. The Hamiltonian has a local Coulomb repulsion $U$ and a disorder potential with local energies randomly distributed in the interval $(-W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites have the same amplitude $t$. We identify three different phase…
Nodal semimetals (e.g. Dirac, Weyl and nodal-line semimetals, graphene, etc.) and systems of pinned particles with power-law interactions (trapped ultracold ions, nitrogen defects in diamonds, spins in solids, etc.) are presently at the centre of attention of large communities of researchers working in condensed-matter and atomic, molecular and optical physics. Although seemingly unrelated, both classes of systems are abundant with novel fundamental thermodynamic and transport phenomena. In this paper, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped …
Experimental results on the metal-insulator transitions and the anomalous properties of strongly interacting two-dimensional electron systems are reviewed and critically analyzed. Special attention is given to recent results for the strongly enhanced spin susceptibility and effective mass in low-disordered silicon MOSFETs.
The metallic or insulating nature of the paramagnetic phase of the colossal-magnetoresistance manganites is investigated via a double exchange Hamiltonian with diagonal disorder. Mobility edge trajectory is determined with the transfer matrix method. Density of states calculations indicate that random hopping alone is not sufficient to induce Anderson localization at the Fermi level with 20-30% doping. We argue that the metal-insulator transtion is likely due to the formation of localized polarons from nonuniform extended states as the effective band width is reduced by random hoppings and ele…
Experimental results on the metal-insulator transition and related phenomena in strongly interacting two-dimensional electron systems are discussed. Special attention is given to recent results for the strongly enhanced spin susceptibility, effective mass, and thermopower in low-disordered silicon MOSFETs.
Motivated by the recent experiments that reported signatures of many-body localization of ultracold atoms in optical lattices [M. Schreiber {\it et al.}, Science {\bf 349}, 842 (2015)], we study dynamics of highly excited states in the strongly disordered Hubbard model in one dimension. Owing to the $SU(2)$ spin symmetry, spin degrees of freedom form a delocalized thermal bath with a narrow bandwidth. The spin bath mediates slow particle transport, eventually leading to delocalization of particles. The particle hopping rate is exponentially small in $t/W$ ($t$, $W$ being hopping and disorder s…
We show that the effect of disorder on a Mott-Hubbard insulator of interacting electrons produces a quantum phase transition from an antiferromagnetic to a paramagnetic phase governed by a percolation of the singly occupied weakly disordered sites. Near the transition, we propose that a new type of defect, formed by the resonant exchange between a spin singlet and a doubly occupied site with an attractive disorder potential, plays an important role. These resonant pair exchange defects reduce the staggered magnetization but enhance the coupling of the two spins and produce characteristic signa…
We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using as a starting point the partition function defined on the Keldysh contour. We extend the Renormalization Group (RG) analysis developed for thermal transport in the disordered Fermi liquid, and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electric conductivity, these scattering processes yield a loga…
The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbors and next-nearest-neighbors hopping. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended ph…
One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermion…
We investigate the effects of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction in graphene by studying numerically the Anderson model with on-site and hopping disorder on a honeycomb lattice at half filling. We evaluate the strength of the interaction as a function of the distance R between two magnetic ions, as well as their lattice positions and orientations. In the clean limit, we find that the strength of the interaction decays as 1/R^3, with its sign and oscillation amplitude showing strong anisotropy. With increasing on-site disorder, the mean amplitude decre…
A model of strongly disordered lattice system with long-range Coulomb interactions between localized charge carriers has been considered. The total electronic energy is characterized by the presence of multiple metastable minima (including the true ground state), and different types of excitation spectra over these minima. A numeric procedure, accounting for all many-body correlations in finite size samples, confirms the existence of Coulomb gap in the single-particle spectrum and also provides corrections to the known mean-field theory results, as asymmetry of the gap at non-half-filling, van…
The response to a parallel magnetic field of the very dilute insulating two-dimensional system of electrons in silicon MOSFET's is dramatic and similar to that found on the conducting side of the metal-insulator transition: there is a large initial increase in resistivity with increasing field, followed by saturation to a value that is approximately constant above a characteristic magnetic field of about one Tesla. This is unexpected behavior in an insulator that exhibits Efros-Shklovskii variable-range hopping in zero field, and appears to be a general feature of very dilute electron systems.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator…
We review the scaling theory of disordered itinerant electrons with e-e interactions. We first show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions (Finkel'stein's model). This model is closely connected to the Fermi liquid, but is more generally applicable, since it can also be viewed as a minimal effective functional describing disordered interacting electrons. Our discussion emphasizes the general structure of the theory, and the connection of the scaling parameters to conservation laws. We t…
