Disordered Fermi Liquid Research Articles

Interplay of superconductivity and localization near a two-dimensional ferromagnetic quantum critical point

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called ``Cooperons'') acquire anomalous dynamical scaling $z=4$, indicating strong non-Fermi liquid behavior.

Observation of Kondo condensation in a degenerately doped silicon metal

When a magnetic moment is embedded in a metal, it captures nearby itinerant electrons to form a so-called Kondo cloud. When magnetic impurities are sufficiently dense that their individual clouds overlap with each other they are expected to form a correlated electronic ground state. This is known as Kondo condensation and can be considered a magnetic version of Bardeen–Cooper–Schrieffer pair formation. Here, we examine this phenomenon by performing electrical transport and high-precision tunnelling density-of-states spectroscopy measurements in a highly P-doped crystalline silicon metal in which disorder-induced localized magnetic moments exist. We detect the Kondo effect in the resistivity of the Si metal at temperatures below 2 K and an unusual pseudogap in the density of states with gap edge peaks below 100 mK. The pseudogap and peaks are tuned by applying an external magnetic field and transformed into a metallic Altshuler–Aronov gap associated with a paramagnetic disordered Fermi liquid phase. We interpret these observations as evidence of Kondo condensation followed by a transition to a disordered Fermi liquid.

Critical anomalous metals near superconductivity in models with random interactions

Anomalous metals are observed in numerous experiments on disordered two-dimensional systems proximate to superconductivity. A characteristic feature of an anomalous metal is that its low temperature conductivity has a weakly temperature dependent value, significantly higher than that of a disordered Fermi liquid. We propose a dynamical mean-field model of an anomalous metal: interacting electrons similar in structure to that of the well-studied universal Hamiltonian of mesoscopic metallic grains, but with independent random interactions between pairs of sites, involving Cooper pair hopping and spin exchange. We find evidence for critical anomalous phases or points between a superconducting phase and a disordered Fermi liquid phase in this model. Our results are obtained by a renormalization group analysis in a weak coupling limit, and a complementary solution at large $M$ when the spin symmetry is generalized to USp($M$). The large $M$ limit describes the anomalous metal by fractionalization of the electron into spinons, holons, and doublons, with these partons forming critical non-Fermi liquids in the Sachdev-Ye-Kitaev class. We compute the low temperature conductivity in the large $M$ limit, and find temperature-independent values moderately enhanced from that in the disordered metal.

Interaction-Induced Metallicity in a Two-Dimensional Disordered Non-Fermi Liquid.

The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. Instead, we start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value pc of the hole doping p away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc and a metallic spin glass with carrier density p for p<pc. Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.6 MoreReceived 24 December 2019Revised 18 February 2020Accepted 23 March 2020DOI:https://doi.org/10.1103/PhysRevX.10.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum criticalityQuantum phase transitionsPhysical SystemsCupratesTechniquesSachdev-Ye-Kitaev modelCondensed Matter, Materials & Applied Physics

Metal-insulator transition in a random Hubbard model

We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site nonrandom repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. [arXiv:2002.07181] can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory, which generalizes the SU(2) spin symmetry to $\mathrm{SU}(M)$ and obtains exponents for the electron and spin correlators which agree with those of Cha et al. This critical point is expected to have the maximal quantum Lyapunov exponent. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.

Solvable model for quantum criticality between the Sachdev-Ye-Kitaev liquid and a disordered Fermi liquid

We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number $N$ of fermions are obtained and show a characteristic scale-invariant $\sim |\omega|^{-1/2}$ behavior of the spectral function below the transition which is replaced by a $\sim |\omega|^{-1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle point equations and discussed in the broader context of the field.

Family of Sachdev-Ye-Kitaev models motivated by experimental considerations

Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain assumptions about the underlying physical system that (i) render all bilinear terms small compared to four-fermion interactions and (ii) ensure that the coupling constants are approximately all-to-all and independent random variables. In this work we explore, both analytically and numerically, the family of models that arises when we relax these assumptions in ways motivated by real physical systems. By relaxing (i) and allowing large bilinear terms, we obtain a novel, exactly-solvable cousin of the SYK model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, $\sim |\omega|^{-1/3}$ scaling of the low-energy spectral density, despite being a non-interacting model. By relaxing (ii), we obtain close relatives of the SYK model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.

Transverse thermoelectric response as a probe for existence of quasiparticles

The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, alpha_{xy}= - alpha_{yx}, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces alpha_{xy} = - alpha_{yx}. This suggests that quasiparticle-free groundstates (so-called non-Fermi liquids) may be detected by examining the relationship between alpha_{xy} and alpha_{yx} in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results: (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles; (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid the latter lead to deviations that vanish as T^3. (iii) We calculate the thermoelectric response in a model of weakly-coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of alpha. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.

Theory of thermal conductivity in the disordered electron liquid

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 logarithmic correction which may compete with the RG-corrections. The interest in this correction arises from the fact that it violates the Wiedemann-Franz law. We checked that the sub-temperature correction to the thermal conductivity is not modified, neither by the inclusion of Fermi liquid interaction amplitudes nor as a result of the RG flow. We thereby expect that the answer obtained for this correction is final. We use the theory to describe thermal transport on the metallic side of the metal-insulator transition in Si MOSFETs.

Renormalization group analysis of thermal transport in the disordered Fermi liquid

We present a detailed study of thermal transport in the disordered Fermi liquid with short-range interactions. At temperatures smaller than the impurity scattering rate, i.e., in the diffusive regime, thermal conductivity acquires non-analytic quantum corrections. When these quantum corrections become large at low temperatures, the calculation of thermal conductivity demands a theoretical approach that treats disorder and interactions on an equal footing. In this paper, we develop such an approach by merging Luttinger's idea of using gravitational potentials for the analysis of thermal phenomena with a renormalization group calculation based on the Keldysh nonlinear sigma model. The gravitational potentials are introduced in the action as auxiliary sources that couple to the heat density. These sources are a convenient tool for generating expressions for the heat density and its correlation function from the partition function. Already in the absence of the gravitational potentials, the nonlinear sigma model contains several temperature-dependent renormalization group charges. When the gravitational potentials are introduced into the model, they acquire an independent renormalization group flow. We show that this flow preserves the phenomenological form of the correlation function, reflecting its relation to the specific heat and the constraints imposed by energy conservation. The main result of our analysis is that the Wiedemann-Franz law holds down to the lowest temperatures even in the presence of disorder and interactions and despite the quantum corrections that arise for both the electric and thermal conductivities.

Thermal transport and Wiedemann-Franz law in the disordered Fermi liquid

We study thermal transport in the disordered Fermi liquid at low temperatures. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron electron interaction. In the present scheme this fundamental relation is closely connected with a fixed point in the multi-parametric RG-flow of the gravitational potentials.

Quantum charge glasses of itinerant fermions with cavity-mediated long-range interactions

We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multi-mode optical cavities. The solution of an infinite-range model yields a metallic phase which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional disordered Fermi liquid, and the insulating electron glass of semiconductors. Prospects for the realization of such glassy phases in cold atom systems are discussed.

Kondo-Anderson transitions

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical power-law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero-temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time-reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature ${T}_{K}$ is derived at the AMIT, in the metallic phase, and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as a function of temperature. We find a phase diagram with finite-temperature transitions among insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions.

Disordered Fermi Liquid in Epitaxial Graphene from Quantum Transport Measurements

We have performed magnetotransport measurements on monolayer epitaxial graphene and analyzed them in the framework of the disordered Fermi liquid theory. We have separated the electron-electron and weak-localization contributions to resistivity and demonstrated the phase coherence over a micrometer length scale, setting the limit of at least 50 ps on the spin relaxation time in this material.

DISORDERED ELECTRON LIQUID WITH INTERACTIONS

The metal–insulator transition (MIT) observed in a two-dimensional dilute electron liquid raises the question about the applicability of the scaling theory of disordered electrons, the approach pioneered by Phil Anderson and his collaborators,8 for the description of this transition. In this context, we review here the scaling theory of disordered electrons with electron–electron interactions. We start with the disordered Fermi liquid, and 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. This model has a direct relation with the disordered Fermi liquid, but can be more generally applicable, since it is a minimal model for disordered interacting electrons. The discussion is mostly about the general structure of the theory emphasizing the connection of the scaling parameters entering the NLSM with conservation laws. Next, we show that the MIT, as described by the NLSM with interactions, is a quantum phase transition and identify the parameters needed for the description of the kinetics and thermodynamics of the interacting liquid in the critical region of the transition. Finally, we discuss the MIT observed in Si -MOSFETs. We consider it as an example of the Anderson transition in the presence of the electron interactions. We demonstrate that the two-parameter RG equations, which treat disorder in the one-loop approximation but incorporate the full dependence on the interaction amplitudes, describe accurately the experimental data in Si -MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The fact that this drop can be reproduced theoretically, together with the argument that Anderson localization should occur at strong disorder, justified the existence of the MIT within the scaling theory.

Crossover from Fermi Liquid to Multichannel Luttinger Liquid in High-Mobility Quantum Wires

We investigate the electrical conductance of long, high-mobility quantum wires formed by the split-gate technique, which allows for adjustment of the wire width and the number of one-dimensional electron subbands, n. In wires with 3<or=n<or=8, a logarithmic temperature dependence of the conductance is observed for 1<T<10 K, which reaches as much as 30% of the Drude conductance. In even narrower wires, the logarithmic dependence changes to a power-law variation. Our observations are shown to be in good agreement with recent theoretical studies, which attribute the logarithmic term to interaction effects in a weakly disordered quasi-one-dimensional conductor. This interaction correction is associated with the emergence of a crossover from a quasi-one-dimensional weakly disordered Fermi liquid to a multichannel Luttinger liquid.

Doping a semiconductor to create an unconventional metal

Landau-Fermi liquid theory, with its pivotal assertion that electrons in metals can be simply understood as independent particles with effective masses replacing the free electron mass, has been astonishingly successful. This is true despite the Coulomb interactions an electron experiences from the host crystal lattice, lattice defects and the other approximately 10(22) cm(-3) electrons. An important extension to the theory accounts for the behaviour of doped semiconductors. Because little in the vast literature on materials contradicts Fermi liquid theory and its extensions, exceptions have attracted great attention, and they include the high-temperature superconductors, silicon-based field-effect transistors that host two-dimensional metals, and certain rare-earth compounds at the threshold of magnetism. The origin of the non-Fermi liquid behaviour in all of these systems remains controversial. Here we report that an entirely different and exceedingly simple class of materials-doped small-bandgap semiconductors near a metal-insulator transition-can also display a non-Fermi liquid state. Remarkably, a modest magnetic field functions as a switch which restores the ordinary disordered Fermi liquid. Our data suggest that we have found a physical realization of the only mathematically rigorous route to a non-Fermi liquid, namely the 'undercompensated Kondo effect', where there are too few mobile electrons to compensate for the spins of unpaired electrons localized on impurity atoms.

Temperature dependent resistivity in the low-resistance region for diffusive transport in two dimensions

The interpretation of the metal-insulator transition phenomena in disordered two-dimensional electron systems in terms of density-dependent scaling variables suggests the existence of a quantum critical point at some critical electron density. However a first principles scaling theory based on renormalization group (RG) methods predicts a strong temperature dependence of the dimensionless resistivity $\mathcal{R}(T)$, even at small $\mathcal{R}(T)$, that is not observed. The observed properties are in fact consistent with a weakly disordered Fermi liquid, and there are no indications of strong temperature dependence induced by scaling. While the RG expansion in a power series in $\mathcal{R}(T)$ has only been evaluated to lowest order, this should be sufficient to describe experiments in the region of very small $\mathcal{R}$. A further apparent anomaly is a return from metal-like to insulating-like behavior for increasing density. We explain these fundamental discrepancies between the first principles theory and experiment. We find that the $\mathcal{R}⪡1$ data in the currently attainable temperature range are in a weak scaling regime described by the logarithmic approximation. We independently determine the density dependent prefactor of the logarithm using data for the spin susceptibility and effective mass. We find good agreement between theory and experiment for $\mathcal{R}(T)$ in the diffusive regime. We point out that there are corrections to the leading logarithm approximation that should be observable at still lower temperatures.

Transport properties of clean and disordered superconductors in matrix field theory

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin-density susceptibility, and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed, respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal-metal state and the superconductor state.