The problem of disordered interacting electrons is considered. We study a model for a generic disordered Fermi liquid without cooper pairs and in the absence of any spin-flip mechanisms. We prove to within logarithmic accuracy that there is a stable renormalization-group fixed point to all orders in a loop expansion. We prove that the conductivity exponent at this fixed point is identically equal to zero, while the spin-diffusion constant scales to zero with an exponent \ensuremath{\gamma}=4+O(d-2). By an explicit two-loop calculation we then show that this fixed point is suppressed by logarithmic terms, but a sizeable scaling region persists. The main conclusion is that the metal-insulator transition is preceded on the metallic side by a near instability in the spin system. There is a scaling region leading from a spin-diffusion phase to a region of very slow spin transport. Throughout this scaling region the charge transport is unaffected. Experiments are discussed in the light of these results, and further experiments to test the theory are proposed.
We consider Finkelshtein's model for a disordered Fermi liquid. We show that logarithmic terms at two-loop order suppress the fixed point proposed by Castellani et al. Spin transport slows down dramatically, and in d=2+\ensuremath{\epsilon} a sizable scaling region exists. We show that in the scaling region the apparent conductivity exponent is zero to all orders in a loop expansion. This implies that the charge transport is unaffected by the crossover in the spin system. Experiments compare favorably with this scenario. Further measurements of the Wilson ratio are proposed.
The authors consider a generic model for a disordered Fermi liquid. By means of an infinite resummation of the loop expansion they show that there is a phase transition involving the spin degrees of freedom which can be identified with a new fixed point in the renormalisation group flow equations. The critical exponents obtained for 2<d<4 are apparently exact. The large-disorder phase is described as an incompletely frozen spin phase with no long-range order and subdiffusive spin transport. The results are in good agreement with experiments on Si:P.
We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in $2+2\ensuremath{\epsilon}$ dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an $\ensuremath{\epsilon}$ expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in $2+2\ensuremath{\epsilon}$ dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action $(\ensuremath{\theta}$ term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as $\ensuremath{\nu}$ and p, control not only the scaling behavior of the conductances ${\ensuremath{\sigma}}_{\mathrm{xx}}$ and ${\ensuremath{\sigma}}_{\mathrm{xy}}$ at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat ${(c}_{v}\ensuremath{\propto}{T}^{p}).$ To extract the numerical values of $\ensuremath{\nu}$ and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.
Understanding the influence of quenched random potential is crucial for comprehending the exotic electronic transport of non-Fermi liquid metals near metallic quantum critical points. In this study, we identify a stable fixed point governing the quantum critical behavior of two-dimensional non-Fermi liquid metals in the presence of a random potential disorder. By performing renormalization group analysis on a dimensional-regularized field theory for Ising-nematic quantum critical points, we systematically investigate the interplay between random potential disorder for electrons and Yukawa-type interactions between electrons and bosonic order-parameter fluctuations in a perturbative epsilon expansion. At the one-loop order, the effective field theory lacks stable fixed points, instead exhibiting a runaway flow toward infinite disorder strength. However, at the two-loop order, the effective field theory converges to a stable fixed point characterized by finite disorder strength, termed the “disordered non-Fermi liquid (DNFL) fixed point”. Our investigation reveals that two-loop vertex corrections induced by Yukawa couplings are pivotal in the emergence of the DNFL fixed point, primarily through screening disorder scattering. Additionally, the DNFL fixed point is distinguished by a substantial anomalous scaling dimension of fermion fields, resulting in pseudogap-like behavior in the electron’s density of states. These findings shed light on the quantum critical behavior of disordered non-Fermi liquid metals, emphasizing the indispensable role of higher-order loop corrections in such comprehension.
We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in
d=3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an
ϵ expansion in
d=2+ϵ dimensions. We find that in
d=2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in
d>2 dimensions
(ϵ>0) occurs for disorder strengths of order
ϵ, and is therefore perturbatively accessible for
ϵ⪡1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.