For nearly a century, the Stoner model has dominated research in itinerant ferromagnetism, yet recent work on ultracold, optically trapped Fermi gases suggests that phase separation of spins occurs independent of long-range mag- netic order. In this paper, we consider the breakdown of the Stoner criterion in a Landau-Fermi liquid with a weak non-zero gauge field. Due to a process analogous to Kohn’s theory of a metal-insulator transition, we find the stability of a Fermi liquid phase in the absence of non-quasiparticle contributions to the response is strongly dependent on Landau parameters of mixed partial waves. Our work paves the way for the description of novel spintronic hardware in the language of Landau-Fermi liquid transport.

The failure of Landau-Fermi liquid theory is often considered a telltale sign of universal, scale-invariant behavior in the emergent field theory of interacting fermions. Nevertheless, there exist borderline cases where weak scale invariance coupled with particle-hole asymmetry can coexist with the Landau quasiparticle paradigm. In this letter, I show explicitly that a Landau-Fermi liquid can exist for weak power-law scaling of the retarded Green's function. Such an exotic variant of the traditional Fermi liquid, although exhibiting a finite quasiparticle weight and large quasiparticle lifetime, is shown to always be incompatible with Luttinger's theorem for any non-trivial scaling. This result yields evidence for a Fermi liquid-like ground state in the high-field, underdoped pseudogap phase of the high-temperature cuprate superconductors.

Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo insulators, and the "Luttinger's theorem-violating" Fermi liquid phase of the underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid theory to a system of itinerant, interacting Majorana-like particles. Building upon a previously introduced model of "nearly self-conjugate" fermionic polarons, a Landau-Majorana kinetic equation is introduced to describe the collective modes and Fermi surface instabilities in a fluid of particles whose fermionic degrees of freedom obey the Majorana reality condition. At large screening, we show that the Landau-Majorana liquid harbors a Lifshitz transition for specific values of the driving frequency. Moreover, we find the dispersion of the zero sound collective mode in such a system, showing that there exists a specific limit where the Landau-Majorana liquid harbors a stability against Pomeranchuk deformations unseen in the conventional Landau-Fermi liquid. With these results, our work paves the way for possible extensions of the Landau quasiparticle paradigm to nontrivial metallic phases of matter.

Luttinger's theorem is a major result in many-body physics that states the volume of the Fermi surface is directly proportional to the particle density. In its "hard" form, Luttinger's theorem implies that the Fermi volume is invariant with respect to interactions (as opposed to a "soft" Luttinger's theorem, where this invariance is lost). Despite it's simplicity, the conditions on the fermionic self energy under which Luttinger's theorem is valid remains a matter of debate, with possible requirements for its validity ranging from particle-hole symmetry to analyticity about the Fermi surface. In this paper, we propose the minimal requirements for the application of a hard Luttinger's Theorem to a generic fermionic system of arbitrary interaction strength by invoking the Atiyah-Singer index theorem to quantify the topologically-robust behavior of a generalized Fermi surface. We show that the applicability of a hard Luttinger's theorem in a D-dimensional system is directly dependent on the existence of a (D-1)-dimensional manifold of gapless chiral excitations at the Fermi level, regardless of whether the system exhibits Luttinger or Fermi surfaces (i.e., manifolds of zeroes of the Green's function and inverse Green's function, respectively). The exact form of the self-energy which guarantees validity of a hard Luttinger's theorem is derived, and agreement with current experiments, numerics, and theories are discussed.

We study the intrinsic effects of dimensional reduction on the transport equation of a perfectly two-dimensional Landau-Fermi liquid. By employing the orthogonality condition on the 2D analog of the Fourier-Legendre expansion, we find that the equilibrium and non-equilibrium properties of the fermionic system differ from its three-dimensional counterpart, with the latter changing drastically. Specifically, the modified Landau-Silin kinetic equation is heavily dependent on the solution of a non-trivial contour integral specific to the 2D liquid. We find the solution to this integral and its generalizations, effectively reducing the problem of solving for the collective excitations of a collisonless two-dimensional Landau-Fermi liquid to solving for the roots of some high-degree polynomial. This analysis ultimately lays the mathematical foundation for the exploration of atypical behavior in the non-equilibrium properties of two-dimensional fermionic liquids in the context of the Landau quasiparticle paradigm.

Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau's Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c0. As a function of the usual dimensionless parameter s=ω/qvF, we find two peculiar results: First, for |s|>1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for |s|<1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ≥1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ωp exhibiting a crossover to the zero sound mode.

We propose a closed form for the statistical distribution of non-interacting Majorana fermions at low temperature. Majorana particles often appear in the contemporary many-body literature in the Kitaev, Fu-Kane, or Sachdev-Ye-Kitaev models, where the Majorana condition of self-conjugacy immediately results in nonconserved particle number, non-trivial braiding statistics, and the absence of a noninteracting limit. We deviate from this description and instead consider a gas of noninteracting, spin-1/2 Majorana fermions that obey the spin-statistics theorem via imposing a condensed matter analog of momentum conservation. This allows us to build a quantum statistical theory of the Majorana system in the low temperature, low density limit without the need to account for strong fluctuations in the particle number. A combinatorial analysis leads to a configurational entropy which deviates from the fermionic result with an increasing number of available microstates. A number-conserving Majorana distribution function is derived which shows signatures of a sharply-defined Fermi surface at finite temperatures. Such a distribution is then re-derived from a microscopic model in the form of a modified Kitaev chain with a bosonic pair interaction. The thermodynamics of this free Majorana system is found to be nearly identical to that of a free Fermi gas, except now distinguished by a two-fold ground state degeneracy and, subsequently, a residual entropy at zero temperature. Despite clear differences with the anyonic or Sachdev-Ye-Kitaev models, we nevertheless find surprising agreement between our theory and experimental signatures of Majorana excitations in several materials. Experimental realization of our exactly solvable model is also discussed in the realm of astrophysical and high-energy phenomena.

We present a novel procedure leading to compact and tractable cubic (𝑝=3) and quartic (𝑝=4) scalar fluctuation-dissipation relations for the classical one-component plasma subjected to a weak external Coulombic perturbation; there is no external magnetic field. The ultimate goal here is to establish a generalized nonlinear fluctuation-dissipation relation in which a single (𝑝+1)-point dynamical structure function is expressed as a linear combination of pth-order external density response functions. When cast in this form, such an architecture, by definition, is invariant with respect to rotation on the (𝑝+1)-sided polygon formed by the wave vector-frequency arguments of the dynamical structure function. The application of this rotation symmetry to suppress unphysical isolated singularities is a basic ingredient of the derivation.

We have derived tractable cubic (p=3) and quartic (p=4) fluctuation-dissipation theorems (FDTs) for the classical one-component plasma in a form that links a single (p+1)-point dynamical structure function to a linear combination of pth-order density response functions amenable to calculation from model plasma kinetic equations. For p greater than or equal to 3, we note the emergence of "remainder" contributions comprised of clusters of lower-order dynamical structure functions which can be ultimately traded for response functions vis-a-vis the linear and quadratic FDTs. Our analysis paves the way for gaining a clear understanding of the structure of the FDT hierarchy.