arXiv subjects

Matthew P. Gochan

Publications and source records attributed to Matthew P. Gochan.

4 recordsLinked to original sources

arXiv2020

Atypical Behavior of Collective Modes in Two-Dimensional Fermi Liquids

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 $c_0$. As a function of the usual dimensionless parameter $s=ω/qv_F$, 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 $\ell\geq 1$ which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency $ω_p$ exhibiting a crossover to the zero sound mode.

cond-mat.str-el↗

arXiv2019

Chebyshev Polynomial Expansion of Two-Dimensional Landau-Fermi liquid Parameters

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.

cond-mat.str-el↗

arXiv2019

Viscosity Bound Violation in Viscoelastic Fermi Liquids

The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been used to determine a lower bound on the ratio of shear viscosity $\left(η\right)$ to entropy density $(s)$ for strongly-coupled field theories with a gravity dual. The conjectured universal lower bound, given as $η/s\geq\hbar/4πk_B$, is a measure of interaction strength in a quantum fluid where equality indicates a perfect quantum fluid. In this paper we study $η/s$ in a Fermi gas in the unitary limit. We show that in addition to a local minimum for $η/s$ at $T\approx 2T_c$ which obeys the lower bound, a more interesting result exists in the violation of the $η/s$ lower bound due to the superfluid fluctuations above $T_c$. To conclude, we examine the viscoelastic properties of the unitary Fermi gas. Previous work brought to light the connection between violation of the $η/s$ bound and a viscoelastic response in the context of holographic solids. We ultimately find that, in addition to holographic solids, all Fermi liquids with a viscoelastic response produced by superfluid fluctuations can violate the universal $η/s$ lower bound.

cond-mat.str-el↗

arXiv2018

Consequences of the Inherent Density Dependence in Dirac Materials

Dirac materials are systems in which the dispersion is linear in the vicinity of the Dirac points. As a consequence of this linear dispersion, these systems exhibit unusual behavior and possess unique physical properties that are of great interest. In this work we utilize the single walled carbon nanotube (SWNT) as a model Dirac material and examine the system within the framework of Tomanaga-Luttinger Liquid theory (TLL) revealing several unconventional properties unique to these systems. Specifically, the exponents of the Green's function are electron density independent leading to electron density independent thermodynamic quantities and speed of sound; both of which are vastly different from traditional TLL behavior. Additionally, we discuss the implications the Virial Theorem has for this system; in particular, the total average ground state energy is given by $E=\mathcal{B}/r_s$ where $\mathcal{B}$ is a constant independent of $r_s$. Finally, experimental techniques are discussed in which these predictions of density independent exponents and their behavior can be verified.

cond-mat.str-el↗