In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
In the present paper we extend the method to detect Pomeranchuk instabilities in lattice systems developed in previous works to study more general situations. The main result presented here is the extension of the method to include finite temperature effects, which allows to compute critical temperatures as a function of interaction strengths and density of carriers. Furthermore, it can be applied to multiband problems which would be relevant to study systems with spin/color degrees of freedom. Altogether, the present extended version provides a potentially powerful technique to investigate microscopic realistic models relevant to e.g. the Fermi liquid to nematic transition extensively studied in connection with different materials such as cuprates, ruthenates, etc.
We develop a procedure for detecting Fermi liquid instabilities by extending the analysis of Pomeranchuk to two-dimensional lattice systems. The method is very general and straightforward to apply, thus, provides a powerful tool for the search of exotic phases. We test it by applying it to a lattice electron model with interactions leading to
s- and
d-wave instabilities.
Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F_{ℓ}≤-1 in the angular momentum ℓ=2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F_{ℓ} of the composite fermion Fermi liquid with a finite layer width. We consider F_{ℓ} in different Landau levels n=0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η_{c} is higher for the n=2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n=2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.
We present a new method to detect Fermi surface instabilities for interacting systems at finite temperature. We first apply it to a list of cases studied previously, recovering already known results in a very economic way, and obtaining most of the information on the phase diagram analytically. As an example, in the continuum limit we obtain the critical temperature as an implicit function of the magnetic field and the chemical potential Tc(μ,h). By applying the method to a model proposed to describe reentrant behavior in Sr3Ru2O7, we reproduce the phase diagram obtained experimentally and show the presence of a non-Fermi Liquid region at temperatures above the nematic phase.
We study the effects of spin-antisymmetric interactions on the stability of a Landau–Fermi liquid on the square lattice, using the generalized Pomeranchuk method for two-dimensional lattice systems. In particular, we analyze interactions that could induce instabilities of the so-called spin-split type, that is when spin-up and spin-down Fermi surfaces are displaced with respect to each other. The phase space is studied as a function of the strength of the interaction V, the electron chemical potential μ and an external magnetic field h. We find that such interactions produce in general an enhancement of the instability region of the Landau–Fermi liquid. More interestingly, in certain regions of the V–μ phase space, we find a reentrant behavior as a function of the magnetic field h, similar to that found in recent experiments, e.g. in URu₂Si₂ and Sr₃Ru₂O₇.
We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic
(n=2) Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, related to the Landau interaction function. We derive ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ${Z}_{\ensuremath{\Gamma}}$, related to the single-particle residue
Z and effective-mass renormalization ${m}^{\ensuremath{\ast}}/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, to obtain and solve a set of coupled nonlinear equations for ${Z}_{\ensuremath{\Gamma}}$,
Z, and ${m}^{\ensuremath{\ast}}/m$. We show that near the transition the system enters a critical FL regime, where ${Z}_{\ensuremath{\Gamma}}\ensuremath{\sim}Z\ensuremath{\propto}{(1+{g}_{c,2})}^{1/2}$ and ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1/Z$, where
gc,2 is the
n=2 charge Landau component which approaches $\ensuremath{-}1$ at the instability. We construct the Landau function of the critical FL and show that all but
gc,2 Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\ensuremath{\Sigma}(K)\ensuremath{\propto}\ensuremath{\int}dPG(P)D(K\ensuremath{-}P)$ is asymptotically exact if one identifies the effective interaction
D with the RPA form of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$.