Interacting Fermi Surface Research Articles

Fermi-surface topology and renormalization of bare ellipticity in an interacting anisotropic electron gas

We investigate effects of electron-electron interactions on the shape of the Fermi surface in an anisotropic two-dimensional electron gas using the `RPA-GW' self-energy approximation. We find that the interacting Fermi surface deviates from an ellipse, but not in an arbitrary way. The interacting Fermi surface has only two qualitatively distinct shapes for most values of $r_s$. The Fermi surface undergoes two distinct transitions between these two shapes as $r_s$ increases. For larger $r_s$, the degree of the deviation from an ellipse rapidly increases, but, in general, our theory provides a justification for the widely used elliptical Fermi surface approximation even for the interacting system since the non-elliptic corrections are quantitatively rather small except for very large $r_s$.

Multiorbital Processes Rule the Nd1−xSrxNiO2 Normal State

The predominant Ni-multiorbital nature of infinite-layer neodynium nickelate at stoichiometry and with doping is revealed. We investigate the correlated electronic structure of NdNiO$_2$ at lower temperatures and show that first-principles many-body theory may account for Kondo(-lattice) features. Yet those are not only based on localized Ni-$d_{x^2-y^2}$ and a Nd-dominated self-doping band, but heavily builds on the participation of Ni-$d_{z^2}$ in a Hund-assisted manner. In a tailored three-orbital study, the half-filled regime of the former inplane Ni orbital remains surprisingly robust even for substantial hole doping $\delta$. Reconstructions of the interacting Fermi surface designate the superconducting region within the experimental phase diagram. They furthermore provide clues to recent Hall measurements as well as to the astounding weakly-insulating behavior at larger experimental $\delta$. Finally, a strong asymmetry between electron and hole doping, with a revival of Ni single-orbital features in the former case, is predicted. Superconductivity in Nd$_{1-x}$Sr$_x$NiO$_2$ is unlike the one in cuprates of distinct multiorbital kind, building up on nearly localized Ni-$d_{x^2-y^2}$ and itinerant Ni-$d_{z^2}$.

Thermopower Enhancement from Engineering the Na0.7CoO2 Interacting Fermiology via Fe Doping

The sodium cobaltate system NaxCoO2 is a prominent representant of strongly correlated materials with promising thermoelectric response. In a combined theoretical and experimental study we show that, by doping the Co site of the compound at x=0.7 with iron, a further increase of the Seebeck coefficient is achieved. The Fe defects give rise to effective hole doping in the high-thermopower region of larger sodium content x. Originally filled hole pockets in the angular-resolved spectral function of the material shift to low energy when introducing Fe, leading to a multisheet interacting Fermi surface. Because of the higher sensitivity of correlated materials to doping, introducing adequate substitutional defects is thus a promising route to manipulate their thermopower.

The ground state construction of bilayer graphene

We consider a model of half-filled bilayer graphene, in which the three dominant Slonczewski–Weiss–McClure hopping parameters are retained, in the presence of short-range interactions. Under a smallness assumption on the interaction strength [Formula: see text] as well as on the inter-layer hopping [Formula: see text], we construct the ground state in the thermodynamic limit, and prove that the pressure and two-point Schwinger function, away from its singularities, are analytic in [Formula: see text], uniformly in [Formula: see text]. The interacting Fermi surface is degenerate, and consists of eight Fermi points, two of which are protected by symmetries, while the locations of the other six are renormalized by the interaction, and the effective dispersion relation at the Fermi points is conical. The construction reveals the presence of different energy regimes, where the effective behavior of correlation functions changes qualitatively. The analysis of the crossover between regimes plays an important role in the proof of analyticity and in the uniform control of the radius of convergence. The proof is based on a rigorous implementation of fermionic renormalization group methods, including determinant estimates for the renormalized expansion.

Conformal field theory approach to Fermi liquids and other highly entangled states

The Fermi surface may be usefully viewed as a collection of 1+1 dimensional chiral conformal field theories. This approach permits straightforward calculation of many anomalous ground state properties of the Fermi gas including entanglement entropy and number fluctuations. The 1+1 dimensional picture also generalizes to finite temperature and the presence of interactions. Finally, I argue that the low energy entanglement structure of Fermi liquid theory is universal, depending only on the geometry of the interacting Fermi surface.

Spectral Properties and Stability in the Two-Dimensional Lattice-Hubbard Model

The two-dimensional Hubbard model on the square lattice is studied in the presence of lattice distortions in the adiabatic approximation. The self energy is computed within perturbation theory up to second order, which provides a way for studying the quasiparticle dispersion. We compute numerically the second order contribution to the self-energy using a standard fast Fourier transform algorithm for finite sizes system. The stability of the lattice distortions is investigated and a schematic phase diagram is drawn. The Fermi surface is analyzed for densities close to half filling, the presence of lattice distortions changes some spectral properties of the model and gives an anisotropic interacting Fermi surface. The spectral function is calculated along several lines in momentum space and the renormalized quasiparticle dispersion is obtained. The behavior of the density of states is shown for different values of the intrasite repulsion U in the different phases.

SINGULAR FERMI SURFACES I: GENERAL POWER COUNTING AND HIGHER DIMENSIONAL CASES

We prove regularity properties of the self-energy, to all orders in perturbation theory, for systems with singular Fermi surfaces which contain Van Hove points where the gradient of the dispersion relation vanishes. In this paper, we show for spatial dimensions d ≥ 3 that despite the Van Hove singularity, the overlapping loop bounds we proved together with E. Trubowitz for regular non-nested Fermi surfaces [J. Stat. Phys.84 (1996) 1209–1336] still hold, provided that the Fermi surface satisfies a no-nesting condition. This implies that for a fixed interacting Fermi surface, the self-energy is a continuously differentiable function of frequency and momentum, so that the quasiparticle weight and the Fermi velocity remain close to their values in the noninteracting system to all orders in perturbation theory. In a companion paper, we treat the more singular two-dimensional case.

Fermi Liquid Behavior in the 2D Hubbard Model at Low Temperatures

We prove that the weak coupling 2D Hubbard model away from half filling is a Landau Fermi liquid up to exponentially small temperatures. In particular we show that the wave function renormalization is an order 1 constant and essentially temperature independent in the considered range of temperatures and that the interacting Fermi surface is a regular convex curve. This result is obtained by deriving a convergent expansion (which is not a power series) for the two point Schwinger function by Renormalization Group methods and proving at each order suitable power counting improvements due to the convexity of the interacting Fermi surface. Convergence follows from determinant bounds for the fermionic expectations.

Fermi surface renormalization in two dimensions

We investigate a two-dimensional totally flat Fermi surface (FS) model using a two-loop field theoretical renormalization group (RG) approach. We take full account of the FS renormalization calculating explicitly how the RG equations for the renormalized chemical potential ( μ R) and coupling functions vary with the parallel momentum ( p ∥) along the Fermi surface. We find non-trivial infrared (IR) stable fixed points for the couplings of the model for any choice of p ∥. In our scheme, the true interacting Fermi surface is directly related to the IR stable fixed point of the renormalized chemical potential. In this way, we show that the renormalized FS develops a small curvature and becomes truncated as a result of interactions.

Continuous Renormalization for Fermions and Fermi Liquid Theory

I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus improves the combinatorial behaviour. The form of the equation is also ideal for the investigation of many-fermion systems, where the propagator is singular on a surface. For these systems, I define a criterion for Fermi liquid behaviour which applies at positive temperatures. As a first step towards establishing such behaviour in d ge 2, I prove basic regularity properties of the interacting Fermi surface to all orders in a skeleton expansion. The proof is a considerable simplification of previous ones.

Strongly Correlated Fermi Liquid and the Normal State of High Tc Superconductors

New insights into the strongly correlated Fermi liquid state of the SU(N) infinite-U Hubbard and t-J models are presented in connection to the metallic state of unbroken symmetry of the copper oxide planes. The nature of single particle and collective excitations is analyzed and the Landau Fermi Liquid parameters are derived. The one-particle spectral function in the Hubbard valence band is obtained with both Hubbard and Gutzwiller-like features. A simple interpretation of the large incoherent background is given in terms of a superposition of quasiparticles and a collective mode describing the propagation of a bare hole in a large U system. The spin exchange interactions produce very low lying collective modes describing the propagation of staggered spin chirality which soften at incommensurate wavevectors. The quasiparticles are strongly scattered by the low lying chirality fluctuations resulting in deviations from canonical Fermi liquid behavior at low energy scales. Of the same origin, the quasiparticle self energy is found to be strongly k-dependent. It leads to corrections to the dispersion and enhancement of the quasiparticle lifetime in the hole-like region of the interacting Fermi surface. The combined effects are sufficient to produce a sign change in the Hall coefficient evaluated for parameters relevant to the copper oxide planes. We show that these models also exhibit a zero temperature fluctuation driven transition from Fermi liquid to non Fermi liquid phase without the onset of magnetic ordering below a critical doping δc=1/4N, whereby providing a microscopic mechanism for the destruction of the Fermi liquid coherence by strong longitudinal gauge fluctuations which represent the effects of the infinite-U constraint.