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arXiv:cond-mat/0601103 · Physical Review B

Pomeranchuk and topological Fermi surface instabilities from central interactions

Jorge Quintanilla, A. J. Schofield

Published Sep 28, 2006• 89 citations
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Abstract

We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except $l=1$ can take place if the interaction is repulsive and has a finite range ${r}_{0}$ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.

DOI
10.1103/physrevb.74.115126

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We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except l=1l=1l=1 can take place if the interaction is repulsive and has a finite range r0{r}_{0}r0​ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.
The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f ( p , p' ) having a sharp peak at | p − p' | = q 0 . It is shown that, in the case of attraction and q 0 = 2 p F the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q 0 , the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ≃ π( p F / q 0 − 1) small hole pockets at the distance p F − q 0 from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L . At q 0 → 0, when the model under study transforms to the two-dimensional Nozières model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.
Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi-liquid behavior over the whole surface except at the Brillouin zone diagonal.
Interactions in Fermi systems can generate a Pomeranchuk instability leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations and exhibits enhanced collective fluctuations. We analyze fluctuation effects in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. Density correlations with a d-wave form factor and the dynamical forward scattering interaction diverge near the instability. The singular forward scattering leads to large self-energy contributions, which destroy Fermi liquid behavior over the whole Fermi surface except at “cold spots” on the Brillouin zone diagonal. The decay rate of single-particle excitations, which is related to the width of the peaks in the spectral function, exceeds the excitation energy in the low-energy limit. The dispersion of the spectra flattens strongly near those portions of the Fermi surface which are remote from the zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots. We discuss the possible relevance of d-wave Fermi surface fluctuations for the “strange metal” behavior observed in the normal phase of cuprates.
Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.
Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and ddd-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the ddd-wave pairing to the (d+s)(d+s)(d+s) wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature TcPI{T}_{\mathrm{c}}^{\mathrm{PI}}TcPI​ for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​. This implies that the filling region for strong Pomeranchuk instability and that for the TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​ dome can be separated, and that Pomeranchuk instability can appear even if the peak of TcPI{T}_{\mathrm{c}}^{\mathrm{PI}}TcPI​ is lower than the peak of TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​. An interesting finding is that the Fermi surface distortion can enhance the superconducting TcSC{T}_{\mathrm{c}}^{\mathrm{SC}}TcSC​ in the overdoped regime, which is explained with a perturbational picture for small distortions.