Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annalen der Physik

Instabilities of a Fermi Gas with Nested Fermi Surfaces

P. Schlottmann

Published Nov 22, 2017• 3 citations
Publisher

Abstract

Abstract The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.

DOI
10.1002/andp.201700263

Related papers

Competition of Fermi surface symmetry breaking and superconductivity

Hiroyuki Yamase, Walter Metzner

We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a $d$-wave Pomeranchuk instability and a BCS pairing interaction driving $d$-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.

arXiv:cond-mat/0701660•Physical Review B•Apr 25, 2007•55 citations

Fermi surface change across a deconfined quantum critical point

Ribhu K. Kaul, Alexei K. Kolezhuk, Michael Levin +2 more

The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.

arXiv:cond-mat/0611536•Nov 20, 2006•0 citations

Nematic order and non-Fermi liquid behavior from a Pomeranchuk instability in a two-dimensional electron system

Walter Metzner, Luca Dell’Anna, Hiroyuki Yamase

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.

Journal of Physics Conference Series•Feb 1, 2009•0 citations

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Samuel Lederer, Yoni Schattner, Erez Berg +1 more

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

arXiv:1612.01542•Proceedings of the National Academy of Sciences•Apr 24, 2017•209 citations

Non-Fermi Liquid Behavior from Critical Fermi Surface Fluctuations

Walter Metzner, Luca Dell’Anna

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.

Progress of Theoretical Physics Supplement•Jan 1, 2008•0 citations

Bond-ordered states and f -wave pairing of spinless fermions on the honeycomb lattice

Stephan Heßelmann, Daniel D. Scherer, Michael M. Scherer +1 more

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.

arXiv:1805.02490•Physical review. B./Physical review. B•Jul 31, 2018•10 citations
Abstract The nesting of the Fermi surfaces of an electron and a hole pocket separated by a vector Q commensurate with the lattice in conjunction with the interaction between the quasiparticles can give rise to a rich phase diagram. Of particular importance is itinerant antiferromagnetic order in the context of pnictides and heavy fermion compounds. By mismatching the nesting the order can gradually be suppressed and as the Néel temperature tends to zero a quantum critical point is obtained. A superconducting dome above the quantum critical point can be induced by the transfer of pairs of electrons between the pockets. The conditions under which such a dome arises are studied. In addition numerous other phases may arise, e.g. charge density waves, non‐Fermi liquid behavior, non‐s‐wave superconductivity, Pomeranchuk instabilities of the Fermi surface, nematic order, and phases with persistent orbital currents.
We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a ddd-wave Pomeranchuk instability and a BCS pairing interaction driving ddd-wave superconductivity. By tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the 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.
Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.
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.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.