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arXiv:1601.05414 · Physical review. B./Physical review. B

Stability of a spin-triplet nematic state near to a quantum critical point

G. Hannappel, Chris Pedder, Frank Krüger, Andrew G. Green

Published Jun 2, 2016• 1 citation
arXivHTMLPDF

Abstract

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean-field level, the interaction drives a continuous Pomeranchuk instability towards $d$-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial-rotation symmetries. This order is characterized by spin-antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is preempted by the formation of a helical spin-triplet $d$-density wave. Such a state is closely related to $d$-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, $p$-wave superconducting state.

DOI
10.1103/physrevb.93.235105

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We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean-field level, the interaction drives a continuous Pomeranchuk instability towards ddd-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial-rotation symmetries. This order is characterized by spin-antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is preempted by the formation of a helical spin-triplet ddd-density wave. Such a state is closely related to ddd-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, ppp-wave superconducting state.
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.
The possibility is investigated that competition between fluctuations at different symmetry-related ordering wave vectors may affect the quantum phase transition between a fermi liquid and a longitudinal spin density wave state, in particular, giving rise to an intermediate ``nematic'' state with broken rotational symmetry but unbroken translational symmetry. At the marginal dimension the nematic transition is found to be preempted by a first-order transition but a weak symmetry breaking field restores a second-order magnetic transition with an intermediate regime in which correlations substantially enhance the broken rotational symmetry. Comparison to recent experiments is made.
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.
The possibility is investigated that competition between fluctuations at different symmetry-related ordering wave vectors may affect the quantum phase transition between a fermi liquid and a longitudinal spin density wave state, in particular giving rise to an intermediate 'nematic' state with broken rotational symmetry but unbroken translational symmetry. At the marginal dimension the nematic transition is found to be preempted by a first order transition but a weak symmetry breaking field restores a second order magnetic transition with an intermediate regime in which correlations substantially enhance the broken rotational symmetry. Comparison to recent experiments is made.
We consider two-dimensional metals near a Pomeranchuk instability which breaks ${90}^{\ensuremath{\circ}}$ lattice rotation symmetry. Such metals realize strongly coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation and, hence, a nonzero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the ddd-wave channel acts as a random ``field'' on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.
We investigate the interplay between superconductivity and nematic order in a two-dimensional electron gas with competing pairing and quadrupolar forward-scattering interactions. The model includes both sss-wave and ddd-wave superconducting channels. We compute the mean-field free energy density and determine the phase diagrams as functions of interaction strengths and temperature by solving a set of coupled self-consistent equations. At zero-temperature, we find that the nematic order competes strongly with ddd-wave superconductivity, leading to a direct first-order phase transition, while its interplay with sss-wave pairing allows for a coexistence phase characterized by an anisotropic Fermi surface with a uniform superconducting gap. At finite-temperatures, quadrupolar interactions promote the emergence of additional superconducting components, giving rise to regimes where sss-wave, ddd-wave, and nematic orders coexist. Our results highlight the role of symmetry and interaction strength in shaping the phase structure and provide a minimal framework to describe intertwined nematic and superconducting phases in correlated electron systems.