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.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.

Physical Review BJan 26, 201021 citations

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

G. Hannappel, Chris Pedder, Frank Krüger +1 more

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.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.

arXiv:1601.05414Physical review. B./Physical review. BJun 2, 20161 citation

Fluctuating stripes in strongly correlated electron systems and the nematic-smectic quantum phase transition

Kai Sun, Benjamin M. Fregoso, Michael J. Lawler +1 more

We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes.'' We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective modes of the electron smectic (or stripe) phase are also investigated. The effects of the low-energy bosonic modes on the fermionic quasiparticles are studied perturbatively, for both a model with full rotational symmetry and for a system with an underlying lattice, which has a discrete point group symmetry. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, around which it is reconstructed, are not governed by a Landau Fermi liquid theory. Surprisingly, the quasiparticles in the smectic phase also exhibit non-Fermi liquid behavior. We also present a detailed analysis of the dynamical susceptibilities in the electron nematic phase close to this QCP (the fluctuating stripe regime) and in the electronic smectic phase.We discuss the quantum phase transition between a quantum nematic metallic state to an electron metallic smectic state in terms of an order-parameter theory coupled to fermionic quasiparticles. Both commensurate and incommensurate smectic (or stripe) cases are studied. Close to the quantum critical point (QCP), the spectrum of fluctuations of the nematic phase has low-energy ``fluctuating stripes.'' We study the quantum critical behavior and find evidence that, contrary to the classical case, the gauge-type of coupling between the nematic and smectic is irrelevant at this QCP. The collective modes of the electron smectic (or stripe) phase are also investigated. The effects of the low-energy bosonic modes on the fermionic quasiparticles are studied perturbatively, for both a model with full rotational symmetry and for a system with an underlying lattice, which has a discrete point group symmetry. We find that at the nematic-smectic critical point, due to the critical smectic fluctuations, the dynamics of the fermionic quasiparticles near several points on the Fermi surface, around which it is reconstructed, are not governed by a Landau Fermi liquid theory. Surprisingly, the quasiparticles in the smectic phase also exhibit non-Fermi liquid behavior. We also present a detailed analysis of the dynamical susceptibilities in the electron nematic phase close to this QCP (the fluctuating stripe regime) and in the electronic smectic phase.

arXiv:0805.3526Physical Review BAug 20, 200854 citations

Formation of an electronic nematic phase in interacting fermion systems

Igor Khavkine, Chung‐Hou Chung, Vadim Oganesyan +1 more

We study the formation of an electronic nematic phase characterized by a broken point-group symmetry in interacting fermion systems within the weak coupling theory. As a function of interaction strength and chemical potential, the phase transition between the isotropic Fermi liquid and nematic phase is first order at zero temperature and becomes second order at a finite temperature. The transition is present for all typical, including quasi-two-dimensional, electronic dispersions on the square lattice and takes place for arbitrarily small interaction when at van Hove filling, thus suppressing the Lifshitz transition. In connection with the formation of the nematic phase, we discuss the origin of the first-order transition and competition with other broken symmetry states.We study the formation of an electronic nematic phase characterized by a broken point-group symmetry in interacting fermion systems within the weak coupling theory. As a function of interaction strength and chemical potential, the phase transition between the isotropic Fermi liquid and nematic phase is first order at zero temperature and becomes second order at a finite temperature. The transition is present for all typical, including quasi-two-dimensional, electronic dispersions on the square lattice and takes place for arbitrarily small interaction when at van Hove filling, thus suppressing the Lifshitz transition. In connection with the formation of the nematic phase, we discuss the origin of the first-order transition and competition with other broken symmetry states.

arXiv:cond-mat/0402565Physical Review BOct 26, 2004102 citations

Pairing instability in a nematic Fermi liquid

Yong Baek Kim, Hae‐Young Kee

Strong interaction between fermions may lead to a novel quantum ground state where the rotational symmetry is spontaneously broken while the translational symmetry is still preserved. Such a 'nematic' Fermi liquid has a spontaneously deformed Fermi surface and supports a gapless Goldstone mode associated with the broken rotational symmetry. We consider a nematic Fermi liquid of fermions carrying two internal quantum numbers that, for example, may represent the layer degree of freedom of a bilayer system. It is found that the effective interaction mediated by a collective mode gives rise to a pairing instability of the underlying fermions under certain conditions, leading to the conclusion that the nematic order could be useful for superconductivity.Strong interaction between fermions may lead to a novel quantum ground state where the rotational symmetry is spontaneously broken while the translational symmetry is still preserved. Such a 'nematic' Fermi liquid has a spontaneously deformed Fermi surface and supports a gapless Goldstone mode associated with the broken rotational symmetry. We consider a nematic Fermi liquid of fermions carrying two internal quantum numbers that, for example, may represent the layer degree of freedom of a bilayer system. It is found that the effective interaction mediated by a collective mode gives rise to a pairing instability of the underlying fermions under certain conditions, leading to the conclusion that the nematic order could be useful for superconductivity.

arXiv:cond-mat/0204037Journal of Physics Condensed MatterApr 24, 200426 citations

Quantum criticality in a two-component two-dimensional nematic metal

Yuhang Xiao, Ning Hao

Nematic fluctuations alter the low-energy electronic behavior and reshape the mean-field phase diagram. We study a two-dimensional nematic metal with a two-component internal degree of freedom. Near the quantum critical point (QCP), longitudinal nematic fluctuations generate the non-Fermi-liquid self-energy $\propto|ω|^{2/3}$ , whereas transverse fluctuations give a subleading logarithmic, marginal-Fermi-liquid correction. Nevertheless, the transverse sector dominates the correction to the phase diagram through a quantum order-by-disorder mechanism: the emergent nematic background reshapes the electronic spectrum, alters the decay of nematic bosons, and produces a negative singular free-energy correction. This correction reconstructs the phase diagram, drives the transition first order, and is described by a scaling function whose two asymptotic limits define two critical regimes with free-energy corrections scaling as $R^{8/3}$ and $R^3$ , respectively, where $R$ is the order-parameter magnitude; their powers follow from the competition between the characteristic momentum of normal-state nematic fluctuations and that of the ordered-state background. These two regimes are experimentally distinguishable through nematic-susceptibility hysteresis measurements. The corrected phase diagram shows that the enlarged nodal $α$ phase masks the otherwise bare QCP, making it inaccessible; consequently, the logarithmic self-energy correction is by no means negligible at low energies.Nematic fluctuations alter the low-energy electronic behavior and reshape the mean-field phase diagram. We study a two-dimensional nematic metal with a two-component internal degree of freedom. Near the quantum critical point (QCP), longitudinal nematic fluctuations generate the non-Fermi-liquid self-energy $\propto|ω|^{2/3}$, whereas transverse fluctuations give a subleading logarithmic, marginal-Fermi-liquid correction. Nevertheless, the transverse sector dominates the correction to the phase diagram through a quantum order-by-disorder mechanism: the emergent nematic background reshapes the electronic spectrum, alters the decay of nematic bosons, and produces a negative singular free-energy correction. This correction reconstructs the phase diagram, drives the transition first order, and is described by a scaling function whose two asymptotic limits define two critical regimes with free-energy corrections scaling as $R^{8/3}$ and $R^3$, respectively, where $R$ is the order-parameter magnitude; their powers follow from the competition between the characteristic momentum of normal-state nematic fluctuations and that of the ordered-state background. These two regimes are experimentally distinguishable through nematic-susceptibility hysteresis measurements. The corrected phase diagram shows that the enlarged nodal $α$ phase masks the otherwise bare QCP, making it inaccessible; consequently, the logarithmic self-energy correction is by no means negligible at low energies.

arXiv:2610.29745Oct 21, 20260 citations

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.

\propto|ω|^{2/3}

, whereas transverse fluctuations give a subleading logarithmic, marginal-Fermi-liquid correction. Nevertheless, the transverse sector dominates the correction to the phase diagram through a quantum order-by-disorder mechanism: the emergent nematic background reshapes the electronic spectrum, alters the decay of nematic bosons, and produces a negative singular free-energy correction. This correction reconstructs the phase diagram, drives the transition first order, and is described by a scaling function whose two asymptotic limits define two critical regimes with free-energy corrections scaling as

R^{8/3}

and

R^3

, respectively, where

R

is the order-parameter magnitude; their powers follow from the competition between the characteristic momentum of normal-state nematic fluctuations and that of the ordered-state background. These two regimes are experimentally distinguishable through nematic-susceptibility hysteresis measurements. The corrected phase diagram shows that the enlarged nodal

α

phase masks the otherwise bare QCP, making it inaccessible; consequently, the logarithmic self-energy correction is by no means negligible at low energies.