Pomeranchuk Instability Research Articles

Probing thedx2−y2-wave Pomeranchuk instability by ultrasound

Selection rules of ultrasound attenuation and sound-velocity renormalization are analyzed in view of their potential application to identify Pomeranchuk instabilities (electronic nematic phase). It is shown that the transverse sound attenuation along [110] direction is enhanced by the Fermi-surface fluctuations near a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave Pomeranchuk instability, while the attenuation along [100] direction remains unaffected. Moreover the fluctuation regime above the instability is analyzed by means of a self-consistent renormalization scheme. The results could be applied directly to ${\text{Sr}}_{3}{\text{Ru}}_{2}{\text{O}}_{7}$ which is a potential candidate for a Pomeranchuk instability at its metamagnetic transition in strong magnetic fields.

Multiscale quantum criticality: Pomeranchuk instability in isotropic metals

As a paradigmatic example of multiscale quantum criticality, we consider the Pomeranchuk instability of an isotropic Fermi liquid in two spatial dimensions, $d=2$. The corresponding Ginzburg-Landau theory for the quadrupolar fluctuations of the Fermi surface consists of two coupled modes, critical at the same point, and characterized by different dynamical exponents: one being ballistic with dynamical exponent $z=2$ and the other one is Landau damped with $z=3$, thus giving rise to multiple dynamical scales. We find that at temperature $T=0$, the ballistic mode governs the low-energy structure of the theory as it possesses the smaller effective dimension $d+z$. Its self-interaction leads to logarithmic singularities, which we treat with the help of the renormalization group. At finite temperature, the coexistence of two different dynamical scales gives rise to a modified quantum-to-classical crossover. It extends over a parametrically large regime with intricate interactions of quantum and classical fluctuations leading to a universal $T$ dependence of the correlation length independent of the interaction amplitude. The multiple scales are also reflected in the phase diagram and in the critical thermodynamics. In particular, we find that the latter cannot be interpreted in terms of only a single dynamical exponent whereas, e.g., the critical specific heat is determined by the $z=3$ mode, the critical compressibility is found to be dominated by the $z=2$ fluctuations.

Erratum: Electrical Resistivity near Pomeranchuk Instability in Two Dimensions [Phys. Rev. Lett.98, 136402 (2007)

Erratum: Electrical Resistivity near Pomeranchuk Instability in Two Dimensions [Phys. Rev. Lett.<b>98</b>, 136402 (2007)

Ultracold gases of ytterbium: ferromagnetism and Mott states in an SU(6) Fermi system

It is argued that an ultracold quantum degenerate gas of ytterbium 173Yb atoms having nuclear spin I=5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU(n>2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU(n) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU(n>2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.

Spontaneous Fermi surface symmetry breaking in bilayer systems

We perform a comprehensive numerical study of d-wave Fermi surface deformations (dFSD) on a square lattice, the so-called d-wave Pomeranchuk instability, including bilayer coupling. Since the order parameter corresponding to the dFSD has Ising symmetry, there are two stacking patterns between the layeres, (+,+) and (+,-). This additional degree of freedom gives rise to a rich variety of phase diagrams. The phase diagrams are classified by means of the energy scale Lambda_{z}, which is defined as the bilayer splitting at the saddle points of the in-plane band dispersion. As long as Lambda_{z} ne 0, a major stacking pattern is usually (+,-), and (+,+) stacking is stabilized as a dominant pattern only when the temperature scale of the dFSD instability becomes much smaller than Lambda_z. For Lambda_{z}=0, the phase diagram depends on the precise form of the bilayer dispersion. We also analyze the effect of a magnetic field on the bilayer model in connection with a possible dFSD instability in the bilyared ruthenate Sr_3Ru_2O_7.

Generalized Pomeranchuk instabilities in graphene

We study the presence of Pomeranchuk instabilities induced by interactions on a Fermi-liquid description of a graphene layer. Using a recently developed generalization of the Pomeranchuk method, we present a phase diagram in the space of fillings versus on-site and nearest-neighbors interactions. We find that for both interactions being repulsive, an instability region exists near the Van Hove filling, in agreement with earlier theoretical work. In contrast, near-half filling, the Fermi-liquid behavior appears to be stable, in agreement with theoretical results and experimental findings using angle-resolved photoemission spectroscopy. The method allows for a description of the phase diagram for arbitrary filling.

Self-Masking of Spontaneous Symmetry Breaking in Layer Materials

We study d-wave Fermi-surface deformations (dFSD), the so-called Pomeranchuk instability, on bilayer and infinite-layer square lattices. Since the order parameter of the dFSD has Ising symmetry, there are two stacking patterns along the c axis: (+, +) and (+, -). We find that, as long as the c axis dispersion is finite at the saddle points of the in-plane band dispersion, the (+, -) stacking is usually favored independently on the details of interlayer coupling, yielding no macroscopic anisotropy. The dFSD provides unique spontaneous symmetry breaking that is self-masked in layer materials.

Theory of reduced singlet pairing without the underlying state of charge stripes in the high-temperature superconductorYBa2Cu3O6.45

Recently, a strongly enhanced $xy$ anisotropy of magnetic excitations was observed in ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{y}$ $({\text{YBCO}}_{y})$, with $y=6.45$ and ${T}_{c}=35\text{ }\text{K}$ [V. Hinkov et al., Science 319, 597 (2008)]. Unlike the observation in ${\text{YBCO}}_{6.6}$ and ${\text{YBCO}}_{6.85}$, the anisotropy grows to be pronounced at lower temperature and at lower energy and is not suppressed by the onset of superconductivity. We propose that the effect of singlet pairing is substantially reduced in ${\text{YBCO}}_{6.45}$. This reduction concomitantly enhances an order competing with singlet pairing, a strong tendency of the so-called $d$-wave Pomeranchuk instability, leading to the magnetic excitations observed experimentally.

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

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 T3/2 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.

Pomeranchuk instability in doped graphene

The density of states of graphene has van Hove singularities that can be reached by chemical doping and have already been explored in photoemission experiments. We show that in the presence of Coulomb interactions the system at the van Hove filling is likely to undergo a Pomeranchuk instability breaking the lattice point group symmetry. In the presence of an on-site Hubbard interaction the system is also unstable toward ferromagnetism. We explore the competition of the two instabilities and build the phase diagram. We also suggest that, for doping levels where the trigonal warping is noticeable, the Fermi liquid state in graphene can be stable up to zero temperature avoiding the Kohn–Luttinger mechanism and providing an example of a two-dimensional Fermi liquid at zero temperature.

Symmetry-breaking Fermi surface deformations from central interactions in two dimensions

We present a mean-field theory of the Pomeranchuk instability in two dimensions, starting from a generic central interaction potential described in terms of a few microscopic parameters. For a significant range of parameters, the instability is found to be pre-empted by a first-order quantum phase transition. We provide the ground-state phase diagram in terms of our generic parameters.

Competition between Pomeranchuk instabilities in the nematic and hexatic channels in a two-dimensional spinless Fermi fluid

We study the competition between the nematic and the hexatic phases of a two-dimensional spinless Fermi fluid near Pomeranchuk instabilities. We show that the general phase diagram of this theory contains a bicritical point where two second-order lines and a first-order nematic/hexatic phase transition meet together. We found that at criticality and deep inside the associated symmetry broken phases, the low energy theory is governed by a dissipative cubic mode, even near the bicritical point where nematic and hexatic fluctuations cannot be distinguished due to very strong dynamical couplings.

Cuprate superconductors in the vicinity of a Pomeranchuk instability

We propose that cuprate superconductors are in the vicinity of a spontaneous d -wave type Fermi surface symmetry breaking, often called a d -wave Pomeranchuk instability. This idea is explored by means of a comprehensive study of magnetic excitations within the slave-boson mean-field theory of the t – J model. We can naturally understand the pronounced xy anisotropy of magnetic excitations in untwinned YBa 2 Cu 3 O y and the sizable change of incommensurability of magnetic excitations at the transition temperature to the low-temperature tetragonal lattice structure in La 2 - x Ba x CuO 4 . In addition, the present theoretical framework allows the understanding of the similarities and differences of magnetic excitations in Y-based and La-based cuprates.

Non-Fermi Liquid Behavior from Critical Fermi Surface Fluctuations

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.

Electronic Higher Multipoles in Solids

This tutorial review discusses basic features of electronic multipoles and their ordering phenomena. Starting with classification of electric and magnetic higher multipoles under spherical symmetry, we proceed to two representative cases with strong spin-orbit interaction. First, staggered octupole orders in Ce1−xLaxB6 and SmRu4P12 are discussed using the crystalline electric field states. Secondly, a scalar component of even higher multipoles in Pr skutterudites is studied where ordering of fourth-rank tensor (hexadecapole) and sixth-rank one (hexacontatetrapole) has been observed. Possibility of a reentrant transition from the multipole ordered state is discussed. Briefly mentioned are multipole aspects of Pomeranchuk instability of itinerant electrons and collective motion of nucleus. It is argued that the multipoles provide a new framework to study the metal-insulator transition.

Pomeranchuk instability: Symmetry-breaking and experimental signatures

We discuss the emergence of symmetry-breaking via the Pomeranchuk instability from interactions that respect the underlying point-group symmetry. We use a variational mean-field theory to consider a 2D continuum and a square lattice. We describe two experimental signatures: a symmetry-breaking pattern of Friedel oscillations around an impurity; and a structural transition.

Theory of spontaneous Fermi surface symmetry breaking for [formula omitted

We show that many salient features observed around the metamagnetic transition in Sr 3 Ru 2 O 7 are described within a simple model, which considers only an instability of the Fermi surface symmetry breaking (Pomeranchuk instability), without invoking a putative metamagnetic quantum critical end point as usually assumed for this compound. In our model, the Pomeranchuk instability and unconventional, non-Fermi liquid type properties arise due to the tuning of the van Hove singularity of either a majority or a minority spin band to the vicinity of the Fermi energy by a magnetic field. The obtained phase diagram, the metamagnetic transition, and the temperature dependence of the magnetic susceptibility and specific heat show striking similarities to the experimental data.

Effect of magnetic field on spontaneous Fermi-surface symmetry breaking

We study magnetic field effects on spontaneous Fermi-surface symmetry breaking with $d$-wave symmetry, the so-called $d$-wave ``Pomeranchuk instability.'' We use a mean-field model of electrons with a pure forward scattering interaction on a square lattice. When either the majority or the minority spin band is tuned close to the van Hove filling by a magnetic field, the Fermi-surface symmetry breaking occurs in both bands, but with a different magnitude of the order parameter. The transition is typically of second order at high temperature and changes to first order at low temperature; the end points of the second order line are tricritical points. This qualitative picture does not change even in the limit of a large magnetic field, although the magnetic field substantially suppresses the transition temperature at the van Hove filling. The field produces neither a quantum critical point nor a quantum critical end point in our model. In the weak coupling limit, typical quantities characterizing the phase diagram have a field-independent single energy scale, while its dimensionless coefficient varies with the field. The field-induced Fermi-surface symmetry breaking is a promising scenario for the bilayer ruthenate ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, and open questions are discussed to establish such a scenario.

Competition of Fermi surface symmetry breaking and superconductivity

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. 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.

Theory of the in-plane anisotropy of magnetic excitations in YBa 2Cu 3O 6+ y

A pronounced xy-anisotropy was observed in recent neutron scattering experiments for magnetic excitations in untwinned YBa 2Cu 3O 6+ y (YBCO). The small anisotropy of the bare band structure due to the orthorhombic crystal symmetry seems to be enhanced by correlation effects. A natural possibility is that the system is close to a Pomeranchuk instability associated with a d-wave Fermi surface deformation (dFSD). We investigate this possibility in the bilayer t– J model within a self-consistent slave-boson mean-field theory. We show that the dFSD correlations drive a pronounced xy-anisotropy of magnetic excitations at low doping and at relatively high temperatures, providing a scenario for the observed xy-anisotropy in optimally doped as well as underdoped YBCO, including the pseudogap phase.