Confined coherence in quasi-one-dimensional metals

We present a functional renormalization group calculation of the effect of strong interactions on the shape of the Fermi surface of weakly coupled metallic chains. In the regime where the bare interchain hopping is small, we show that scattering processes involving large momentum transfers perpendicular to the chains can completely destroy the warping of the true Fermi surface, leading to a confined state where the renormalized interchain hopping vanishes and a coherent motion perpendicular to the chains is impossible.Comment: 4 RevTex pages, 5 figures,final version as published by PR

Effect of Electron-Electron Interactions on Rashba-like and Spin-Split Systems

The role of electron-electron interactions is analyzed for Rashba-like and spin-split systems within a tight-binding single-band Hubbard model with on-site and all nearest-neighbor matrix elements of the Coulomb interaction. By Rashba-like systems we refer to the Dresselhaus and Rashba spin-orbit coupled phases; spin-split systems have spin-up and spin-down Fermi surfaces shifted relative to each other. Both systems break parity but preserve time-reversal symmetry. They belong to a class of symmetry-breaking ground states that satisfy: (i) electron crystal momentum is a good quantum number (ii) these states have no net magnetic moment and (iii) their distribution of `polarized spin' in momentum space breaks the lattice symmetry. In this class, the relevant Coulomb matrix elements are found to be nearest-neighbor exchange $J$, pair-hopping $J'$ and nearest-neighbor repulsion $V$. These ground states lower their energy most effectively through $J$, hence we name them Class $J$ states. The competing effects of $V-J'$ on the direct and exchange energies determine the relative stability of Class $J$ states. We show that the spin-split and Rashba-like phases are the most favored ground states within Class $J$ because they have the minimum anisotropy in `polarized spin'. On a square lattice we find that the spin-split phase is always favored for near-empty bands; above a critical filling, we predict a transition from the paramagnetic to the Rashba-like phase at $J_{c1}$ and a second transition to the spin-split state at $J_{c2}>J_{c1}$. An energetic comparison with ferromagnetism highlights the importance of the role of $V$ in the stability of Class $J$ states. We discuss the relevance of our results to (i) the $\alpha$ and $\beta$ phases proposed by Wu and Zhang in the Fermi Liquid formalism and (ii) experimental observations of spin-orbit splitting in \emph{Au}(111) surface states

Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.Comment: 18 pages, 8 figure

Spontaneous Fermi surface symmetry breaking in bilayered 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.Comment: 18 pages, 7 figure

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 Sr3Ru2O7, and future issues are discussed to establish such a scenario.Comment: 28 pages, 9 figure

Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice

We analyze a mean-field model of electrons with pure forward scattering interactions on a square lattice which exhibits spontaneous Fermi surface symmetry breaking with a d-wave order parameter: the surface expands along the kx-axis and shrinks along the ky-axis (or vice versa). The symmetry-broken phase is stabilized below a dome-shaped transition line Tc(mu), with a maximal Tc near van Hove filling. The phase transition is usually first order at the edges of the transition line, and always second order around its center. The d-wave compressibility of the Fermi surface is however strongly enhanced even near the first order transition down to zero temperature. In the weak coupling limit the phase diagram is fully determined by a single non-universal energy scale, and hence dimensionless ratios of different characteristic quantities are universal. Adding a uniform repulsion to the forward scattering interaction, the two tricritical points at the ends of the second order transition line are shifted to lower temperatures. For a particularly favorable choice of hopping and interaction parameters one of the first order edges is replaced completely by a second order transition line, leading to a quantum critical point.Comment: 23 pages, 8 figure

Probing the d_{x2-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_{x2-y2}-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 Sr3Ru2O7 which is a potential candidate for a Pomeranchuk instability at its metamagnetic transition in strong magnetic fields.Comment: 14 pages, 12 figure

Pomeranchuk Instability in a non-Fermi Liquid from Holography

The Pomeranchuk instability, in which an isotropic Fermi surface distorts and becomes anisotropic due to strong interactions, is a possible mechanism for the growing number of experimental systems which display transport properties that differ along the $x$ and $y$ axes. We show here that the gauge-gravity duality can be used to describe such an instability in fermionic systems. Our holographic model consists of fermions in a background which describes the causal propagation of a massive neutral spin-two field in an asymptotically AdS spacetime. The Fermi surfaces in the boundary theory distort spontaneously and become anisotropic once the neutral massive spin-two field develops a normalizable mode in the bulk. Analysis of the fermionic correlators reveals that the low-lying fermionic excitations are non-Fermi liquid-like both before and after the Fermi surface shape distortion. Further, the spectral weight along the Fermi surface is angularly dependent and can be made to vanish along certain directions.Comment: Updated version to appear in PRD. New version has WKB analysis of spectral intensity in ordered phas

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.Comment: 14 pages, 10 figure

Electrical resistivity near Pomeranchuk instability in two dimensions

We analyze the DC charge transport in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. The transport decay rate is linear in temperature everywhere on the Fermi surface except at cold spots on the Brillouin zone diagonal. For pure systems, this leads to a DC resistivity proportional to T^{3/2} in the low-temperature limit. In the presence of impurities the residual impurity resistance at T=0 is approached linearly at low temperatures.Comment: 9 pages, no figure