arXiv subjects

Michael J. Lawler

Publications and source records attributed to Michael J. Lawler.

49 records · Page 3Linked to original sources

arXiv2010

Nematic Fermi Fluids in Condensed Matter Physics

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classical nematics generally occur in liquids of rod-like molecules; given that electrons are point-like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. That such phases exist in nature was established by dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007. In this paper, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

cond-mat.str-el↗

arXiv2009

Fluctuating Stripes in Strongly Correlated Electron Systems and the Nematic-Smectic Quantum Phase Transition

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. On the other hand, the quasiparticles in the smectic phase exhibit 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.

cond-mat.str-el↗

arXiv2009

Neel and Valence Bond Crystal Order on a Distorted Kagome Lattice: Implications For Zn-Paratacamite

Zn-Paratacamite is a rare spin 1/2 antiferromagnetic insulator with an ideal kagome lattice structure in part of its phase diagram. As a function of Zn doping, this material undergoes a structural distortion which relieves the frustration and introduces magnetic order in the ground state, though the precise nature of the order is not clear at this point. In this paper, we present strong evidence for Neel ordering in the strongly distorted phase of Zn-Paratacamite through the application of quantum Monte-Carlo techniques. These numerical results support a recent Schwinger-boson mean field theory of Zn-Paratacamite. For weak distortion, close to the ideal kagome limit, our results indicate a regime with no Neel order but with a broken glide-plane symmetry. For this model the glide-plane symmetry is broken by any valence bond crystal. Hence, our results lend support to recent proposals of a valence bond crystal ground state for the undistorted lattice. The phase transition between the two phases could be in the deconfined universality class if it is not a first order transition.

cond-mat.str-el↗

arXiv2008

Interference of nematic quantum critical quasiparticles: a route to the octet model

Repeated observations of inhomogeneity in cuperate superconductors[1-5] make one immediately question the existance of coherent quasiparticles(qp's) and the applicability of a momentum space picture. Yet, obversations of interference effects[6-9] suggest that the qp's maintain a remarkable coherence under special circumstances. In particular, quasi-particle interference (QPI) imaging using scanning tunneling spectroscopy revealed a highly unusual form of coherence: accumulation of coherence only at special points in momentum space with a particular energy dispersion[5-7]. Here we show that nematic quantum critical fluctuations[10], combined with the known extreme velocity anisotropy[11] provide a natural mechanism for the accumulation of coherence at those special points. Our results raise the intriguing question of whether the nematic fluctuations provide the unique mechanism for such a phenomenon.

cond-mat.supr-con↗

arXiv2008

Theory of spin nematic to spin-Peierls quantum phase transition in ultracold spin-1 atoms in optical lattices

We present a theory of the anisotropy tuned quantum phase transition between spin nematic and spin-Peierls phases in S=1 systems with significant bi-quadratic exchange interactions. Based on quantum Monte Carlo studies on finite size systems, [K. Harada et al., J. Phys. Soc. Jpn. 76, 013703 (2007)] it has been proposed that this phase transition is second order with new deconfined fractional excitations that are absent in either of the two phases [T. Grover and T. Senthil, Phys. Rev. Lett. 98, 247202 (2007)]. The possibility of a weak first order transition, however, cannot be ruled out. To elucidate the nature of the transition, we construct a large-N SO(3N) model for this phase transition and find in the $N\to\infty$ limit that the transition is generically of first order. Furthermore, we find a critical point in the 1D limit, where two transition lines, separating spin nematic, ferromagnetic, and spin-Peierls phases, meet. Our study indicates that the spin nematic phase is absent in 1D, while its correlation length diverges at the critical point. Predictions for $^{23}$Na atoms trapped in an optical lattice, where this quantum phase transition naturally arises, are discussed.

cond-mat.str-el↗

arXiv2008

Quantum order by disorder in frustrated diamond lattice antiferromagnets

We present a quantum theory of frustrated diamond lattice antiferromagnets. Considering quantum fluctuations as the predominant mechanism relieving spin frustration, we find a rich phase diagram comprising of six phases with coplanar spiral ordering in addition to the Néel phase. By computing the specific heat of these ordered phases, we obtain a remarkable agreement between $(k,k,0)$-spiral ordering and the experimental specific heat data for the diamond lattice spinel compounds MnSc$_2$S$_4$, Co$_3$O$_4$ and CoRh$_2$O$_4$, i.e. specific heat data is a strong evidence for $(k,k,0)$-spiral ordering in all of these materials. This prediction can be tested in future neutron scattering experiments on Co$_3$O$_4$ and CoRh$_2$O$_4$, and is consistent with existing neutron scattering data on MnSc$_2$S$_4$. Based on this agreement we infer a monotonically increasing relationship between frustration and the strength of quantum fluctuations.

cond-mat.str-el↗

arXiv2008

Theory of the nodal nematic quantum phase transition in superconductors

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.

cond-mat.supr-con↗

arXiv2008

Theory of Néel and Valence-Bond-Solid Phases on the Kagome Lattice of Zn-paratacamite

Recently, neutron scattering data on powder samples of Zn-paratacamite, Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_{2}$, with small Zn concentration has been interpreted as evidence for valence bond solid and Néel ordering [1]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and X-ray scattering experiments that can test our predictions.

cond-mat.str-el↗

arXiv2007

Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8

Recent experiments on the "hyper-kagome" lattice system Na$_4$Ir$_3$O$_8$ have demonstrated that it is a rare example of a three dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semi-classical limit we predict, based on large-N calculations, that an unusual $\vec q=0$ coplaner magnetically ordered ground state is stabilized with no local "weather vane" modes. This phase melts in the quantum limit and a gapped topological Z$_2$ spin liquid phase emerges. In the vicinity of this quantum phase transition, we study the dynamic spin structure factor and comment on the relevance of our results for future neutron scattering experiments.

cond-mat.str-el↗

arXiv2006

`Local' Quantum Criticality at the Nematic Quantum Phase Transition

We discuss the finite temperature properties of the fermion correlation function near the fixed point theory of the nematic quantum critical point (QCP) of a metallic Fermi system. We show that though the fixed point theory is above its upper critical dimension, the equal time fermion correlation function takes on a universal scaling form in the vicinity of the QCP. We find that in the quantum critical regime, this equal-time correlation function has an ultra local behavior in space, while the low-frequency behavior of the equal-position auto correlation function is that of a Fermi liquid up to subdominant terms. This behavior should also apply to other quantum phase transitions of metallic Fermi systems.

cond-mat.str-el↗

arXiv2006

Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments

A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal ``T-junction'' as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a non-equilibrium calculation of the quantum noise in the T-junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of $\cosθ$ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a ``bunching'' effect, while higher states in the Jain sequences exhibit an ``anti-bunching'' effect.

cond-mat.mes-hall↗

arXiv2005

Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid

We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent $z=3$. Going beyond this framework, we study the behavior of the fermion degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law $|x|^{-1} \exp(-\textrm{const.} |x|^{1/3})$ and we verify explicitely the vanishing of the fermion residue utilizing this expression. In contrast, the fermion auto-correlation function has the behavior $|t|^{-1} \exp(-{\rm const}. |t|^{-2/3})$. In this regime we also find that, at low frequency, the single-particle fermion density-of-states behaves as $N^*(ω)=N^*(0)+ B ω^{2/3} \logω+...$, where $N^*(0)$ is larger than the free Fermi value, N(0), and $B$ is a constant. These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.

cond-mat.str-el↗

arXiv2004

Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group

In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct fixed point has the form of an array of sliding Luttinger liquids which is free from superficially "irrelevant operators". Similar considerations apply to all theories with sliding symmetries.

cond-mat.mes-hall↗