arXiv subjects

Michael J. Lawler

Publications and source records attributed to Michael J. Lawler.

At least 37 records · Page 2Linked to original sources

arXiv2018

A classification of magnetic frustration and metamaterials from topology

We study the relationship between the physics of topology and zero modes in frustrated systems and metama- terials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kind of zero modes in form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple question: are the robust features of frustration topologically protected and if so can we classify different types of frustration using topology? In answering these questions we invoke the tools of topological mechanics to identify the key agent at play, namely the rigidity matrix, which is a non-Hermitian matrix and decides the topology of spin-wave zero modes in a frustrated magnet or phonon modes in metamaterials. Further developments of the theory rely on combining the recent developments in our understanding of Maxwell constraint counting and generalizing the ten-fold way classification of Hermitian matrices to non-Hermitian matrices. The result is a three-fold way classification for each Maxwell counting index. We illustrate the clas- sification by demonstrating the existence of a new vortex-like invariant for real rigidity matrices using random matrices and through example frustrated spin models. So by classifying all the rigidity matrices, we answer the question of the origin of frustration (i.e. zero modes in the form of accidental degeneracy) in a wide class of frustrated magnets and metamaterials by linking it to topological invariants.

cond-mat.str-el↗

arXiv2018

Magnetic-field Induced Pair Density Wave State in the Cuprate Vortex Halo

When very high magnetic fields suppress the superconductivity in underdoped cuprates, an exceptional new electronic phase appears. It supports remarkable and unexplained quantum oscillations and exhibits an unidentified density wave (DW) state. Although generally referred to as a "charge" density wave (CDW) because of the observed charge density modulations, theory indicates that this could actually be the far more elusive electron-pair density wave state (PDW). To search for evidence of a field-induced PDW in cuprates, we visualize the modulations in the density of electronic states $N(\bf{r})$ within the halo surrounding Bi$_2$Sr$_2$CaCu$_2$O$_8$ vortex cores. This reveals multiple signatures of a field-induced PDW, including two sets of $N(\bf{r})$ modulations occurring at wavevectors $\bf{Q}_P$ and $2\bf{Q}_P$, both having predominantly $s$-symmetry form factors, the amplitude of the latter decaying twice as rapidly as the former, along with induced energy-gap modulations at $\bf{Q}_P$ . Such a microscopic phenomenology is in detailed agreement with theory for a field-induced primary PDW that generates secondary CDWs within the vortex halo. These data indicate that the fundamental state generated by increasing magnetic fields from the underdoped cuprate superconducting phase is actually a PDW with approximately eight CuO$_2$ unit-cell periodicity ($λ= 8a_0$) and predominantly $d$-symmetry form factor.

cond-mat.supr-con↗

arXiv2017

Mechanism for nematic superconductivity in FeSe

Despite its seemingly simple composition and structure, the pairing mechanism of FeSe remains an open problem due to several striking phenomena. Among them are nematic order without magnetic order, nodeless gap and unusual inelastic neutron spectra with a broad continuum, and gap anisotropy consistent with orbital selection of unknown origin. Here we propose a microscopic description of a nematic quantum spin liquid that reproduces key features of neutron spectra. We then study how the spin fluctuations of the local moments lead to pairing within a spin-fermion model. We find the resulting superconducting order parameter to be nodeless $s\pm d$-wave within each domain. Further we show that orbital dependent Hund's coupling can readily capture observed gap anisotropy. Our prediction calls for inelastic neutron scattering in a detwinned sample.

cond-mat.str-el↗

arXiv2017

Properties of spin 1/2 triangular lattice antiferromagnets: CuRE2Ge2O8 (RE=Y, La)

We found new two-dimensional (2D) quantum (S=1/2) antiferromagnetic systems: CuRE2Ge2O8 (RE=Y and La). According to our analysis of high-resolution X-ray and neutron diffraction experiments, the Cu-network of CuRE2Ge2O8 (RE=Y and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular b-axis. Our bulk characterizations from 0.08 to 400 K show that they undergo a long-range order at 0.51(1) and 1.09(4) K for the Y and La systems, respectively. Interestingly, they also exhibit field induced phase transitions. For theoretical understanding, we carried out the density functional theory (DFT) band calculations to find that they are typical charge-transfer-type insulators with a gap of Eg = 2 eV. Taken together, our observations make CuRE2Ge2O8 (RE=Y and La) additional examples of low-dimensional quantum spin triangular antiferromagnets with the low-temperature magnetic ordering.

cond-mat.mtrl-sci↗

arXiv2016

Observation of semi-localized dispersive states in the strongly correlated electron-doped ferromagnet Eu$_{1-x}$Gd$_{x}$O

Chemical substitution plays a key role in controlling the electronic and magnetic properties of complex materials. For instance, in EuO, carrier doping can induce a spin-polarized metallic state, colossal magnetoresistance, and significantly enhance the Curie temperature. Here, we employ a combination of molecular-beam epitaxy, angle-resolved photoemission spectroscopy, and an effective model calculation to investigate and understand how semi-localized states evolve in lightly electron doped Eu$_{1-x}$Gd$_{x}$O above the ferromagnetic Curie temperature. Our studies reveal a characteristic length scale for the spatial extent of the donor wavefunctions which remains constant as a function of doping, consistent with recent tunneling studies of doped EuO. Our work sheds light on the nature of the semiconductor-to-metal transition in Eu$_{1-x}$Gd$_{x}$O and should be generally applicable for doped complex oxides.

cond-mat.str-el↗

arXiv2016

Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems

Half-filled Landau levels form a zoo of strongly correlated phases. These include non-Fermi liquids (NFL), fractional quantum Hall (FQH) states, nematic phases, and FQH nematic phases. This diversity poses the question: what keeps the balance between the seemingly unrelated phases? The answer is elusive because the Halperin-Lee-Read (HLR) description that offers a natural departure point is inherent strongly coupled. But the observed nematic phases suggest nematic fluctuations play an important role. To study this possibility, we apply a recently formulated controlled double expansion approach in large-$N$ composite fermion flavors and small $ε$ non-analytic bosonic action to the case with both gauge and nematic boson fluctuations. In the vicinity of a nematic quantum critical line (NQCL), we find that depending on the amount of screening of the gauge- and nematic-mediated interactions controlled by $ε$'s, the RG flow points to all four mentioned correlated phases. When pairing preempts the nematic phase, NFL behavior is possible at temperatures above the pairing transition. We conclude by discussing measurements at low tilt angles which could reveal the stabilization of the FQH phase by nematic fluctuations.

cond-mat.str-el↗

arXiv2016

Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets

I generalize the theory of phonon topological band structures of isostatic lattices to frustrated antiferromagnets. I achieve this with a discovery of a many-body supersymmetry (SUSY) in the phonon problem of balls and springs and its connection to local constraints satisfied by ground states. The Witten index of the SUSY model demands the Maxwell-Calladine index of mechanical structures. "Spontaneous supersymmetry breaking" is identified as the need to gap all modes in the bulk to create the topological isostatic lattice state. Since ground states of magnetic systems also satisfy local constraint conditions (such as the vanishing of the total spin on a triangle) I identify a similar SUSY structure for many common models of antiferromagnets including the square, triangluar, kagome, pyrochlore nearest neighbor antiferromagnets, and the $J_2 = J_1/2$ square lattice antiferromagnet. Remarkably, the kagome family of antiferromagnets is the analog of topological isostatic lattices among this collections of models. Thus, a solid state realization of the theory of phonon topological band structure may be found in frustrated magnetic materials.

cond-mat.str-el↗

arXiv2016

Topological Superconductivity in Metal/Quantum-Spin-Ice Heterostructures

The original proposal to achieve superconductivity by starting from a quantum spin-liquid (QSL) and doping it with charge carriers, as proposed by Anderson in 1987, has yet to be realized. Here we propose an alternative strategy: use a QSL as a substrate for heterostructure growth of metallic films to design exotic superconductors. By spatially separating the two key ingredients of superconductivity, i.e., charge carriers (metal) and pairing interaction (QSL), the proposed setup naturally lands on the parameter regime conducive to a controlled theoretical prediction. Moreover, the proposed setup allows us to "customize" electron-electron interaction imprinted on the metallic layer. The QSL material of our choice is quantum spin ice well-known for its emergent gauge-field description of spin frustration. Assuming the metallic layer forms an isotropic single Fermi pocket, we predict that the coupling between the emergent gauge-field and the electrons of the metallic layer will drive topological odd-parity pairing. We further present guiding principles for materializing the suitable heterostructure using ab initio calculations and describe the band structure we predict for the case of Y$_2$Sn$_{2-x}$Sb$_x$O$_7$ grown on the (111) surface of Pr$_2$Zr$_2$O$_7$. Using this microscopic information, we predict topological odd-parity superconductivity at a few Kelvin in this heterostructure, which is comparable to the $T_c$ of the only other confirmed odd-parity superconductor Sr$_2$RuO$_4$.

cond-mat.str-el↗

arXiv2015

Decision making by Berry's flux

Order by disorder is a decision making process for frustrated systems but often leads to simple answers. We study order by disorder in the kagome Kondo model known for its complexity seeking rich decision making capabilities. At half filling and large Kondo coupling to hopping ratio $J_K/t$, the full manifold of 120$^o$ kagome ground states are degenerate at second order in $t/J_K$. We show this degeneracy lifts at sixth order when a fermion can hop around a hexagon and feel the Berry flux induced by a given spin texture. Using Monte-Carlo we then seek the ground state of this sixth order Hamiltonian and find in a 4x4 unit cell system that a co-planar 2x4 unit cell order is selected over the $\sqrt{3}\times\sqrt{3}$, $q=0$ and cuboc1 states, a result that survives even in the thermodynamic limit. This state is selected for its SU(2) flux properties induced by the spin texture and is analogous to the integer quantum Hall effect. Given the existence of numerous quantum Hall plateaus in other systems, the existence of this 2x4 unit cell state suggests that complex decision making is possible on the manifold of 120$^o$ states and achievable in different kagome-Kondo models.

cond-mat.str-el↗

arXiv2015

Spin liquid phases of Mott insulating ultracold bosons

Mott insulating ultracold gases posses a unique whole-atom exchange interaction which enables large quantum fluctuations between the Zeeman sublevels of each atom. By strengthening this interaction---either through the use of large-spin atoms, or by tuning the particle-particle interactions via optical Feshbach resonance---one may enhance fluctuations and facilitate the appearance of the long sought-after quantum spin liquid phase---all in the highly tunable environment of cold atoms. To illustrate the relationship between the spin magnitude, interaction strength, and resulting magnetic phases, we present and solve a mean field theory for bosons optically confined to the one particle-per-site Mott state, using both analytic and numerical methods. We find on a square lattice with bosons of hyperfine spin $f>2$, that making the repulsive s-wave scattering length through the singlet channel small---relative to the higher-order scattering channels---accesses a short-range resonating valence bond (s-RVB) spin liquid phase.

cond-mat.quant-gas↗

arXiv2015

Phase diagram of the Kondo lattice model on the Kagome lattice

We consider the potential for novel forms of magnetism arising from the subtle interplay between electrons and spins in the under-screened kagome Kondo lattice model. At weak coupling, we show that incommensurate non-coplanar multi-wave vector magnetic orders arise at nearly all fillings and that this results from Fermi surface effects that introduces competing interactions between the spins. At strong coupling, we find that such complex order survives near half filling despite the presence of ferromagnetism at all other fillings. We show this arises due to state selection among a massive degeneracy of states at infinite coupling. Finally, we show that at intermediate filling, only commensurate orders seem to survive. But these orders still include non-coplanar magnetism. So, the mere presence of both local moments and itinerant electrons enables complex orders to form unlike any currently observed in kagome materials.

cond-mat.str-el↗

arXiv2015

Anomalous Scaling of the Penetration Depth in Nodal Superconductors

Recent findings of anomalous super-linear scaling of low temperature ($T$) penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates which are poster child nodal superconductors have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points. Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group calculation for the problem of two dimensional superconductors with point nodes, we show that quantum critical fluctuations associated with point group symmetry reduction result in non-universal logarithmic corrections to the $T$-dependence of the PD. The resulting apparent power law depends on the bare velocity anisotropy ratio. We then compare our results to data sets from two distinct nodal superconductors: YBa$_2$Cu$_3$O$_{6.95}$ and CeCoIn$_5$. Considering all symmetry-lowering possibilities of the point group of interest, $C_{4v}$, we find our results to be remarkably consistent with YBa$_2$Cu$_3$O$_{6.95}$ being near vertical nematic QCP, and CeCoIn$_5$ being near diagonal nematic QCP. Our results motivate search for diagonal nematic fluctuations in CeCoIn$_5$.

cond-mat.str-el↗

arXiv2013

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.

cond-mat.str-el↗

arXiv2012

Striped spin liquid crystal ground state instability of kagome antiferromagnets

The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to $Z_2$. Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-Paratacamite suggesting it may already be realized in these materials.

cond-mat.str-el↗

arXiv2012

Electronic Liquid Crystal Physics of Underdoped Cuprates

Recent observations of broken symmetries have partly demystified the pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC) nematic order and its unexpectedly strong coupling to the phase of the fluctuating stripes in the pseudogap states of underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. In particular, we focus on the analysis techniques that reveal this evidence in scanning tunneling spectroscopy data, the definition of the extracted IUC nematic order parameter, and a phenomenological theory of the coupling between the IUC nematic order and the previously reported coexisting fluctuating stripes. We also present a microscopic mechanism of IUC nematic order driven by on-site and near-neighbor repulsions. Finally we discuss open questions in the context of these results.

cond-mat.supr-con↗

arXiv2012

Picometer Registration of Zinc Impurity States in Bi2Sr2CaCu2O8+d for Phase Determination in Intra-unit-cell Fourier Transform STM

Direct visualization of electronic-structure symmetry within each crystalline unit cell is a new technique for complex electronic matter research. By studying the Bragg peaks in Fourier transforms of electronic structure images, and particularly by resolving both the real and imaginary components of the Bragg amplitudes, distinct types of intra-unit cell symmetry breaking can be studied. However, establishing the precise symmetry point of each unit cell in real space is crucial in defining the phase for such Bragg-peak Fourier analysis. Exemplary of this challenge is the high temperature superconductor Bi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, while it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry point. Here we demonstrate, by imaging with picometer precision the electronic impurity states at individual Zn atoms substituted at Cu sites, that the phase established using the Bi lattice produces a ~2% (2pi) error relative to the actual Cu lattice. Such a phase assignment error would not diminish reliability in the determination of intra-unit-cell rotational symmetry breaking at the CuO2 plane. Moreover, this type of impurity atom substitution at the relevant symmetry site can be of general utility in phase determination for Bragg-peak Fourier analysis of intra-unit-cell symmetry.

cond-mat.supr-con↗

arXiv2011

Spectroscopic Imaging STM Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High-Tc Superconductors

One of the key motivations for the development of atomically resolved spectroscopic imaging STM (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E|=Δ0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k=\pm(π/a0,0) to k=\pm(0, π/a0). In both the dSC and PG phases, the only broken symmetries detected in the |E|\leq Δ0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E| Δ1 which is associated conventionally with the 'antinodal' states near k=\pm(π/a0,0) and k=\pm(0, π/a0). We find that these states break the 90o-rotational (C4) symmetry of electronic structure within CuO2 unit cells, at least down to 180o rotational (C2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C4 symmetry breaking coexists at |E| Δ1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The properties of these two classes of |E| Δ1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E| Δ1 and |E|\leqΔ0, and to understand how this impacts the electronic phase diagram and the mechanism of high-Tc superconductivity, represents one of a key challenges for cuprate studies.

cond-mat.supr-con↗

arXiv2010

Spin-charge interplay in electronic liquid crystals: fluctuating spin stripe driven by charge nematic

We study the interplay between charge and spin ordering in electronic liquid crystalline states with a particular emphasis on fluctuating spin stripe phenomena observed in recent neutron scattering experiments\cite{Hinkov2008, Haug2009}. Based on a phenomenological model, we propose that charge nematic ordering is indeed behind the formation of temperature dependent incommensurate inelastic peaks near wavevector $(π,π)$ in the dynamic structure factor of YBa$_2$Cu$_3$O$_{6+y}$. We strengthen this claim by providing a compelling fit to the experimental data which cannot be reproduced by a number of other ordering possibilities.

cond-mat.str-el↗