Broken Translational Symmetry Research Articles

Stability of the Weyl-semimetal phase on the pyrochlore lattice

Motivated by the proposal of a Weyl-semimetal phase in pyrochlore iridates, we consider a Hubbard-type model on the pyrochlore lattice. To shed light on the question as to why such a state has not been observed experimentally, its robustness is analyzed. On the one hand, we study the possible phases when the system is doped. Magnetic frustration favors several phases with magnetic and charge order that do not occur at half filling, including additional Weyl-semimetal states close to quarter filling. On the other hand, we search for density waves that break translational symmetry and destroy the Weyl-semimetal phase close to half filling. The uniform Weyl semimetal is found to be stable, which we attribute to the low density of states close to the Fermi energy.

Primordial standing waves

We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial translational invariance, and isolate the pieces of the most general such theory that comply with, or break translational symmetry. We find that, in order to characterize statistically translationally invariant standing waves, it is essential to consider the correlator $\langle c_0({\mathbf k}) c_0({\mathbf k}')\rangle$ in addition to the better known $\langle c_0({\mathbf k}) c_0^\dagger({\mathbf k}')\rangle$ (where $c_0({\mathbf k})$ are the complex amplitudes of travelling waves). We then examine how the standard process of "squeezing" (responsible for converting travelling waves into standing waves while the fluctuations are outside the horizon) reacts to being fed primordial standing waves. For translationally invariant systems only one type of standing wave, with the correct temporal phase (the "sine wave"), survives squeezing. Primordial standing waves might therefore be invisible at late times -- or not -- depending on their phase. Theories with modified dispersion relations behave differently in this respect, since only standing waves with the opposite temporal phase survive at late times.

Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at $J^{\rm dim}_{\rm c} \approx 0.89t$ frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a $90^{\circ}$ quantum spin spiral with quasi-long-range order at $J^{\rm mag}_{\rm c} \approx 0.84t$. The quantum-critical point is characterized by a closure of the spin gap (with decreasing $J$) and a divergence of the spin-correlation length and of the spin-structure factor $S(q)$ at wave vector $q=\pi/2$. This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all $J>0$ at half-filling.

High field charge order across the phase diagram of YBa2Cu3Oy

In hole-doped cuprates there is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry. In YBa2Cu3Oy charge order emerges in two steps: a 2D order found at zero field and at high temperature inside the pseudogap phase, and a 3D order that is superimposed below the superconducting transition Tc when superconductivity is weakened by a magnetic field. Several issues still need to be addressed such as the effect of disorder, the relationship between those charge orders and their respective impact on the Fermi surface. Here, we report high magnetic field sound velocity measurements of the 3D charge order in underdoped YBa2Cu3Oy in a large doping range. We found that the 3D charge order exists over the same doping range as its 2D counterpart, indicating an intimate connection between the two distinct orders. Moreover, our data suggest that 3D charge order has only a limited impact on low-lying electronic states of YBa2Cu3Oy.

Impact of local symmetry breaking on the physical properties of tetrahedral liquids

Water and silica are the most important materials with local tetrahedral symmetry. They have similar crystalline polymorphs and exhibit anomalous density maximum in the liquid state. However, water and silica also show very different characteristics. For instance, the density of water varies much more sharply than that of liquid silica near the maximum as temperature changes. More notably, silica is a very good glass-former, but water is an extremely poor one. The physical origins of these similarities and differences still remain elusive, due to the lack of a microscopic understanding of the structural ordering in these two important liquids. Here, by accessing microscopic structural information by computer simulations, we reveal that local translational symmetry breaking is responsible for the density anomalies. On the other hand, the difference in the degree of local orientational symmetry breaking between water and silica, which originates from the difference in their bonding nature, causes not only the difference in the sharpness of density anomalies, but also their distinct glass-forming abilities. Our work not only shows the crucial roles of local translational and orientational symmetry breaking in the physical properties of the two extremely important materials, water and silica, but also provides a unified scenario applicable for other tetrahedral liquids such as Si, Ge, C, BeF2, and GeO2.

Pinning of longitudinal phonons in holographic spontaneous helices

We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode — a longitudinal phonon — in a holographic model with Bianchi VII helical symmetry. For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup. We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature. In addition, we extract the optical conductivity as a function of frequency, which reveals a metal-insulator transition as a consequence of the pinning.

Activation of B1 silent Raman modes and its potential origin as source for phonon-assisted replicas in photoluminescence response in N-doped ZnO nanowires

ZnO nanowires are grown by metal organic chemical vapor deposition using two different zinc precursors, i.e., dimethylzinc-triethylamine which contains nitrogen, and diethylzinc which does not. The growth conditions are varied using different oxygen/zinc pressure ratios (RO/Zn). Temperature dependent Raman spectroscopy shows that the additional Raman modes are related to B1 modes which are activated because of translational symmetry breaking resulting from the nitrogen substitution on oxygen sites and/or Zn-O bond breaking caused by complex defects. Simultaneously, the antiparallel atomic displacements which are at the origin of B1 phonon vibrations are no more compensated, allowing B1 modes to acquire a polar character. The resulting polar phonons, and especially B12 located at 580 cm−1 (i.e., 72 meV), are therefore believed to strongly couple to photogenerated electrons through a Fröhlich mechanism and could lead or contribute to the phonon-assisted replicas observed in the photoluminescence (PL) spectrum. Finally, we also discuss the possible defects involved in the Raman and PL responses including native donor and acceptor defects and their interaction with the N-dopant, depending on the growth conditions.

Black hole elasticity and gapped transverse phonons in holography

We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons — the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.

Activated Wetting of Nanostructured Surfaces: Reaction Coordinates, Finite Size Effects, and Simulation Pitfalls.

A liquid in contact with a textured surface can be found in two states, Wenzel and Cassie. In the Wenzel state the liquid completely wets the corrugations while in the Cassie state the liquid is suspended over the corrugations with air or vapor trapped below. The superhydrophobic properties of the Cassie state are exploited for self-cleaning, drag reduction, drug delivery, etc., while in the Wenzel state most of these properties are lost; it is therefore of great fundamental and technological interest to investigate the kinetics and mechanism of the Cassie-Wenzel transition. Computationally, the Cassie-Wenzel transition is often investigated using enhanced sampling ("rare events") techniques based on the use of collective variables (CVs). The choice of the CVs is a crucial task because it affects the free-energy profile, the estimation of the free-energy barriers, and the evaluation of the mechanism of the process. Here we investigate possible simulation artifacts introduced by common CVs adopted for the study of the Cassie-Wenzel transition: the average particle density in the corrugation of a textured surface and the coarse-grained density field at various levels of coarse graining. We also investigate possible additional artifacts associated with finite size effects. We focus on a pillared surface, a system often used in technological applications. We show that the use of a highly coarse-grained density (a single CV) of the fluid in the interpillar region brings to severe artifacts: errors of hundreds of kBT in the difference of free energy between the Cassie and Wenzel states, of tens of kBT in the estimate of the free-energy barriers, and erroneous wetting mechanisms. A proper description of the wetting mechanism and its energetics apparently requires a fine discretization of the density field. Concerning the finite-size effects, we have found that the typical systems employed in simulations of the Cassie-Wenzel transition, containing a single pillar within periodic boundary conditions, prevent the complete break of translational symmetry of the liquid-vapor meniscus during the process. Capturing this break of symmetry is crucial for describing the transition state along the wetting process and the early stage of the opposite process, the Wenzel-Cassie transition.

Achieving High Thermoelectric Figure of Merit in Polycrystalline SnSe via Introducing Sn Vacancies.

Thermoelectric power generation technology has emerged as a clean "heat engine" that can convert heat to electricity. Recently, the discovery of an ultrahigh thermoelectric figure of merit in SnSe crystals has drawn a great deal of attention. In view of their facile processing and scale-up applications, polycrystalline SnSe materials with ZT values comparable to those of the SnSe crystals are greatly desired. Here we achieve a record high ZT value ∼2.1 at 873 K in polycrystalline Sn1-xSe with Sn vacancies. We demonstrate that the carrier concentration increases by artificially introducing Sn vacancies, contributing significantly to the enhancements of electrical conductivity and thermoelectric power factor. The detailed analysis of the data in the light of first-principles calculations results indicates that the increased carrier concentration can be attributed to the Sn-vacancy-induced Fermi level downshift and the interplay between the vacancy states and valence bands. Furthermore, vacancies break translation symmetry and thus enhance phonon scattering, leading to extralow thermal conductivity. Such high ZT value ∼2.1 is achieved by synergistically optimizing both electrical- and thermal-transport properties of polycrystalline SnSe. The vast increase in ZT for polycrystalline SnSe may accelerate practical applications of this material in highly effective solid-state thermoelectric devices.

Time Crystal Behavior of Excited Eigenstates.

In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Wilczek, spontaneous breaking of time translation symmetry cannot be observed if one starts with the ground state. We point out that the symmetry breaking can take place if the system is prepared in an excited eigenstate. The latter can be realized experimentally in ultracold atomic gases. We simulate the process of the spontaneous symmetry breaking due to measurements of particle positions and analyze the lifetime of the resulting symmetry broken state.

Spontaneous ordering at the free surface of molecular clusters

The present paper seeks to establish a theoretical framework to account for the spontaneous molecular ordering at free surfaces of molecular aggregates. It is shown that within a multipole representation of the molecular interactions, ordering is the effect of the interplay of two fundamental causes: the translational symmetry breaking of the bulk phase at the interface and the interactions of multipoles of different parity. Quantitative analysis of the order parameter demonstrates the building up of ordering at different length scales with range depending on the strength of the interactions.

Pinning of holographic sliding stripes

In a holographic probe-brane model exhibiting a spontaneously spatially modulated ground state, we introduce explicit sources of symmetry breaking in the form of ionic and antiferromagnetic lattices. For the first time in a holographic model, we demonstrate pinning, in which the translational Goldstone mode is lifted by the introduction of explicit sources of translational symmetry breaking. The numerically computed optical conductivity fits very well to a Drude-Lorentz model with a small residual metallicity, precisely matching analytic formulas for the DC conductivity. We also find an instability of the striped phase in the presence of a large-amplitude ionic lattice.

Raman scattering study of the tetragonal magnetic phase in Sr1−xNaxFe2As2 : Structural symmetry and electronic gap

We use inelastic light scattering to study Sr$_{1-x}$Na$_x$Fe$_2$As$_2$ ($x\approx0.34$), which exhibits a robust tetragonal magnetic phase that restores the four-fold rotation symmetry inside the orthorhombic magnetic phase. With cooling, we observe splitting and recombination of an $E_g$ phonon peak upon entering the orthorhombic and tetragonal magnetic phases, respectively, consistent with the reentrant phase behavior. Our electronic Raman data reveal a pronounced feature that is clearly associated with the tetragonal magnetic phase, suggesting the opening of an electronic gap. No phonon back-folding behavior can be detected above the noise level, which implies that any lattice translation symmetry breaking in the tetragonal magnetic phase must be very weak.

Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves.

We present a minimal bottom-up extension of the Chern-Simons bulk action for holographic translational symmetry breaking that naturally gives rise to pair density waves. We construct stationary inhomogeneous black hole solutions in which both the U(1) symmetry and spatially translational symmetry are spontaneously broken at a finite temperature and charge density. This novel solution provides a dual description of a superconducting phase intertwined with charge, current, and parity orders.

Bott periodicity for the topological classification of gapped states of matter with reflection symmetry

Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-2 and four period-8 cycles, similar to the Bott periodicity found for topological insulators and superconductors without spatial symmetries. With the help of the dimensional reduction scheme, the classification in arbitrary dimensions $d\ensuremath{\ge}1$ can be obtained from the classification in one dimension, for which we present a derivation based on relative homotopy groups and exact sequences to classify one-dimensional insulators and superconductors with reflection symmetry. The resulting classification is fully consistent with a comprehensive classification obtained recently by Shiozaki and Sato [Phys. Rev. B 90, 165114 (2014)]. The use of a scattering-matrix-inspired method allows us to address the second descendant ${\mathbb{Z}}_{2}$ phase, for which the topological nontrivial phase was previously reported to be vulnerable to perturbations that break translation symmetry.

Defect Modes Control in Coupled Magnonic Crystals

We report on the theoretical study of magnetostatic surface wave propagation through the two side-coupled 1-D magnonic crystals (MCs) with broken translational symmetry. Using the transfer matrix method, we obtained transmission and reflection coefficients. Existence of two defect modes in such four-port planar structure was shown. We consider the possibility of controlling the position of defect modes by changing coupling between MCs. Comparison between investigated structure with coupled defect-free magnonic crystals was provided.

Magnetic Properties of Fibonacci-Modulated Fe-Au Multilayer Metamaterials.

Herein we experimentally study magnetic multilayer metamaterials with broken translational symmetry. Epitaxially-grown iron-gold (Fe-Au) multilayers modulated using Fibonacci sequence—referred to as magnetic inverse Fibonacci-modulated multilayers (IFMs)—are prepared using ultra-high-vacuum vapor deposition. Experimental results of in-situ reflection high-energy electron diffraction, magnetization curves, and ferromagnetic resonance demonstrate that the epitaxially-grown Fe-Au IFMs have quasi-isotropic magnetization, in contrast to the in-plane magnetization easy axis in the periodic multilayers.

Backreacted DBI magnetotransport with momentum dissipation

We examine magnetotransport in a holographic Dirac-Born-Infeld model, taking into account the effects of backreaction on the geometry. The theory we consider includes axionic scalars, introduced to break translational symmetry and generate momentum dissipation. The generic structure of the DC conductivity matrix for these theories is extremely rich, and is significantly more complex than that obtained in the probe approximation. We find new classes of black brane solutions, including geometries that exhibit Lifshitz scaling and hyperscaling violation, and examine their implications on the transport properties of the system. Depending on the choice of theory parameters, these backgrounds can lead to metallic or insulating behavior. Negative magnetoresistance is observed in a family of dynoic solutions. Some of the new backreacted geometries also support magnetic-field-induced metal-insulator transitions.

Scanning tunneling microscopy and spectroscopy of finite-size twisted bilayer graphene

Nanoscale twisted bilayer graphene (TBG) is quite instable and will change its structure to Bernal (or AB-stacking) bilayer with a much lower energy. Therefore, the lack of nanoscale TBG makes its electronic properties not accessible in experiment up to now. In this work, a special confined TBG is obtained in the overlaid area of two continuous misoriented graphene sheets. The width of the confined region of the TBG changes gradually from about 22 nm to 0 nm. By using scanning tunnelling microscopy, we studied carefully the structure and the electronic properties of the nanoscale TBG. Our results indicate that the low-energy electronic properties, including twist-induced van Hove singularities (VHSs) and spatial modulation of local density-of-state, are strongly affected by the translational symmetry breaking of the nanoscale TBG. Whereas, the electronic properties above the energy of the VHSs are almost not influenced by the quantum confinement even when the width of the TBG is reduced to only a single moire spot.