Commensurate Crystal Research Articles

4He monolayer on graphene: a quantum Monte Carlo study

We revisit the problem of adsorption of a single 4He layer on graphene, focusing on the commensurate (C 1/3) crystalline phase, specifically on whether it may possess a nonzero superfluid response, and on the existence of superfluid phases, either (metastable) liquid or vacancy-doped crystalline. We make use of canonical quantum Monte Carlo simulations at zero and finite temperature, based on a realistic microscopic model of the system. Our results confirm the absence of any superfluid response in the commensurate crystal, and that no thermodynamically stable uniform phase exists at lower coverage. No evidence of a possibly long-lived, metastable superfluid phase at C 1/3 coverage is found. Altogether, the results of ground-state projection methods and finite-temperature simulations are entirely consistent.

Topologically-imposed vacancies and mobile solid 3He on carbon nanotube

Low dimensional fermionic quantum systems are exceptionally interesting because they reveal distinctive physical phenomena, including among others, topologically protected excitations, edge states, frustration, and fractionalization. Our aim was to confine 3He on a suspended carbon nanotube to form 2-dimensional Fermi-system. Here we report our measurements of the mechanical resonance of the nanotube with adsorbed sub-monolayer down to 10 mK. At intermediate coverages we have observed the famous 1/3 commensurate solid. However, at larger monolayer densities we have observed a quantum phase transition from 1/3 solid to an unknown, soft, and mobile solid phase. We interpret this mobile solid phase as a bosonic commensurate crystal consisting of helium dimers with topologically-induced zero-point vacancies which are delocalized at low temperatures. We thus demonstrate that 3He on a nanotube merges both fermionic and bosonic phenomena, with a quantum phase transition between fermionic solid 1/3 phase and the observed bosonic dimer solid.

Quantum Smectic Gauge Theory.

We present a gauge theory formulation of a two-dimensional quantum smectic and its relatives, motivated by their realizations in correlated quantum matter. The description gives a unified treatment of phonons and topological defects, respectively, encoded in a pair of coupled gauge fields and corresponding charges. The charges exhibit subdimensional constrained quantum dynamics and anomalously slow highly anisotropic diffusion of disclinations inside a smectic. This approach gives a transparent description of a multistage quantum melting transition of a two-dimensional commensurate crystal (through an incommensurate crystal-a supersolid) into a quantum smectic, which subsequently melts into a quantum nematic and isotropic superfluids, all in terms of a sequence of Higgs transitions.

Excited-state Wigner crystals.

Wigner crystals (WCs) are electronic phases peculiar to low-density systems, particularly in the uniform electron gas. Since its introduction in the early twentieth century, this model has remained essential to many aspects of electronic structure theory and condensed-matter physics. Although the (lowest-energy) ground-state WC (GSWC) has been thoroughly studied, the properties of excited-state WCs (ESWCs) are basically unknown. To bridge this gap, we present a well-defined procedure to obtain an entire family of ESWCs in a one-dimensional electron gas using a symmetry-broken mean-field approach. While the GSWC is a commensurate crystal (i.e., the number of density maxima equals the number of electrons), these ESWCs are incommensurate crystals exhibiting more or less maxima. Interestingly, they are lower in energy than the (uniform) Fermi fluid state. For some of these ESWCs, we have found asymmetrical band gaps, which would lead to anisotropic conductivity. These properties are associated with unusual characteristics in their electronic structure.

Elastic constants of incommensurate solid4He from diffusion Monte Carlo simulations

We study the elastic properties of incommensurate solid ${}^{4}$He in the limit of zero temperature. Specifically, we calculate the pressure dependence of the five elastic constants (${C}_{11}$, ${C}_{12}$, ${C}_{13}$, ${C}_{33}$, and ${C}_{44}$), longitudinal and transversal speeds of sound, and the $T=0$ Debye temperature of incommensurate and commensurate hcp ${}^{4}$He using the diffusion Monte Carlo method. Our results show that under compression, the commensurate crystal is globally stiffer than the incommensurate, however at pressures close to melting (i.e., $P\ensuremath{\sim}25$ bar) some of the elastic constants accounting for strain deformations of the hcp basal plane (${C}_{12}$ and ${C}_{13}$) are slightly larger in the incommensurate solid. Also, we find that upon the introduction of tiny concentrations of point defects, the shear modulus of ${}^{4}$He (${C}_{44}$) undergoes a small reduction.

Path-integral ground-state Monte Carlo study of two-dimensional solidHe4

We have studied a two-dimensional (2D) triangular commensurate crystal of $^{4}\mathrm{He}$ with the exact $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ path-integral ground-state (PIGS) Monte Carlo method. We have projected onto the true ground state two qualitatively different wave functions, a Jastrow-Nosanow wave function and a translationally invariant shadow wave function. The PIGS method passes this hard test of validity and applicability by obtaining the convergence to the same properties, both the diagonal ones as well as the off-diagonal one-body density matrix ${\ensuremath{\rho}}_{1}$. Thus, the commensurate 2D $^{4}\mathrm{He}$ crystal at $T=0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is exactly solved, we find no Bose-Einstein condensation (BEC), and ${\ensuremath{\rho}}_{1}$ shows a dominant exponential decay in the large distance range. The structure found in ${\ensuremath{\rho}}_{1}$ is due to virtual vacancy-interstitial pairs and this shows up in the momentum distribution. Our result indicates that BEC in 2D solid $^{4}\mathrm{He}$ can only arise in the presence of some kind of disorder, either intrinsic or extrinsic.

Quantum Monte Carlo study of a two-species bosonic Hubbard model

We consider a two-species hard-core boson Hubbard model for a supersolid, where the two types of bosons represent vacancies and interstitials doped into a commensurate crystal. The on-site inter-species interaction may create bound states of vacancies and interstitials facilitating vacancy condensation at lower energies than in a single-species model, as suggested in an earlier mean field study. Here we carry out quantum Monte Carlo simulation to study possible supersolid phases of the model, corresponding to superfluid phases of the vacancies or interstitials. At low temperatures, we find three distinct superfluid phases. The extent of the phases and the nature of the phase transitions are discussed in comparison to mean-field theory.

Growth of single crystals belonging to a family of one-dimensional oxides: commensurate and incommensurate structures

Mixtures of alkaline earth carbonates together with nickel or copper oxide and iridium, ruthenium, platinum or rhodium metal in a carbonate flux at 1050–1150°C leads to the formation of black crystals. These crystals, whose habit is either hexagonal plates or hexagonal rods, belong to a family of perovskite related phases of general composition [A] x [(A′,B)O 3]. Preliminary diffraction experiments indicate that these crystals form with a composite structure, some commensurate and others incommensurate. The structures of the commensurate crystals were determined by single-crystal X-ray diffraction, while the structures of the incommensurate crystals are being investigated by powder diffraction. Several commensurate and incommensurate single crystals and their growth conditions are discussed in this paper.

Incommensurate modulation and the crystal structure of ganophyllite

Incommensurate modulation in ganophyllite crystals was investigated with selected-area electron diffraction (SAED), high-resolution transmission electron microscopy (HRTEM), analytical electron microscopy (AEM), and single-crystal X-ray diffraction (XRD) techniques. The XRD data were used to perform a new subcell (a = 5.550 Å, b = 13.539 Å, c = 25.134 Å, β = 93.928°) refinement of the structure with a higher precision than previous refinements (R = 0.041). Although supercell reflections were too weak for collection with the diffractometer, the supercell was modeled by comparing experimental SAED patterns and HRTEM images to their simulated counterparts. These simulations indicate that incommensurate modulation arises from offsets in the location of inverted tetrahedra between adjacent [100] strips. The true supercell of incommensurate crystals involves a tripling of the subcell a axis and at least a twelvefold increase in the b axis; previously identified supercell reflections are actually aggregates of extremely closely spaced reflections in incommensurate crystals. Unlike commensurate crystals, the subcell c axis of incommensurate ganophyllite is not doubled. AEM data suggest that the occurrence of commensurate or incommensurate forms is not compositionally dependent.

Towards a more comprehensive crystallography

Despite the intrinsic difference from the point of view of structure of various types of crystals, such as commensurate, incommensurately modulated, intergrowth crystals and quasicrystals, a common approach to their symmetry seems to be possible which eventually will lead to a more comprehensive crystallography. The unifying elements become apparent through treatments which, at first, seem to be contradictory with the geometry of the crystal structures involved. Examples are the description of aperiodic crystals in terms of lattice-periodic structures (going beyond three-dimensionality), the investigation of scaling symmetry in quasicrystals by means of a Z-module of translations generating a dense set of translationally equivalent atomic positions (going beyond discreteness) and finally the characterization of Euclidean properties of normal crystals through non-Euclidean symmetries (going beyond Euclidean metric). These changing approaches do not modify, however, the fundamental nature of crystals to be three-dimensional, discrete and Euclidean. They only allow implicit symmetry groups like the superspace groups (unifying the crystallography of incommensurate and commensurate crystals) and the multimetrical space groups (unifying the possible symmetries of quasicrystals and normal crystals) to be made explicit. Aspects of crystal diffraction, morphology and crystal structure are presented from this unifying point of view, without intending to cover the whole crystallography.

Uniaxial incommensurate overlayers with two-component displacement vector

Uniaxial structures which consist of commensurate adatom rows are considered. According to experiment these structures are in the incommensurate state compressed normal to the rows and frequently tilted due to a shift of the rows parallel to each other. A simple theoretical model of these structures of constructed. For the ground state of this model both tilted and untilted phases are found. The possible phase transitions are considered. Upon heating at fixed coverage there can be phase transitions from untilted incommensurate to commensurate or disordered phases, and from tilted incommensurate to untilted incommensurate or disordered phases. Upon a change of coverage at constant temperature a commensurate crystal can undergo phase transformations to a commensurate structure with vacancies, to a fluid phase, or to an incommensurate untilted phase, depending on the system parameters. Possible phase diagrams are constructed.

Vacancy ordered phases and one-dimensional quasiperiodicity

The metastable vacancy ordered phases observed in aluminium transition metal alloys on rapid solidification or vapour deposition can be considered as a periodic arrangement of a truncated quasiperiodic string based on the Fibonacci sequence along the 〈111〉 stacking direction of the original CsCl cell. Using the projection formalism developed in the context of quasicrystals, the diffraction patterns of the vacancy ordered phases are calculated for both commensurate and incommensurate projection from a periodic cubic cell in four dimensions. These are compared with experimentally observed patterns. It is shown that at increasingly longer periodicity the patterns from commensurate crystals become indistinguishable from the truly quasiperiodic one. It is suggested that there is a strong link between vacancy ordered phases and quasicrystals.