Research

18 pages, 2471 KiB

Open AccessFeature PaperArticle

Simulations of Dynamical Electronic Vortices in Charge and Spin Density Waves

by Natasha Kirova and Serguei Brazovskii

Symmetry 2023, 15(4), 915; https://doi.org/10.3390/sym15040915 - 14 Apr 2023

Viewed by 1199

Charge and spin density waves are typical symmetry broken states of quasi one-dimensional electronic systems. They demonstrate such common features of all incommensurate electronic crystals as a spectacular non-linear conduction by means of the collective sliding and susceptibility to the electric field. These [...] Read more.

Charge and spin density waves are typical symmetry broken states of quasi one-dimensional electronic systems. They demonstrate such common features of all incommensurate electronic crystals as a spectacular non-linear conduction by means of the collective sliding and susceptibility to the electric field. These phenomena ultimately require for emergence of static and transient topological defects: there are dislocations as space vortices and space-time vortices known as phase slip centers, i.e., a kind of instantons. Dislocations are statically built-in under a transverse electric field; their sweeping provides a conversion among the normal carriers and condensate which ensures the onset of the collective sliding. A special realization in a high magnetic field, when the density wave is driven by the Hall voltage, originated by quantized normal carriers, reveals the dynamic vorticity serving to annihilate compensating normal and collective currents. Spin density waves, with their rich multiplicative order parameter, bring to life complex objects with half-integer topologically bound vorticities in charge and spin degrees of freedom. We present the basic concepts and modelling results of the stationary states and their transient dynamics involving vorticity. The models take into account multiple fields in their mutual non-linear interactions: the complex order parameter, the self-consistent electric field, and the reaction of normal carriers. We explore the traditional time-dependent Ginzburg–Landau approach and introduce its generalization allowing the treatment of intrinsic normal carriers. The main insights and illustrations come from numerical solutions to partial differential equations for the dissipative dynamics of one and two space dimensions. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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15 pages, 2453 KiB

Open AccessArticle

Pattern Formation and Aggregation in Ensembles of Solitons in Quasi One-Dimensional Electronic Systems

by Petr Karpov and Serguei Brazovskii

Symmetry 2022, 14(5), 972; https://doi.org/10.3390/sym14050972 - 10 May 2022

Cited by 2 | Viewed by 1102

Abstract

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex [...] Read more.

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex order parameter

A exp (i θ)

gives rise to phase vortices, amplitudes solitons, and their combinations. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge doping. The long-range ordering in dimensions above one imposes super-long-range confinement forces upon the solitons, leading to a sequence of phase transitions in their ensembles. The higher-temperature T transition enforces the confinement of solitons into topologically bound complexes: pairs of kinks or the amplitude solitons dressed by exotic half-integer vortices. At a second lower T transition, the solitons aggregate into rods of bi-kinks or into walls of amplitude solitons terminated by rings of half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. Here, we summarize results of a numerical modeling for different symmetries, for charged and neutral soliton, in two and three dimensions. The efficient Monte Carlo algorithm, preserving the number of solitons, was employed which substantially facilitates the calculations, allowing to extend them to the three-dimensional case and to include the long-range Coulomb interactions. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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10 pages, 3034 KiB

Open AccessFeature PaperArticle

Electronic Dislocation Dynamics in Metastable Wigner Crystal States

by Andrej Kranjec, Petr Karpov, Yevhenii Vaskivskyi, Jaka Vodeb, Yaroslav Gerasimenko and Dragan Mihailovic

Symmetry 2022, 14(5), 926; https://doi.org/10.3390/sym14050926 - 01 May 2022

Cited by 2 | Viewed by 1684

Abstract

Metastable states appear in many areas of physics as a result of symmetry-breaking phase transitions. An important challenge is to understand the microscopic mechanisms which lead to the formation of the energy barrier separating a metastable state from the ground state. In this [...] Read more.

Metastable states appear in many areas of physics as a result of symmetry-breaking phase transitions. An important challenge is to understand the microscopic mechanisms which lead to the formation of the energy barrier separating a metastable state from the ground state. In this paper, we describe an experimental example of the hidden metastable domain state in 1T-TaS₂, created by photoexcitation or carrier injection. The system is an example of a charge density wave superlattice in the Wigner crystal limit displaying discommensurations and domain formation when additional charge is injected either through contacts or by photoexcitation. The domain walls and their crossings in particular display interesting, topologically entangled structures, which have a crucial role in the metastability of the system. We model the properties of experimentally observed thermally activated dynamics of topologically protected defects—dislocations—whose annihilation dynamics can be observed experimentally by scanning tunnelling microscopy as emergent phenomena described by a doped Wigner crystal. The different dynamics of trivial and non-trivial topological defects are quite striking. Trivial defects appear to annihilate quite rapidly at low temperatures on the timescale of the experiments, while non-trivial defects annihilate rarely, if at all. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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15 pages, 5661 KiB

Open AccessArticle

Assessing Bound States in a One-Dimensional Topological Superconductor: Majorana versus Tamm

by Lucia Vigliotti, Fabio Cavaliere, Matteo Carrega and Niccolò Traverso Ziani

Symmetry 2021, 13(6), 1100; https://doi.org/10.3390/sym13061100 - 21 Jun 2021

Cited by 1 | Viewed by 2003

Abstract

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. Here, we study a model in which [...] Read more.

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. Here, we study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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Review

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26 pages, 8612 KiB

Open AccessReview

Tracking Defects of Electronic Crystals by Coherent X-ray Diffraction

by David Le Bolloc’h, Ewen Bellec, Natacha Kirova and Vincent L. R. Jacques

Symmetry 2023, 15(7), 1449; https://doi.org/10.3390/sym15071449 - 20 Jul 2023

Cited by 1 | Viewed by 1183

Abstract

In this article, we review different studies based on advanced X-ray diffraction techniques—especially coherent X-ray diffraction—that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and Spin density Wave (SDW), through their local phase. After a brief [...] Read more.

In this article, we review different studies based on advanced X-ray diffraction techniques—especially coherent X-ray diffraction—that allowed us to reveal the behaviour of such symmetry-breaking systems as Charge Density Wave (CDW) and Spin density Wave (SDW), through their local phase. After a brief introduction on the added value of using coherent X-rays, we show how the method can be applied to CDW and SDW systems, in both static and dynamical regimes. The approach allowed us to probe the particular sliding state of CDWs systems by observing them through their phase fluctuations, to which coherent X-rays are particularly sensitive. Several compounds stabilizing a CDW phase able to slide are presented, each with a different but clearly pronounced signature of the sliding state. Two main features emerge from this series of experiments which have been little treated until now, the influence of CDW pinning by the sample surfaces and the propagation of periodic phase defects such as charge solitons across the entire sample. Phase models describing the spatial and temporal properties of sliding CDWs are presented in the last part of this review. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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27 pages, 8555 KiB

Open AccessFeature PaperReview

Topological Excitations in Neutral–Ionic Transition Systems

by Keishi Sunami, Ryosuke Takehara, Kazuya Miyagawa, Hiroshi Okamoto and Kazushi Kanoda

Symmetry 2022, 14(5), 925; https://doi.org/10.3390/sym14050925 - 01 May 2022

Cited by 2 | Viewed by 6137

Abstract

The existence and physical properties of topological excitations in ferroelectrics, especially mobile topological boundaries in one dimension, are of profound interest. Notably, topological excitations emerging in association with the neutral–ionic (NI) phase transition are theoretically suggested to carry fractional charges and cause anomalous [...] Read more.

The existence and physical properties of topological excitations in ferroelectrics, especially mobile topological boundaries in one dimension, are of profound interest. Notably, topological excitations emerging in association with the neutral–ionic (NI) phase transition are theoretically suggested to carry fractional charges and cause anomalous charge transport. In recent years, we experimentally demonstrated mobile topological excitations in a quasi-one-dimensional (1D) ferroelectric, tetrathiafulvalene-p-chloranil [TTF-CA; TTF (C₆H₄S₄) and CA (C₆Cl₄O₂)], which shows the NI transition, using NMR, NQR, and electrical resistivity measurements. Thermally activated topological excitations carry charges and spins in the NI crossover region and in the ionic phase with a dimer liquid. Moreover, free solitons show a binding transition upon a space-inversion symmetry-breaking ferroelectric order. In this article, we review the recent progress in the study of mobile topological excitations emerging in TTF-CA, along with earlier reports that intensively studied these phenomena, aiming to provide the foundations of the physics of electrical conductivity and magnetism carried by topological excitations in the 1D ferroelectric. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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13 pages, 940 KiB

Open AccessReview

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

by John M. Tranquada

Symmetry 2021, 13(12), 2365; https://doi.org/10.3390/sym13122365 - 08 Dec 2021

Cited by 7 | Viewed by 2924

Abstract

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with [...] Read more.

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La

_{2 - x}

Ba

_{x}

CuO

_{4}

with

x = 1 / 8

. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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Other

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8 pages, 2103 KiB

Open AccessPerspective

Scanning Probe Microscopy Investigation of Topological Defects

by Jan Seidel

Symmetry 2022, 14(6), 1098; https://doi.org/10.3390/sym14061098 - 27 May 2022

Cited by 3 | Viewed by 1663

Abstract

Symmetry lowering phase transitions in ferroelectrics, magnets, and materials with various other forms of inherent order lead to the formation of topological defects. Their non-trivial real-space topology is characterized by a topological charge, which represents the topological invariant. The study of topological defects [...] Read more.

Symmetry lowering phase transitions in ferroelectrics, magnets, and materials with various other forms of inherent order lead to the formation of topological defects. Their non-trivial real-space topology is characterized by a topological charge, which represents the topological invariant. The study of topological defects in such materials has seen increased interest over the last decade. Among the methods used for their study, scanning probe microscopy (SPM) with its many variants has provided valuable new insight into these structures at the nanoscale. In this perspective, various approaches are discussed, and different techniques are compared with regard to their ability to investigate topological defect properties. Full article

(This article belongs to the Special Issue Topological Objects in Correlated Electronic Systems)

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