Spelling suggestions: "subject:"dreiecksgitter"" "subject:"dreiecksgittern""
1 |
Das Hubbard-Modell auf dem anisotropen und isotropen Dreieckgitter in der Fluktuations-Austausch-NäherungRenner, Marcus Wolfgang. Unknown Date (has links) (PDF)
Techn. Universiẗat, Diss., 2004--Braunschweig.
|
2 |
Mesh compressionGumhold, Stefan. Unknown Date (has links) (PDF)
University, Diss., 2000--Tübingen.
|
3 |
Epitaxy and Spectroscopy of Two-Dimensional Adatom Systems: the Elemental Topological Insulator Indenene on SiC / Epitaxie und Spektroskopie zweidimensionaler Adatom Systeme: der elementare Topologische Isolator Indenene auf SiCBauernfeind, Maximilian Josef Xaver January 2023 (has links) (PDF)
Two-dimensional (2D) topological insulators are a new class of materials with properties that are
promising for potential future applications in quantum computers. For example, stanene represents
a possible candidate for a topological insulator made of Sn atoms arranged in a hexagonal
lattice. However, it has a relatively fragile low-energy spectrum and sensitive topology. Therefore,
to experimentally realize stanene in the topologically non-trivial phase, a suitable substrate
that accommodates stanene without compromising these topological properties must be found.
A heterostructure consisting of a SiC substrate with a buffer layer of adsorbed group-III elements
constitutes a possible solution for this problem. In this work, 2D adatom systems of Al and In
were grown epitaxially on SiC(0001) and then investigated structurally and spectroscopically by
scanning tunneling microscopy (STM) and photoelectron spectroscopy.
Al films in the high coverage regime \( (\Theta_{ML}\approx2\) ML\( ) \) exhibit unusually large, triangular- and
rectangular-shaped surface unit cells. Here, the low-energy electron diffraction (LEED)
pattern is brought into accordance with the surface topography derived from STM. Another Al
reconstruction, the quasi-one-dimensional (1D) Al phase, exhibits a striped surface corrugation,
which could be the result of the strain imprinted by the overlayer-substrate lattice mismatch.
It is suggested that Al atoms in different surface areas can occupy hexagonal close-packed and
face-centered cubic lattice sites, respectively, which in turn lead to close-packed transition regions
forming the stripe-like corrugations. On the basis of the well-known herringbone reconstruction
from Au(111), a first structural model is proposed, which fits well to the structural data from
STM. Ultimately, however, thermal treatments of the sample could not generate lower coverage
phases, i.e. in particular, a buffer layer structure.
Strong metallic signatures are found for In high coverage films \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) by
scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES),
which form a \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \) surface reconstruction. In all these In phases
electrons follow the nearly-free electron model. Similar to the Al films, thermal treatments could
not obtain the buffer layer system.
Surprisingly, in the course of this investigation a triangular In lattice featuring a \( (1\times1) \)
periodicity is observed to host massive Dirac-like bands at \( K/K^{\prime} \) in ARPES. Based on this
strong electronic similarity with graphene at the Brillouin zone boundary, this new structure is
referred to as \textit{indenene}. An extensive theoretical analysis uncovers the emergence of an electronic
honeycomb network based on triangularly arranged In \textit{p} orbitals. Due to strong atomic spin-orbit
coupling and a comparably small substrate-induced in-plane inversion symmetry breaking this
material system is rendered topologically non-trivial. In indenene, the topology is intimately
linked to a bulk observable, i.e., the energy-dependent charge accumulation sequence within the
surface unit cell, which is experimentally exploited in STS to confirm the non-trivial topological
character. The band gap at \( K/K^{\prime} \), a signature of massive Dirac fermions, is estimated by
ARPES to approximately 125 meV. Further investigations by X-ray standing wave, STM, and
LEED confirm the structural properties of indenene. Thus, this thesis presents the growth and
characterization of the novel quantum spin Hall insulator material indenene. / Zweidimensionale (2D) topologische Isolatoren sind eine neue Materialklasse mit vielversprechenden
Eigenschaften für potenzielle zukünftige Anwendungen in Quantencomputern. Stanene stellt
hier beispielsweise einen möglichen Kandidaten für einen topologischen Isolator dar. Diese 2D-Schicht
besteht aus Sn-Atomen, angeordnet in einem hexagonalen Gitter. Allerdings weist
dieses Gitter ein relativ fragiles Niederenergiespektrum und eine empfindliche Topologie auf.
Um Stanene daher in der topologisch nicht-trivialen Phase experimentell realisieren zu können,
muss ein geeignetes Substrat gefunden werden, das Stanene aufnehmen kann, ohne die topologischen
Eigenschaften zu beeinträchtigen. Eine Heterostruktur aus einem SiC-Substrat mit
einer Pufferschicht aus adsorbierten Gruppe-III Elementen stellt hier eine mögliche Lösung für
dieses Problem dar. Im Hinblick darauf wurden für diese Arbeit 2D-Adatomsysteme aus Al und
In epitaktisch auf SiC(0001) gewachsen und mittels Rastertunnelmikroskopie (engl.: scanning
tunneling microscopy, STM) und Photoelektronenspektroskopie strukturell und spektroskopisch
untersucht.
Al-Schichten mit hoher Bedeckung \( (\Theta_{ML}\approx2\) ML\( ) \) weisen ungewöhnlich große, dreieckig
und rechteckig geformte Oberflächeneinheitszellen auf. Hierbei wird das Beugungsmuster der
niederenergetischen Elektronenbeugung (engl.: low-energy electron diffraction, LEED) mit der
aus STM abgeleiteten Oberflächentopographie in Einklang gebracht. Eine andere Al-Rekonstruktion,
die quasi-eindimensionale (1D) Al-Phase, zeigt eine gestreifte Oberflächenkorrugation, die
ein Ergebnis der Verspannung durch die Fehlanpassung des Al-Gitters auf dem Substratgitter
sein könnte. Es wird vorgeschlagen, dass Al-Atome in verschiedenen Oberflächenbereichen sowohl
jeweils hexagonal-dichtgepackte als auch kubisch flächenzentrierte Gitterplätze einnehmen können.
In Übergangsregionen zwischen beiden Bereichen erzeugt dies dicht gepackte Al-Atome,
die wiederum die streifenartigen Korrugationen hervorrufen. Auf der Basis der bekannten Fischgrätenrekonstruktion
von Au(111) wird ein erstes Strukturmodell vorgeschlagen, das gut mit
strukturellen STM-Daten übereinstimmt. Letztendlich konnten jedoch durch thermische Behandlungen
der Probe keine Phasen mit geringerer Bedeckung, das heißt insbesondere die Pufferschichtstruktur,
erzeugt werden.
In-Hochbedeckungsphasen \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) weisen ein ausgeprägtes metallisches Verhalten
auf in der Rastertunnelspektroskopie (engl.: scanning tunneling spectroscopy, STS) und
winkelaufgelösten Photoelektronenspektroskopie (engl.: angle-resolved photoelectron spectroscopy,
ARPES). Zudem bilden diese Phasen eine \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \)-Oberflächenrekonstruktion
aus. In all diesen Phasen folgen die Elektronen dem Modell der quasifreien Elektronen. Ähnlich zu den
Al-Filmen konnte auch hier nach thermischen Behandlungen der Probe keine Pufferschichtstruktur erzeugt werden.
Überraschenderweise tritt im Laufe dieser Untersuchung ein Dreiecksgitter aus In-Atomen
mit einer \( (1\times1) \)-Periodizität auf, das bei \( K/K^{\prime} \) massive Dirac-artige Bänder in ARPES zeigt.
Aufgrund der starken Ähnlichkeit mit der Graphene-Bandstruktur am Brillouinzonenrand, wird
dieses neuartige Materialsystem \textit{Indenene} benannt. Eine umfangreiche theoretische Untersuchung
legt die Entstehung eines elektronischen Honigwabennetzwerks offen, dass sich aufgrund von
dreieckig angeordneten In \textit{p}-Orbitalen bildet. Durch starke atomare Spin-Bahn-Wechselwirkung
und einen vergleichsweisen schwachen substratinduzierten Inversionssymmetriebruch in der Ebene,
ist dieses Materialsystem topologisch nicht-trivial. In Indenene ist die Topologie eng mit einer
Volumenobservablen, genauer die energieabhängige Ladungsakkumulationsequenz innerhalb der
Oberflächeneinheitszelle, verknüpft. Diese Sequenz wird mittels STS experimentell ausgenutzt,
um den topologisch nicht-trivialen Charakter zu bestätigen. Die Bandlücke bei \( K/K^{\prime} \), charakteristisch
für massive Dirac-Fermionen, wird mittels ARPES auf ungefähr 125 meV abgeschätzt.
Weitere Untersuchungen basierend auf stehenden Röntgenwellen, STM, und LEED bestätigen die
strukturellen Eigenschaften von Indenene. Dementsprechend wird in dieser Arbeit dasWachstum
und auch die Charakterisierung des neuartigen Quanten Spin Hall Isolators Indenene vorgestellt.
|
4 |
Geometric algorithms for object placement and planarity in a terrainRay, Rahul. Unknown Date (has links) (PDF)
University, Diss., 2004--Saarbrücken.
|
5 |
Fractional Moments and Singular Field ResponseWollny, Alexander 07 March 2017 (has links) (PDF)
In this PhD thesis, the physics of vacancies in two-dimensional ordered Heisenberg antiferromagnets is investigated. We use semi-classical methods to study the influence of a single vacancy in long-range ordered states, with a focus on non-collinear order. Here, on a classical level, a magnetic distortion is created as the spins readjust in response to the vacancy.
We use the non-collinear $120^\\circ$ state on the frustrated triangular lattice as an example, where we determine the impurity contributions to the magnetization and susceptibility. An important discovery is the vacancy moment not being quantized due to non-universal partial screening. The resulting effective moment $m_0 \\ll S$ can be observed as a fractional prefactor to an impurity-induced Curie response $m_0^2/(3k_BT)$ at finite temperature. This is in sharp contrast to collinearly ordered states. Here the moment is always quantized to the bulk spin value, $m_0=S$.
Furthermore, we present a detailed analysis of the vacancy-induced distortion cloud. Due to Goldstone modes, it decays algebraically as $r^{-3}$ with distance $r$ to the vacancy. Using leading-order $1/S$-expansion, we determine the quantum corrections to both size and direction of the distorted magnetic moments.
Secondly, we study the same problem in the presence of an external magnetic field $h$, both for the square and triangular lattice. For the triangular lattice we use a biquadratic exchange term $K$ to stabilize a unique ground state from a degenerate manifold. The finite-field vacancy moment $m(h)$ is generated by field-dependent screening clouds, as different non-collinear bulk states evolve with increasing field. These distortion clouds decay exponentially on a magnetic length scale $l_h\\propto 1/h$. Most importantly, we find that the magnetic-field linear-response limit $h \\rightarrow 0^+$ is generically singular for $SU(2)$ ordered local-moment antiferromagnets, as the vacancy moment in zero field differs fundamentally from even an infinitesimal but finite field, $m(h \\rightarrow 0^+)\\neq m_0$.
Moreover, a part of the screening cloud itself becomes universally singular. Particularly for spin-flop states, this leads to a semi-classical version of perfect screening. We present general arguments to support these claims, as well as microscopic calculations. Another remarkable result is an impurity-induced quantum phase transition for overcompensated vacancies in the $M=1/3$ plateau phase on the triangular lattice with $K<0$. We close our analysis with a discussion about important limits for finite vacancy concentrations, as well as a possible experimental verification of our predictions.
|
6 |
Ab initio insights into the electronic structure of 3d-systems with linear coordination and triangular-lattice 4f -systemsZangenehpourzadeh, Ziba 13 January 2021 (has links)
This work outlines the numerical strategies for two sets of problems of great importance in correlated materials research. First, we analyze the electronic structure and magnetic properties of 3d transition metals with linear coordination. Second, we study the mutiplet structure of 4f ions arranged on the 2D triangular-lattice.
|
7 |
Fractional Moments and Singular Field Response: Vacancies in Two-Dimensional Ordered AntiferromagnetsWollny, Alexander 07 March 2017 (has links)
In this PhD thesis, the physics of vacancies in two-dimensional ordered Heisenberg antiferromagnets is investigated. We use semi-classical methods to study the influence of a single vacancy in long-range ordered states, with a focus on non-collinear order. Here, on a classical level, a magnetic distortion is created as the spins readjust in response to the vacancy.
We use the non-collinear $120^\\circ$ state on the frustrated triangular lattice as an example, where we determine the impurity contributions to the magnetization and susceptibility. An important discovery is the vacancy moment not being quantized due to non-universal partial screening. The resulting effective moment $m_0 \\ll S$ can be observed as a fractional prefactor to an impurity-induced Curie response $m_0^2/(3k_BT)$ at finite temperature. This is in sharp contrast to collinearly ordered states. Here the moment is always quantized to the bulk spin value, $m_0=S$.
Furthermore, we present a detailed analysis of the vacancy-induced distortion cloud. Due to Goldstone modes, it decays algebraically as $r^{-3}$ with distance $r$ to the vacancy. Using leading-order $1/S$-expansion, we determine the quantum corrections to both size and direction of the distorted magnetic moments.
Secondly, we study the same problem in the presence of an external magnetic field $h$, both for the square and triangular lattice. For the triangular lattice we use a biquadratic exchange term $K$ to stabilize a unique ground state from a degenerate manifold. The finite-field vacancy moment $m(h)$ is generated by field-dependent screening clouds, as different non-collinear bulk states evolve with increasing field. These distortion clouds decay exponentially on a magnetic length scale $l_h\\propto 1/h$. Most importantly, we find that the magnetic-field linear-response limit $h \\rightarrow 0^+$ is generically singular for $SU(2)$ ordered local-moment antiferromagnets, as the vacancy moment in zero field differs fundamentally from even an infinitesimal but finite field, $m(h \\rightarrow 0^+)\\neq m_0$.
Moreover, a part of the screening cloud itself becomes universally singular. Particularly for spin-flop states, this leads to a semi-classical version of perfect screening. We present general arguments to support these claims, as well as microscopic calculations. Another remarkable result is an impurity-induced quantum phase transition for overcompensated vacancies in the $M=1/3$ plateau phase on the triangular lattice with $K<0$. We close our analysis with a discussion about important limits for finite vacancy concentrations, as well as a possible experimental verification of our predictions.
|
8 |
Advanced Cluster Methods for Correlated-Electron SystemsFischer, André 12 January 2016 (has links) (PDF)
In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear.
Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects.
Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom.
For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results.
Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.
|
9 |
Advanced Cluster Methods for Correlated-Electron SystemsFischer, André 27 October 2015 (has links)
In this thesis, quantum cluster methods are used to calculate electronic properties of correlated-electron systems. A special focus lies in the determination of the ground state properties of a 3/4 filled triangular lattice within the one-band Hubbard model. At this filling, the electronic density of states exhibits a so-called van Hove singularity and the Fermi surface becomes perfectly nested, causing an instability towards a variety of spin-density-wave (SDW) and superconducting states. While chiral d+id-wave superconductivity has been proposed as the ground state in the weak coupling limit, the situation towards strong interactions is unclear.
Additionally, quantum cluster methods are used here to investigate the interplay of Coulomb interactions and symmetry-breaking mechanisms within the nematic phase of iron-pnictide superconductors. The transition from a tetragonal to an orthorhombic phase is accompanied by a significant change in electronic properties, while long-range magnetic order is not established yet. The driving force of this transition may not only be phonons but also magnetic or orbital fluctuations. The signatures of these scenarios are studied with quantum cluster methods to identify the most important effects.
Here, cluster perturbation theory (CPT) and its variational extention, the variational cluster approach (VCA) are used to treat the respective systems on a level beyond mean-field theory. Short-range correlations are incorporated numerically exactly by exact diagonalization (ED). In the VCA, long-range interactions are included by variational optimization of a fictitious symmetry-breaking field based on a self-energy functional approach. Due to limitations of ED, cluster sizes are limited to a small number of degrees of freedom.
For the 3/4 filled triangular lattice, the VCA is performed for different cluster symmetries. A strong symmetry dependence and finite-size effects make a comparison of the results from different clusters difficult. The ground state in the weak-coupling limit is superconducting with chiral d+id-wave symmetry, in accordance to previous renormalization group approaches. In the regime of strong interactions SDW states are preferred over superconductivity and a collinaer SDW state with nonuniform spin moments on a quadrupled unit cell has the lowest grand potential. At strong coupling, inclusion of short-range quantum fluctuations turns out to favor this collinear state over the chiral phase predicted by mean-field theory. At intermediate interactions, no robust conclusion can be drawn from the results.
Symmetry-breaking mechanisms within the nematic phase of the iron-pnictides are studied using a three-band model for the iron planes on a 4-site cluster. CPT allows a local breaking of the symmetry within the cluster without imposing long-range magnetic order. This is a crucial step beyond mean-field approaches to the magnetically ordered state, where such a nematic phase cannot easily be investigated. Three mechanisms are included to break the fourfold lattice symmetry down to a twofold symmetry. The effects of anisotropic magnetic couplings are compared to an orbital ordering field and anisotropic hoppings. All three mechanisms lead to similar features in the spectral density. Since the anisotropy of the hopping parameters has to be very large to obtain similar results as observed in ARPES, a phonon-driven transition is unlikely.
|
Page generated in 0.0565 seconds