25 research outputs found
Three-band Hubbard model for NaIrO: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material
NaIrO was one of the first materials proposed to feature the
Kane-Mele type topological insulator phase. Contemporaneously it was claimed
that the very same material is in a Mott insulating phase which is described by
the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott
insulating behavior in conjunction with antiferromagnetic long-range order.
Further refined experiments established antiferromagnetic order of zigzag type
which is not captured by the KH model. Since then several extensions and
modifications of the KH model were proposed in order to describe the
experimental findings. Here we suggest that adding charge fluctuations to the
KH model represents an alternative explanation of zigzag antiferromagnetism.
Moreover, a phenomenological three-band Hubbard model unifies all the pieces of
the puzzle: topological insulator physics for weak and KH model for strong
electron-electron interactions as well as a zigzag antiferromagnet at
intermediate interaction strength.Comment: 5 pages, 3 figures; v2 (as published): added discussion about kinetic
energy scale C; more realistic values of C shift the zigzag AFM phase to
larger values of
Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
In the quest for quantum spin liquids in three spatial dimensions (3D), we
study the half-filled Hubbard model on the simple cubic lattice with hopping
processes up to third neighbors. Employing the variational cluster approach
(VCA), we determine the zero-temperature phase diagram: In addition to a
paramagnetic metal at small interaction strength and various
antiferromagnetic insulators at large , we find an intermediate-
antiferromagnetic metal. Most interestingly, we also identify a non-magnetic
insulating region, extending from intermediate to strong . Using VCA results
in the large- limit, we establish the phase diagram of the corresponding
-- Heisenberg model. This is qualitatively confirmed - including
the non-magnetic region - using spin-wave theory. Further analysis reveals a
striking similarity to the behavior of the - square-lattice
Heisenberg model, suggesting that the non-magnetic region hosts a 3D
spin-liquid phase.Comment: 5 pages, 4 figures; final version incl. discussion about material
Rashba spin-orbit coupling in the Kane-Mele-Hubbard model
Spin-orbit (SO) coupling is the crucial parameter to drive topological-insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1)-conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the variational cluster approach (VCA) to determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCA analysis of the KMH model in the presence of U(1)-conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a weak topological-semiconductor phase which persist in the presence of interactions
Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material
Na2IrO3 was one of the first materials proposed to feature the Kane-Mele-type
topological insulator phase. Contemporaneously it was claimed that the very
same material is in a Mott insulating phase which is described by the Kitaev-
Heisenberg (KH) model. First experiments indeed revealed Mott insulating
behavior in conjunction with antiferromagnetic long-range order. Further
refined experiments established antiferromagnetic order of zigzag type which
is not captured by the KH model. Since then several extensions and
modifications of the KH model were proposed in order to describe the
experimental findings. Here we suggest that adding charge fluctuations to the
KH model represents an alternative explanation of zigzag antiferromagnetism.
Moreover, a phenomenological three-band Hubbard model unifies all the pieces
of the puzzle: topological insulator physics for weak and KH model for strong
electron-electron interactions as well as a zigzag antiferromagnet at
intermediate interaction strength
Quantum paramagnet in a flux triangular lattice Hubbard model
We propose the flux triangular lattice Hubbard model (-THM) as a
prototypical setup to stabilize magnetically disordered quantum states of
matter in the presence of charge fluctuations. The quantum paramagnetic domain
of the -THM which we identify for intermediate Hubbard U is framed by a
Dirac semi-metal for weak coupling and by 120 N\'eel order for
strong coupling. Generalizing the Klein duality from spin Hamiltonians to
tight-binding models, the -THM maps to a Hubbard model which corresponds
to the Heisenberg-Kitaev model in its strong coupling
limit. The -THM provides a promising microscopic testing ground for exotic
finite-U spin liquid ground states amenable to numerical investigation.Comment: 4+e pages, 3 figures; version to appear in Phys. Rev. Let
Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
We investigate the role of quantum fluctuations in topological quantum phase
transitions of quantum spin Hall insulators and quantum anomalous Hall
insulators. Employing the variational cluster approximation to obtain the
single-particle Green's function of the interacting many-body system, we
characterize different phases by direct calculation of the recently proposed
topological order parameter for interacting systems. We pinpoint the influence
of quantum fluctuations on the quantum spin Hall to Mott insulator transition
in several models. Furthermore, we propose a general mechanism by which a
topological quantum phase transition can be driven by the divergence of the
self energy induced by interactions
Nonmagnetic insolatores in hexagonal lattice models
Wir untersuchen zunächst das Hubbard-Modell des anisotropen Dreiecksgitters als effektive Beschreibung der Mott-Phase in verschiedenen organischen Verbindungen mit dreieckiger Gitterstruktur. Um die Eigenschaften am absoluten Nullpunkt zu bestimmen benutzen wir die variationelle Cluster Näherung (engl. variational cluster approximation VCA) und erhalten das Phasendiagramm als Funktion der Anisotropie und der Wechselwirkungsstärke. Wir finden für schwache Wechselwirkung ein Metall. Für starke Wechselwirkung finden wir je nach Stärke der Anisotropie eine Néel oder eine 120◦-Néel antiferromagnetische Ordnung. In einem Bereich mittlerer Wechselwirkung entsteht in der Nähe des isotropen Dreiecksgitters ein nichtmagnetischer Isolator. Der Metall-Isolator-Übergang hängt maßgeblich von der Anisotropie ab, genauso wie die Art der magnetischen Ordnung und das Erscheinen und die Ausdehnung der nichtmagnetischen Isolatorphase.
Spin-Bahn Kopplung ist der ausschlaggebende Parameter, der elektronische Bandmodelle in topologische Isolatoren wandelt. Spin-Bahn Kopplung im Allgemeinen beinhaltet auch den Rashba Term, der die SU(2) Symmetrie vollständig bricht. Sobald man auch Wechselwirkungen berücksichtigt, müssen sich viele theoretische Methoden auf die Analyse vereinfachter Modelle beschränken, die nur Spin-Bahn Kopplungen enthalten, welche die U(1) Symmetrie erhalten und damit eine Rashba Kopplung ausschließen. Wir versuchen diese bisher bestehende Lücke zu schließen und untersuchen das Kane-Mele Hubbard (KMH) Modell mit Rashba Spin-Bahn Kopplung und präsentieren eine systematische Analyse des Effekts der Rashba Spin-Bahn Kopplung in einem korrelierten zweidimensionalen topologischen Isolator. Wir wenden die VCA auf dieses Problem an und bestimmen das Phasendiagramm mit Wechselwirkung durch die Berechnung der lokalen Zustandsdichte, der Magnetisierung, der Einteilchenspektralfunktion und der Randzustände. Nach einer ausführlichen Auswertung des KMH-Modells, bei erhaltener U(1) Symmetrie, finden wir auch für endliche Wechselwirkung, dass eine zusätzliche Rashba Kopplung zu neuen elektronischen Phasen führt, wie eine metallische Phase und eine topologische Isolatorphase ohne Bandlücke in der lokalen Zustandsdichte, die aber eine direkte Bandlücke für jeden Wellenvektor besitzt.
Für eine Klasse von 5d Übergangsmetallen untersuchen wir ein KMH ähnliches Modell mit multidirektionaler Spin-Bahn Kopplung, das wegen seiner Relevanz für die Natrium-Iridate (engl. sodium iridate) als SI Modell bezeichnet wird. Diese intrinsische Kopplung bricht die SU(2) Symmetrie bereits vollständig und dennoch erhält man wegen der speziellen Form für starke Wechselwirkung wieder einen rotationssymmetrischen Néel-AFM Isolator. Der topologische Isolator des SIH-Modells ist adiabatisch mit dem des KMH-Modells verbunden, jedoch sind die Randströme hier nicht mehr spinpolarisiert.
Wir verallgemeinern das Konzept der Klein-Transformation, das bereits erfolgreich auf Spin-Hamiltonians angewandt wurde, und wenden es auf ein Hubbard-Modell mit rein imaginären spinabhängigen Hüpfen an, das im Grenzfall unendlicher Wechselwirkung in das Kitaev-Heisenberg Modell übergeht. Dadurch erhält man ein Modell des Dreiecksgitters mit reellen spinunabhängigen Hüpfen, das aber eine mehratomige Einheitszelle besitzt. Für schwache Wechselwirkung ist das System ein Dirac Halbmetall und für starke Wechselwirkung erhält man eine 120◦-Néel antiferromagnetische Ordnung. Für mittlere Wechselwirkung findet man aber einen relativ großen Bereich in dem eine nichtmagnetische Isolatorphase stabil ist. Unsere Ergebnisse deuten auf die mögliche Existenz einer Quanten Spinflüssigkeit hin.We investigate the anisotropic triangular Hubbard model as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation (VCA) to treat the zero temperature phasediagram as a function of anisotropy and interaction strength. The metal-insulator transition substantially depends on the anisotropy, so does the nature of magnetism and the emergence of a nonmagnetic insulating phase establishing a spin liquid candidate regime. For weak interactions we find a metal for all anisotropies. Depending on the strength of anisotropy we find a Néel- or a 120◦-Néel-AFM order in the limit of square and triangular lattice. The non-magnetic insulating phase is located around the isotropic triangular lattice for intermediate interaction strength and is bounded by the metallic phase to weaker interactions, the Néel-AFM insulator for less anisotropy and the 120◦-Néel-AFM insulator for stronger interaction strength [1].
Spin-orbit (SO) coupling is the crucial parameter to drive topological insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1) conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the VCAto determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCAanalysis of the KMH model in the presence of U(1) conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a direct-gap only topological insulating phase which persist in the presence of interactions [2].
In 5d transition-metal oxides, both the spin-orbit interaction and the electron correlation emerge at comparable orders of magnitude. In these systems, a variety of specifically tailored crystal structures are available, enabling the
design of robust topological insulators. We study theoretically a monolayer of the 5d-compound Na2IrO3, modeled by a Hubbard-type of Hamiltonian on a honeycomb lattice where the spin symmetry is not conserved. Based on a VCAcalculation, the zero temperature phase diagram is obtained.
We generalize the concept of Klein-dualities, successfully applied to spin Hamiltonians in the past, for tight-binding models and, as such, for Hubbard models. Specifically, we consider an imaginary spin-dependent hopping problem supplemented with an on-site Coulomb interaction which corresponds in the strong coupling limit to the Kitaev-Heisenberg model on the triangular lattice. After applying the Klein-transformation, we obtain a real and spin-independent model which we study in detail using the VCA. For weak interactions, the system is a Dirac semi-metal; for strong interactions, it acquires magnetic order being of 120◦-Néel type. For intermediate interactions, there is a large non-magnetic insulator phase. Our results point towards the possibility of a quantum spin liquid phase