Fate of a topological invariant for correlated lattice electrons at finite temperature

Abstract

Electrons on a two-dimensional (2$d$) lattice which is exposed to a strong uniform magnetic field show intriguing physical phenomena. The spectrum of such systems exhibits a complex (multi-)band structure known as Hofstadter's butterfly. For fillings at which the system is a band insulator one observes a quantized integer-valued Hall conductivity ${\sigma }_{xy}$ corresponding to a topological invariant, the first Chern number ${\mathcal{C}}_1$. This is robust against many-body interactions as long as no changes in the gap structure occur. Strictly speaking, this stability holds only at zero temperatures $T$ while for $T>0$ correlation effects have to be taken into account. In this work, we address this question by presenting a dynamical mean field theory (DMFT) study of the Hubbard model in a uniform magnetic field. The inclusion of local correlations at finite temperature leads to (i) a shrinking of the integer plateaus of ${\sigma }_{xy}$ as a function of the chemical potential and (ii) eventually to a deviation from these integer values. We demonstrate that these effects can be related to a correlation-driven narrowing and filling of the band gap, respectively.

arXiv comment11 pages, 8 figures

References in corpus (24)

• Quantum Spin Hall Effect in Graphene
• Topological Field Theory of Time-Reversal Invariant Insulators
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Interacting topological insulators: a review
• Simplified topological invariants for interacting insulators
• Correlation effects in two-dimensional topological insulators
• Local Electronic Correlation at the Two-Particle Level
• Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Quantum Spin Hall Insulators with Interactions and Lattice Anisotropy
• Interaction effects and quantum phase transitions in topological insulators
• First order character and observable signatures of topological quantum phase transitions
• Solving Dynamical Mean-Field Theory at very low temperature using Lanczos Exact Diagonalization
• Optical properties of correlated materials -- Generalized Peierls approach and its application to VO2
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Fluctuation driven topological Hund insulators
• Correlation effects on a topological insulator at finite temperatures
• Phase diagram of the Kane-Mele-Coulomb model
• Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
• Topological order in a correlated Chern insulator
• Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model
• Topological Phase Transition in the Hofstadter-Hubbard Model
• Origin of the anomalous Hall Effect in overdoped n-type cuprates: current vertex corrections due to antiferromagnetic fluctuations
• Nature of continuous phase transitions in interacting topological insulators

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• Thermodynamics of correlated electrons in a magnetic field
• Hall map and breakdown of Fermi liquid theory in the vicinity of a Mott insulator
• Topological nature of Hubbard bands in strongly correlated systems
• Local vs non-local correlation effects in interacting quantum spin Hall insulators
• Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
• Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides
• Quantum Transport Theory of Strongly Correlated Matter
• Interacting Chern Insulator in Infinite Spatial Dimensions
• Hall response of locally correlated two-dimensional electrons at low density
• Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition
• Orbital Magnetic Field Driven Metal-Insulator Transition in Strongly Correlated Electron Systems
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Low-frequency magnetic oscillations induced by strongly electron correlations
• Universal low-density power laws of the dc conductivity and Hall constant in the self-consistent Born approximation
• Quasiparticle approach to the transport in infinite-layer nickelates
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics
• Density of states of the Hubbard model supplemented with the quantizing magnetic field
• Prototypical many-body signatures in transport properties of semiconductors
• Hall Coefficient and Resistivity in the Doped Bilayer Hubbard Model