Fate of Quantum Anomalous Hall Effect in the Presence of External Magnetic Fields and Particle-Hole Asymmetry

Abstract

The quantum anomalous Hall (QAH) effect, a condensed matter analog of the parity anomaly, is characterized by a quantized Hall conductivity in the absence of an external magnetic field. However, it has been recently shown that, even in the presence of Landau levels, the QAH effect can be distinguished from the conventional quantum Hall (QH) effect due to the parity anomaly. As a signature of this effect, we predicted coexistent counterpropagating QAH and QH edge states. In the present work, we generalize these findings to QAH insulators with broken particle-hole symmetry. In particular, we derive the connection to the spectral asymmetry, which is a topological quantity arising in the context of Dirac-like systems. Moreover, it is shown that, depending on the magnetic field direction, particle-hole asymmetry strengthens or weakens the hybridization of the counterpropagating QH and QAH edge states. Implications for ferro- or paramagnetic topological insulators are derived which paves the way towards identifying signatures of the QAH effect even in external magnetic fields.

arXiv comment17 pages, 9 figures Changes: In Sec. VI standard deviation was corrected by factor \sqrt{2}

References in corpus (25)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• The Quantum Spin Hall Effect: Theory and Experiment
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Massive Dirac fermions and spin physics in an ultrathin film of topological insulator
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Fermion Path Integrals And Topological Phases
• Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state
• Anomalous Edge Transport in the Quantum Anomalous Hall State
• Ballistic quantum spin Hall state and enhanced edge backscattering in strong magnetic fields
• Magnetic properties of HgTe quantum wells
• Topological Insulators Avoid the Parity Anomaly
• Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
• Robust Helical Edge Transport in Quantum Spin Hall Quantum Wells
• Reentrant topological phases in Mn-doped HgTe quantum wells
• Spherical topological-insulator nanoparticles: Quantum size effects and optical transitions
• Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system
• A k.p treatment of edge states in narrow 2D topological insulators, with standard boundary conditions for the wave function and its derivative

Cited by in corpus (14)

• Magnetic-field-induced robust zero Hall plateau state in MnBi${}_2$Te${}_4$ Chern insulator
• Electric control of a canted-antiferromagnetic Chern insulator
• Induced superconducting correlations in the quantum anomalous Hall insulator
• Temperature and Chemical Potential Dependence of the Parity Anomaly in Quantum Anomalous Hall Insulators
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Signature of Parity Anomaly: Crossover from One Half to Integer Quantized Hall Conductance in a Finite Magnetic Field
• Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly
• Electric and magnetic fields tuned spin-polarized topological phases in two-dimensional ferromagnetic MnBi${}_4$Te${}_7$
• Parity symmetry as the origin of 'spin' in the quantum spin Hall effect
• Spectral asymmetry induces a re-entrant quantum Hall effect in a topological insulator
• The emergence of net chirality in two-dimensional Dirac fermions system with altermagnetic mass
• Hard wall edge confinement in 2D topological insulators and the energy of the Dirac Point
• Dissipative Callan-Harvey mechanism in 2+1 D Dirac system: The fate of edge states along a domain wall
• Counterpropagating topological and quantum Hall edge channels