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Register a new userMagnonic Floquet Hofstadter Butterfly
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Added by
Solomon Akaraka Owerre
Publication date
2018
fields
Physics
and research's language is
English
Authors
S. A. Owerre
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We introduce the magnonic Floquet Hofstadter butterfly in the two-dimensional insulating honeycomb ferromagnet. We show that when the insulating honeycomb ferromagnet is irradiated by an oscillating space- and time-dependent electric field, the hopping magnetic dipole moment (i.e. magnon quasiparticles) accumulate the Aharonov-Casher phase. In the case of only space-dependent electric field, we realize the magnonic Hofstadter spectrum with similar fractal structure as graphene subject to a perpendicular magnetic field, but with no spin degeneracy due to broken time-reversal symmetry by the ferromagnetic order. In addition, the magnonic Dirac points and Landau levels occur at finite energy as expected in a bosonic system. Remarkably, this discrepancy does not affect the topological invariant of the system. Consequently, the magnonic Chern number assumes odd values and the magnon Hall conductance gets quantized by odd integers. In the case of both space- and time-dependent electric field, the theoretical framework is studied by the Floquet formalism. We show that the magnonic Floquet Hofstadter spectrum emerges entirely from the oscillating space- and time-dependent electric field, which is in stark contrast to electronic Floquet Hofstadter spectrum, where irradiation by circularly polarized light and a perpendicular magnetic field are applied independently. We study the deformation of the fractal structure at different laser frequencies and amplitudes, and analyze the topological phase transitions associated with gap openings in the magnonic Floquet Hofstadter butterfly.
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We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Hofstadter spectrum is analyzed for different regimes of the driving frequency. For lower frequencies, resonances of various copies of the spectrum lead to intricate formations of topological gaps. In the Landau-level regime, new wing-like gaps emerge upon reducing the driving frequency, thus revealing the possibility of dynamically tuning the formation of the Hofstadter butterfly. In this regime, an effective model may be analytically derived, which allows us to retrace the energy levels that exhibit avoided crossings and ultimately lead to gap structures with a wing-like shape. At high frequencies, we find that gaps open for various fluxes at $E=0$, and upon increasing the amplitude of the driving, gaps also close and reopen at other energies. The topological invariants of these gaps are calculated and the resulting spectrum is elucidated. We suggest opportunities for experimental realization and discuss similarities with Landau-level structures in non-driven systems.
We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that mTBLG realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by explicitly computing the chiral edge states. Our theory paves the way for an effective practical realization of FTIs in equilibrium solid state systems.
We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas-van Alphen (dHvA) oscillation of magnetization bears the energy structure of Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.
Electrons on the lattice subject to a strong magnetic field exhibit the fractal spectrum of electrons, which is known as the Hofstadter butterfly. In this work, we investigate unconventional superconductivity in a three-dimensional Hofstadter butterfly system. While it is generally difficult to achieve the Hofstadter regime, we show that the quasi-two-dimensional materials with a tilted magnetic field produce the large-scale superlattices, which generate the Hofstadter butterfly even at the moderate magnetic field strength. We first show that the van-Hove singularities of the butterfly flat bands greatly elevate the superconducting critical temperature, offering a new mechanism of field-enhanced superconductivity. Furthermore, we demonstrate that the quantum geometry of the Landau mini-bands plays a crucial role in the description of the superconductivity, which is shown to be clearly distinct from the conventional superconductors. Finally, we discuss the relevance of our results to the recently discovered re-entrant superconductivity of UTe2 in strong magnetic fields.
We study irradiated two-dimensional insulating bilayer honeycomb ferromagnets and antiferromagnets coupled antiferromagnetically with a zero net magnetization. The former is realized in the recently synthesized bilayer honeycomb chromium triiodide CrI$_{bf 3}$. In both systems, we show that circularly-polarized electric field breaks time-reversal symmetry and induces a dynamical Dzyaloshinskii-Moriya interaction in each honeycomb layer. However, the resulting bilayer antiferromagnetic system still preserves a combination of time-reversal and space-inversion ($mathcal{PT}$) symmetry. We show that the magnon topology of the bilayer antiferromagnetic system is characterized by a $pmb{mathbb{Z}_2}$ Floquet topological invariant. Therefore, the system realizes a magnonic Floquet quantum spin Hall insulator with spin filtered magnon edge states. This leads to a non-vanishing Floquet magnon spin Nernst effect, whereas the Floquet magnon thermal Hall effect vanishes due to $mathcal{PT}$ symmetry. We study the rich $pmb{mathbb{Z}_2}$ Floquet topological magnon phase diagram of the system as a function of the light amplitudes and polarizations. We further discuss the great impact of the results on future experimental realizations.
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