Universal semiclassical equations based on the quantum metric
arXiv:2106.12383 · doi:10.1103/PhysRevB.104.134312
Abstract
We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific cases of the Rashba Hamiltonian with and without a Zeeman term. The semiclassical trajectories are in full agreement with the ones found by solving the Schrödinger equation. This formalism successfully describes the adiabatic limit and the anomalous Hall effect traditionally attributed to Berry curvature. It also describes the opposite limit of coherent band superposition giving rise to a spatially oscillating Zitterbewegung motion. At , such wavepacket exhibits a circular trajectory in real space, with its radius given by the square root of the quantum metric. This quantity appears as a universal length scale, providing a geometrical origin of the Compton wavelength.
References in corpus (39)
- Topological Insulators
- Topological Photonics
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Quantum simulation of the Dirac equation
- Superfluidity in topologically nontrivial flat bands
- Berry phase effect in anomalous thermoelectric transport
- Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
- Observation of Zitterbewegung in a spin-orbit coupled Bose-Einstein condensate
- Band geometry of fractional topological insulators
- Band geometry, Berry curvature and superfluid weight
- Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
- Geometric approach to Hamiltonian dynamics and statistical mechanics
- Direct observation of zitterbewegung in a Bose-Einstein condensate
- Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
- Geometric orbital susceptibility: quantum metric without Berry curvature
- Spin transverse force on spin current in an electric field
- Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
- Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
- Non-Abelian Gauge Fields in Photonic Cavities and Photonic Superfluids
- SU(2)xU(1) unified theory for charge, orbit and spin currents
- Coherent wave-packet evolution in coupled bands
- Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
- Non-Abelian gauge field theory of the spin-orbit interaction and a perfect spin filter
- Geometric stability of topological lattice phases
- Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
- Kähler geometry and Chern insulators: Relations between topology and the quantum metric
- Non-Abelian gauge field optics
- Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
- Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects
- Quantum metric and wavepackets at exceptional points in non-Hermitian systems
- The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
- Non-Abelian Bloch oscillations in higher-order topological insulators
- Wave packet dynamics of Bogoliubov quasiparticles: quantum metric effects
- Zitterbewegung of exciton-polaritons
- Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
- Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric
- Optical simulation of the free Dirac equation
- Geometric mass acquisition via quantum metric: an effective band mass theorem for the helicity bands
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- Nontrivial quantum geometry of degenerate flat bands
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- Quantum metric dependent anomalous velocity in systems subject to complex electric fields
- Domain-wall topology induced by spontaneous symmetry breaking in polariton graphene
- Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant