Squeezing Quantum States in Three-Dimensional Twisted Crystals

TL;DR

This paper introduces a novel approach to analyze three-dimensional twisted crystals by using squeezed coherent states in Fock space, revealing unique phase space dynamics and edge states influenced by the Coriolis force.

Contribution

It proposes replacing traditional Bloch band analysis with a squeezed state representation, offering new insights into the complex physics of twisted crystals.

Findings

Reorganization of Hilbert space highlights the role of Coriolis force.

Unconventional phase space dynamics observed.

Edge state structures are characterized in the new framework.

Abstract

A fundamental idea in wave mechanics is that propagation in a periodic medium can be described by Bloch waves whose conserved crystal momenta define their transformations when displaced by the set of discrete lattice translations. In ordered materials where incommensurate spatial periods compete, this general principle is rendered ineffective, often with dramatic consequences. Examples are crystals with broken symmetries from charge or spin density waves, quasiperiodic lattices that produce diffraction patterns with crystallographically forbidden point symmetries, and stacks of two-dimensional lattices with a relative rotation (twist) between layers. In special cases when there is a small difference between the competing periods, a useful work-around is a continuum description where a periodic long-wavelength field produces Bragg scattering that coherently mixes short-wavelength carrier waves. In this work, we advocate an alternative approach to study three-dimensional twisted crystals that replaces their spectrally congested momentum-space Bloch band structures with a representation using squeezed coherent states in a Fock space of free-particle vortex states. This reorganization of the Hilbert space highlights the crucial role of the Coriolis force in the equations of motion that leads to unconventional phase space dynamics and edge state structure generic to a family of complex crystals.