Berry Phase and Pseudospin Winding Number in Bilayer Graphene

Ever since the novel quantum Hall effect in bilayer graphene was discovered, and explained by a Berry phase of 2pi [K. S. Novoselov et al., "Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene", Nature Phys. 2, 177 (2006)], it has been widely accepted that the low-energy electronic wavefunction in this system is described by a non-trivial Berry phase of 2pi, different from the zero phase of a conventional two-dimensional electron gas. Here, we show that (i) the relevant Berry phase for bilayer graphene is not different from that for a conventional two-dimensional electron gas (as expected, given that Berry phase is only meaningful modulo 2pi) and that (ii) what is actually observed in the quantum Hall measurements is not the absolute value of the Berry phase but the pseudospin winding number.Comment: 6 pages, 3 figures, published versio

Making Massless Dirac Fermions from Patterned Two-Dimensional Electron Gases

Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.Comment: 5 pages, 4 figures, significant revision of abstract, text, and figure

Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics

The anharmonic lattice is a representative example of an interacting bosonic many-body system. The self-consistent harmonic approximation has proven versatile for the study of the equilibrium properties of anharmonic lattices. However, the study of dynamical properties therewithin resorts to an ansatz, whose validity has not yet been theoretically proven. Here, we apply the time-dependent variational principle, a recently emerging useful tool for studying the dynamic properties of interacting many-body systems, to the anharmonic lattice Hamiltonian at finite temperature using the Gaussian states as the variational manifold. We derive an analytic formula for the position-position correlation function and the phonon self-energy, proving the dynamical ansatz of the self-consistent harmonic approximation. We establish a fruitful connection between time-dependent variational principle and the anharmonic lattice Hamiltonian, providing insights in both fields. Our work expands the range of applicability of time-dependent variational principle to first-principles lattice Hamiltonians and lays the groundwork for the study of dynamical properties of the anharmonic lattice using a fully variational framework.Comment: v2: Added a citation to L. Monacelli and F. Mauri, "Time-Dependent Self Consistent Harmonic Approximation: Anharmonic nuclear quantum dynamics and time correlation functions," arXiv:2011.14986 and a note on i