Instability of quadratic band degeneracies and the emergence of Dirac points

• URL: http://arxiv.org/abs/2404.05886v3
• Date: Mon, 14 Oct 2024 18:04:42 GMT
• Title: Instability of quadratic band degeneracies and the emergence of Dirac points
• Authors: Jonah Chaban, Michael I. Weinstein,
• Abstract summary: quadratic band degeneracy points occurring over the high-symmetry quasimomentum $boldsymbolM$ are Dirac points. Wavepackets spectrally localized near either $boldsymbolD+$ or $boldsymbolD-$ are governed by a system of Dirac equations with an advection term.
• Score: 0.0
• License:
• Abstract: Consider the Schr\"{o}dinger operator $H = -\Delta + V$, where the potential $V$ is real, $\mathbb{Z}^2$-periodic, and additionally invariant under the symmetry group of the square. We show that, under typical small linear deformations of $V$, the quadratic band degeneracy points occurring over the high-symmetry quasimomentum $\boldsymbol{M}$ (see [27, 28]) each split into two separated degeneracies over perturbed quasimomenta $\boldsymbol{D}^+$ and $\boldsymbol{D}^-$, and that these degeneracies are Dirac points. The local character of the degenerate dispersion surfaces about the emergent Dirac points are tilted, elliptical cones. Correspondingly, the dynamics of wavepackets spectrally localized near either $\boldsymbol{D}^+$ or $\boldsymbol{D}^-$ are governed by a system of Dirac equations with an advection term. Symmetry-breaking perturbations and induced band topology are also discussed.

Related papers

• Multipartite entanglement in the diagonal symmetric subspace [41.94295877935867]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• DHR bimodules of quasi-local algebras and symmetric quantum cellular automata [0.0]
  We show that for the double spin flip action $mathbbZ/2mathbbZtimes mathbbZ/2mathbbZZcurvearrowright mathbbC2otimes mathbbC2$, the group of symmetric QCA modulo symmetric finite depth circuits in 1D contains a copy of $S_3$, hence is non-abelian.
  arXiv  Detail & Related papers  (2023-03-31T18:33:07Z)
• Exact solution of a non-Hermitian $\mathscr{PT}$-symmetric Heisenberg spin chain [0.0]
  We construct the exact solution of a non-Hermitian $mathscrPT$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that both $A$ and $B$ type phases can be further divided into sub-phases which exhibit different ground states.
  arXiv  Detail & Related papers  (2023-01-15T02:32:44Z)
• Spectral properties of the 2D magnetic Weyl-Dirac operator with a short-range potential [0.0]
  We study the spectral properties of the Weyl-Dirac or massless Dirac operators in dimension 2 in a homogeneous magnetic field. As a by-product of this, we have the stability of bipolarons in graphene in the presence of magnetic fields.
  arXiv  Detail & Related papers  (2022-11-12T23:29:23Z)
• Existence of the transfer matrix for a class of nonlocal potentials in two dimensions [0.0]
  Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schr"odinger equation, $(-nabla2+v)psi=k2psi$ for a local potential $v$, they arise in dimensions greater than one and are present regardless of the details of $v$.
  arXiv  Detail & Related papers  (2022-07-20T17:34:05Z)
• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension [0.0]
  We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_omega,lambda:=beginbmatrix-fraclambda+omegax&-partial_x.
  arXiv  Detail & Related papers  (2021-07-08T11:48:57Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.