Contributor info: Prof. Manuel Calixto

Alberto Mayorgas, Manuel Calixto, Nicolás A. Cordero, Elvira Romera, Octavio Héctor Castaños Garza

SciPost Phys. Core 7, 029 (2024) · published 13 May 2024 | Toggle abstract · pdf

The time evolution of a wave packet is a tool to detect topological phase transitions in two-dimensional Dirac materials, such as graphene and silicene. Here we extend the analysis to HgTe/CdTe quantum wells and study the evolution of their electron current wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We show that the two different periodicities that appear in this temporal evolution reach a minimum near the critical thickness, where the system goes from normal to inverted regime. Moreover, the maximum of the electron current amplitude changes with the layer thickness, identifying that current maxima reach their higher value at the critical thickness. Thus, we can characterize the topological phase transitions in terms of the periodicity and amplitude of the electron currents.

Manuel Calixto, Alberto Mayorgas, Nicolás A. Cordero, Elvira Romera, Octavio Héctor Castaños Garza

SciPost Phys. 16, 077 (2024) · published 18 March 2024 | Toggle abstract · pdf

We analyze the magneto-optical conductivity (and related magnitudes like transmittance and Faraday rotation of the irradiated polarized light) of some elemental two-dimensional Dirac materials of group IV (graphene analogues, buckled honeycomb lattices, like silicene, germanene, stannane, etc.), group V (phosphorene), and zincblende heterostructures (like HgTe/CdTe quantum wells) near the Dirac and gamma points, under out-of-plane magnetic and electric fields, to characterize topological-band insulator phase transitions and their critical points. We provide plots of the Faraday angle and transmittance as a function of the polarized light frequency, for different external electric and magnetic fields, chemical potential, HgTe layer thickness and temperature, to tune the material magneto-optical properties. We have shown that absortance/transmittance acquires extremal values at the critical point, where the Faraday angle changes sign, thus providing fine markers of the topological phase transition. In the case of non-topological materials as phosphorene, a minimum of the transmittance is also observed due to the energy gap closing by an external electric field.

Alberto Mayorgas, J. Guerrero, Manuel Calixto

SciPost Phys. Proc. 14, 036 (2023) · published 24 November 2023 | Toggle abstract · pdf

We define the concept of Mixed Symmetry Quantum Phase Transition (MSQPT), considering each permutation symmetry sector $\mu$ of an identical particles system, as singularities in the properties of the lowest-energy state into each $\mu$ when shifting a Hamiltonian control parameter $\lambda$. A three-level Lipkin-Meshkov-Glick (LMG) model is chosen to typify our construction. Firstly, we analyze the finite number $N$ of particles case, proving the presence of MSQPT precursors. Then, in the thermodynamic limit $N\to∞$, we calculate the lowest-energy density inside each sector $\mu$, augmenting the control parameter space by $\mu$, and showing a phase diagram with four different quantum phases.

Julio Guerrero, Antonio Sojo, Alberto Mayorgas, Manuel Calixto

SciPost Phys. Proc. 14, 029 (2023) · published 24 November 2023 | Toggle abstract · pdf

Along this paper, we analyze the entanglement properties of symmetric multi-quDits systems in a special type of states created from the generalization to U(D) of the usual spin coherent states. By means of parity operators, we define what we call multicomponent Schrödinger cat states as parity adapted coherent states. Introducing the tool of information diagrams, i.e. representations of pairs of entropy measures, we analyze the correlation structure of this type of states and their M-wise reduced density matrices.

Manuel Calixto, Alberto Mayorgas, Julio Guerrero

SciPost Phys. Proc. 14, 021 (2023) · published 23 November 2023 | Toggle abstract · pdf

Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N)/U(M)×U(N-M). Replacing U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N)-spin-wave coherent excitations (skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.