Abstracts

The lattice mismatch between two two-dimensional materials gives rise to a naturally occurring moiré. Following work by Engelke and collaborators [1], it is now established that moirés can be understood within the framework of topology. Using words from Sethna, the moiré is re-expressed in a parameter space [2] in which the two lattices are matched, and the vertical displacement of the atoms on the upper lattice as different locations within the moiré are explored becomes the order parameter. This topological space is described by a “punctured torus.” Working on this “parameter space,” we registered changes in the local potential within multiple unit cell realizations from a slightly strained graphene/hBN moiré and calculated local changes to the on-site energies and first-nearest neighbor tight-binding elements. This process leads to a distortion of the graphene Hamiltonian which, like those described before [3,4], develops a Berry dipole. Now, thinking of the evolution of lattice registries within the moiré in a semiclassical way akin to that from “strain engineering of graphene [5],” we unexpectedly observe the Berry dipole to wind within the moiré [6].

[1] R. Engelke et al., PRB 107, 125413 (2023). 

[2] J. P. Sethna. Statistical Mechanics: Entropy, Order Parameters, and Complexity. Oxford U. Press (2006).

[3] I. Sodemann and L. Fu. PRL 115, 216806 (2015).

[4] R. Battilomo, N. Scopigno, and C. Ortix. PRL 123, 196403 (2019).

[5] G. Naumis et al., RPP 80, 096501 (2017).

[6] A. Huaman and S. Barraza-Lopez. Under review.

In this talk, we present the experimental realization of room-temperature intercavity Frenkel polaritons excited across two strongly coupled cavities. This setup enables the formation of a tuneable heavy-polariton state, analogous to slow light, even without a periodic in-plane potential. Our photonic architecture, built on a simple three-level scheme, spatially separates photons and excitons into distinct cavities while maintaining a balanced mixing degree. This unique configuration reveals a dynamic competition between many-body scattering processes and the intrinsic polariton characteristics, resulting in an extended fluorescence lifetime. We further explore potential applications, including topological phases for polaritons.

In the framework of axion electrodynamics to describe light-matter interaction in topological insulators (TIs), we find novel electromagnetic field solutions. In particular, due to the topological magnetoelectric polarizability values of the different media, we demonstrate the existence of totally transverse electromagnetic (TEM) waves within TI waveguides that are forbidden in Maxwell's theory for non magnetoelectric media. This work reveals a unique polarization rotation effect in TI waveguides, distinct from well known magneto-optical phenomena like Faraday and Kerr rotations. This rotation, predicted to be experimentally observable, provides a direct signature of the topological magnetoelectric effect.

The realization of TEM modes in TI waveguides offers exciting prospects for novel photonic devices. For instance, the absence of critical angles for total internal reflection enables highly flexible and bendable waveguides with minimal losses, paving the way for advanced integrated photonic circuits and miniaturized optical components.

The twisted bilayer graphene exhibits flat energy bands near the zero Fermi energy at the so-called magic angles. At the Dirac points of the system an effective renormalized Fermi velocity with a large density of states is found, which yield unconventional superconducting behavior. Here by means of the following quantum information concepts: the fidelity, the linear entropy, and entanglement measures of bipartite composite system, one can capture singularities in the vicinity of the magic angles. A truncated basis is considered in the Moire Brillouin zone, which depends on the number of higher-order nearest neighbors. The basis is characterized by the quantum states |l, m, s >, with l =1,2 indicating the layer, m=(m1, m2), the Moire reciprocal lattice vectors, and s the triangular sub-lattices of graphene A,B.

In this presentation, we explore preliminary studies on the topological and geometrical properties of quantum 2D Dirac materials. Initially, we examine how fluctuations in the Dirac field produce temperature-dependent corrections to the Helfrich-Canham formulation, which describes the classical elasticity of graphene membranes at equilibrium. We highlight the emergent shapes predicted by the effective model, taking into account terms up to quadratic order in Ricci curvature, and discuss the constraints necessary for their observation. Through a mechanical stability analysis, we present a phase diagram featuring a critical temperature that serves to differentiate between the phases of carbon nanotubes and fullerenes. Finally, we continue our investigation into topological states in curved materials, focusing specifically on spherical membranes, such as fullerenes.

The search of quantum liquid behavior in one-dimensional systems is a current topic of interest in the field of quantum materials. Interestingly, metalloporphyrin can be used as building blocks units due to their unique versatility, allowing the formation of a variety of nanostructures with different dimensionalities. In particular, the synthesis of one-dimensional triply linked metalloporphyrin tapes has been reported. Thus, we have performed a first principles study of the electronic properties for fused metalloporphyrin tapes by means of the Density Functional Theory. For structural optimization, we have used the Generalized Gradient Approximation in the Perdew-Burke-Ernzerhof parameterization for the exchange-correlation functional. For the electronic structure calculations, we have used the Heyd–Scuseria–Ernzerhof exchange-correlation functional, in order to obtain accurate band structure. For the periodic systems, we have found that the band gap decreases as we go from H2P, MgP to ZnP tapes and the low energy bands shows hyperbolic dispersion, resembling a massive Dirac fermions behavior. 

Additionally, we have evaluated the energy gap of finite ZnP-tapes as a function of length (L) and found that the energy gap scales as 1/L. This result is analyzed and discussed in the light of a quantum confinement model. The author thankfully acknowledges computer resources, technical advice and support provided by Laboratorio Nacional de Supercómputo del Sureste de México (LNS), a member of the CONACYT national laboratories, with project No. 202303063N.

In this presentation, we will examine the role of non-commutative quantum field theories in condensed matter physics. Specifically, we will delve into a non-commutative quantum field theory for a Fermi liquid to gain insight into the key components of this approach. Additionally, we will discuss how an effective theory can be developed to describe anyons.

Non-Hermitian physics has emerged as a powerful framework for understanding systems with gain, loss, or non-reciprocal couplings, revealing unexpected phenomena at the interface of topology and quantum mechanics [1,2,3]. In this talk, I will discuss how our early work helped identify the localization of states at boundaries [4], now known as the non-Hermitian skin effect [5], and its implications for bulk-boundary correspondence. I will also present a broader perspective on this field, including our recent efforts to bridge quantum measurements with classical emulators [6,7,8].

[1] R. Lin, T. Tai, L. Li, and C. H. Lee, Frontiers of Physics 18, 53605 (2023).  http://dx.doi.org/10.1007/s11467-023-1309-z

[2] V. M. Martinez Alvarez, J. E. Barrios Vargas, M. Berdakin, and L. E. F. Foa Torres, Eur. Phys. J. Spec. Top. (2018), https://doi.org/10.1140/epjst/e2018-800091-5

[3] L. E. F. Foa Torres, Journal of Physics: Materials 3, 014002 (2020), https://iopscience.iop.org/article/10.1088/2515-7639/ab4092/meta

[4] V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Phys. Rev. B 97, 121401(R) (2018). https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.121401

[5] S. Yao and Z. Wang,  Phys. Rev. Lett. 121, 086803 (2018). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.086803

[6] L. E. F. Foa Torres and S. Roche, arXiv:2408.04629 (2024). https://arxiv.org/abs/2408.04629

[7] L. E. F. Foa Torres, to be published.

[8] For related research see https://www.foatorres.com/

Topological phases arise as the parameters of a quantum system are varied as a function of time. Under the adiabatic approximation, the time dependency can be removed and the Berry topological phase can be obtained from a trajectory on the parameters space. Although this approach is usually applied in solid state physics without further reflection, in many cases, say in Dirac or Weyl materials, the adiabatic approximation is never met as the system is gapless. Yet it is still possible to use other topological invariants, in particular the Aharanov-Anandan phase that provides information not only about the topology but also about band transitions. Therefore, here the problem of graphene under electromagnetic radiation is analyzed from a time-driven perspective, allowing to show how the Aharanov-Anandan and Berry phases provide alternative information about the topology including interband transitions.  This allows to perform Floquet time driven topological engineering.

Long-range interactions and spin-orbit coupling are the essential ingredients behind the emergence of Skyrmions in spinor condensates confined in the two-dimensional space. Cloud and droplet phases of the two-component condensate immerse in a time dependent magnetic field in absence of spin-orbit coupling are first tracked as a function of the coupling interaction parameters, to discern the parameter regions for which the Bose superfluids have extended phases occupying the whole space. Skyrmion states appearing in square and hexagonal lattices are then classified in terms of the topological charge. The plethora of phases observed are the result of numerical experiments within the mean-field Gross-Pitaevskii scheme.

Chiral edge states (CES) play a crucial role in explaining the quantization of the Hall conductance of a 2D system in a strong magnetic field. The number of CES is linked to the TKNN topological invariant [1], known as the Chern number (C), which can be adjusted by the applied magnetic field. In particular, the vacuum surrounding the system has a trivial Chern number (C=0), while the magnetic field induces a non-trivial Chern number (C≠0) in the 2D system. The interface where the topological invariant changes is referred to as a domain wall (DW), and this change is responsible for the emergence of CES. This study addresses the case of a multi-domain Chern insulator by considering a non-uniform magnetic field to examine the impact of DWs on resistance and current quantization [2,3]. The transport properties are then analyzed using the Landauer-Buttiker formalism, with magnetic fields introduced as Peierls phases [3]. It is found that introducing decoherence and finite temperature into the model results in quantized resistances that are in good agreement with experimental observations of multi-domain intrinsic topological insulators. Results were obtained in collaboration with my student, Ricardo Y. Díaz-Bonifaz. This work was supported by UNAM-PAPIIT IN109022 and IN116025. Computations were performed at Miztli under Project LANCAD-UNAM-DGTIC-329.

[1] D.J. Thouless, M. Kohmoto, M.P. Nightingale and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).

[2] R.Y. Díaz-Bonifaz and C. Ramírez, Physica E 164, 116056 (2024).

[3] R.Y Díaz-Bonifaz and C. Ramírez, J. Phys.: Condens. Matter 37, 105301 (2025).

In this talk I review the dynamics of Dirac electrons in low dimensions in the presence of external electromagnetic fields which enter through minimal and non-minimal coupling into the Dirac equation. Some physical consequences are preliminarily discussed in the context of Topological Quantum Materials.

In this talk we present strategies to control and manipulate the electronic transport in 2D materials. In the first part, we demonstrate that the current can be guided along well-defined paths by the engineering Kekulé-O distortions. A grain boundary in these distortions separates the system into topologically distinct regions and induces a domain wall state. This ballistic state is independent of the orientation of the grain boundary with respect to the graphene lattice and allows the current to be guided along arbitrary paths. Since the state has a gap, the current flow can be switched by electrostatic gates [1]. In the second part of the talk, we present results on edge states in twisted graphene bilayers. These states carry electronic current and can generate a non-local resistance, which is due to the fact that these states are localized only at certain edges of the system, depending on how the nanoribbon has been cut [2].

[1] S. Galván y García, Y. Betancur-Ocampo, F. Sánchez-Ochoa, TS: Atomically thin current pathways in graphene through Kekulé-O engineering: Nano Letters 24, 2322 (2024)

[2] J.A. Sánchez-Sánchez, M. Navarro-Espino, J.E. Barrios-Vargas, TS: Edge-state transport in twisted bilayer graphene, arXiv:2407:04668 (accepted at Phys. Rev. B)

We introduce a time-dependent extension of the quantum geometric tensor to characterize the geometry of the time-parameter space for a quantum state, accounting for small variations in both time and wave function parameters. Unlike the standard quantum geometric tensor, this new tensor include additional temporal components, allowing for analyzing systems with non-time-separable or explicitly time-dependent quantum states, revealing new insights about these systems. Notably, the time-time component of this tensor is linked to the energy dispersion of the system. The real part of this new tensor defines a time-dependent quantum metric that extends the concept of the quantum metric tensor, while the imaginary part generalizes the Berry curvature.  We applied this framework to a chain of generalized harmonic/inverted oscillators. Our analysis reveals intriguing results regarding the scalar curvature linked to the time-dependent quantum geometric tensor, as well as the behavior of the generalized Berry curvature during the transition from harmonic to inverted oscillators. Notably, our tensor identifies the system’s ground state by exhibiting a minimum in certain components. We also examine entanglement in the chain through purity analysis, demonstrating that the purity for any excited state is zero during these transitions.