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Barra, F., Lund, F., Mujica, N., & Rica, S. (2012). Shear modulus of an elastic solid under external pressure as a function of temperature: The case of helium. Phys. Rev. B, 85(6), 6 pp.
Abstract: The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of experimental conditions for solid helium, suggesting, in this case, that dislocation loops can be generated by a pressure-assisted thermally activated process. It is also pointed out that pinned dislocation segments can alter the shear response of solid helium by an amount consistent with current measurements, without any unpinning.
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Cisternas, J., Mellado, P., Urbina, F., Portilla, C., Carrasco, M., & Concha, A. (2021). Stable and unstable trajectories in a dipolar chain. Phys. Rev. B, 103(13), 134443.
Abstract: In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most of the times if the experimental realization is adiabatic, they are considered just a nuisance. Here we use a small number of XY magnetic dipoles subject to an external magnetic field for studying the origin of their collective magnetic response. Using bifurcation theory we have found all the possible solutions being stable or unstable, and explored how those solutions are naturally connected by points where the symmetries of the system are lost or restored. Unstable solutions that reveal the symmetries of the system are found to be the culprit that shape hysteresis loops in this system. The complexity of the solutions for the nonlinear dynamics is analyzed using the concept of boundary basin entropy, finding that the damping timescale is critical for the emergence of fractal structures in the basins of attraction. Furthermore, we numerically found domain wall solutions that are the smallest possible realizations of transverse walls and vortex walls in magnetism. We experimentally confirmed their existence and stability showing that our system is a suitable platform to study domain wall dynamics at the macroscale.
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Mellado, P. (2020). Timescales in the thermal dynamics of magnetic dipolar clusters. Phys. Rev. B, 102(21), 214442.
Abstract: The collective behavior of thermally active structures offers clues on the emergent degrees of freedom and the physical mechanisms that determine the low-energy state of a variety of systems. Here, the thermally active dynamics of magnetic dipoles at square plaquettes is modeled in terms of Brownian oscillators in contact with a heat bath. Solution of the Langevin equation for a set of interacting x-y dipoles allows the identification of the timescales and correlation length that reveal how interactions, temperature, damping, and inertia may determine the frequency modes of edge and bulk magnetic mesospins in artificial dipolar systems.
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Mellado, P., Petrova, O., & Tchernyshyov, O. (2015). Projective symmetry of partons in the Kitaev honeycomb model. Phys. Rev. B, 91(4), 4 pp.
Abstract: Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities do not reflect the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.
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Petrova, O., Mellado, P., & Tchernyshyov, O. (2013). Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model. Phys. Rev. B, 88(14), 4 pp.
Abstract: We study the gapped phase of Kitaev's honeycomb model (a Z(2) spin liquid) in the presence of lattice defects. We find that some dislocations and bond defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z(2) gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z(2) vortex around a dislocation. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes.
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Petrova, O., Mellado, P., & Tchernyshyov, O. (2014). Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model. Phys. Rev. B, 90(13), 14 pp.
Abstract: We study the gapped phase of Kitaev's honeycomb model (a Z(2) spin liquid) on a lattice with topological defects. We find that some dislocations and string defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z(2) gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z(2) vortex around one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.
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Rademaker, L., & Mellado, P. (2018). Charge-transfer insulation in twisted bilayer graphene. Phys. Rev. B, 98(23), 7 pp.
Abstract: We studied the real-space structure of states in twisted bilayer graphene at the magic angle theta = 1.08 degrees. The flat bands close to charge neutrality are composed of a mix of “ring” and “center” orbitals around the AA stacking region. An effective model with localized orbitals is constructed which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge transfer at half filling of the flat bands from the center to the ring orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be J = 3.3 K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields (p + ip)-wave, whereas electron-doping yields (d + id)-wave pairing symmetry.
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Rademaker, L., Abanin, D. A., & Mellado, P. (2019). Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene. Phys. Rev. B, 100(20), 6 pp.
Abstract: Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each moire unit cell. Here, we show, using unbiased real-space self-consistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified “ring” orbitals in the AB/BA region and “center” orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the Gamma point, leading to a further flattening of the flat bands and a pinning of the Van Hove singularity at the Fermi level. The charge smoothening will affect the subtle competition between different possible correlated phases.
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Rica, S. (2011). Phenomenological Ginzburg-Landau theory for supersolidity. Phys. Rev. B, 84(18), 8 pp.
Abstract: A Ginzburg-Landau theory is proposed in which the supersolid state is viewed as a system displaying features of an ordinary solid and of a superfluid. The theory shows that the superfluid part is responsible for a nonclassical rotational inertia (NCRI) behavior, but the ordinary part (the lattice) is responsible for elastic behaviors usually seen in solids. Moreover, the superfluid part contributes to an excess of heat capacity near the supersolid-ordinary solid transition. The theory provides a coherent picture, at least at the macroscopic scale, of supersolidity that reconciles (NCRI) and the heat-capacity measurements. The parameters of the Ginzburg-Landau free energy are estimated using experimental data, hence a healing length of the order of 100 nm and a critical speed of the order of 0.1 m/s are predicted, both results consistent with recent studies by Kubota and co-workers.
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Vidal-Silva, N., & Troncoso, R. E. (2022). Time-dependent strain-tuned topological magnon phase transition. Phys. Rev. B, 106(22), 224401.
Abstract: ollinear magnets in honeycomb lattices under the action of time-dependent strains are investigated. Given the limits of high-frequency periodically varying deformations, we derive an effective Floquet theory for spin systems that results in the emergence of a spin chirality. We find that the coupling between magnons and spin chirality depends on the details of the strain such as the spatial dependence and applied direction. Magnonic fluctuations about the ferromagnetic state are determined, and it is found that spatially homogeneous strains drive the magnon system into topologically protected phases. In particular, we show that certain uniform strain fields play the role of an out-of-plane nearest-neighbor Dzyaloshinskii-Moriya interaction. Furthermore, we explore the application of nonuniform strains, which lead to a confinement of magnon states that for uniaxial strains propagates along the direction that preserves translational symmetry. Our work demonstrates a direct way in which to manipulate the magnon spectrum based on time-dependent strain engineering that is relevant for exploring topological transitions in quantum magnonics.
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