We present a model for a Chern insulator on the square lattice with complex first and second neig... more We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers ±1. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering.
Searching for triplet superconductivity has been pursued intensively in a broad field of material... more Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model, we reveal a spin triplet pairing in doped MoS2 by employing both the finite temperature determinant quantum Monte Carlo approach and the ground state constrained-phase quantum Monte Carlo method. In a wide filling region of n = 0.60−0.80 around charge neutrality n = 2/3, the f-wave pairing dominates over other symmetries. The pairing susceptibility strongly increases as the on-site Coulomb interaction increases, and it is insensitive to spin-orbit coupling.
Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Bu... more Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate multilayered van der Waals structures for arbitrary lattice mismatch and/or misalignment between different layers. We demonstrate how the developed formalism can be used to model angle-resolved photoemission spectroscopy measurements, and scanning tunnelling spectroscopy which can probe the local and total density of states. The general method is then applied to incommensurate twisted trilayer graphene structures. It is found that the coupling between the three layers can significantly affect the low energy spectral properties, which cannot be simply attributed to the pairwise hybridization between the layers.
We find that quasiperiodicity-induced transitions between extended and localized phases in generi... more We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-André model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously stu...
Edge-magnetism in zigzag transition-metal dichalcogenide nanoribbons is studied using a threeband... more Edge-magnetism in zigzag transition-metal dichalcogenide nanoribbons is studied using a threeband tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge-magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics.
We study the localization properties of electrons in incommensurate twisted bilayer graphene for ... more We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance of samples with fixed width decreases with the system size in the longitudinal direction for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability/quasiperiodicity effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.
We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on th... more We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using exact diagonalization (ED) and a mean-field (MF) variational approach. This model, governed by both onsite and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Besides, a third one, a topologically non-trivial insulator with non-local order is manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground-state, associated with a finite Chern number, are no longer present, resulting on a topologically trivial wave-function. Here, at the largest cluster accessible to ED, we unveil a regime displaying both charge density ordering accompanied by an SU(2) symmetry broken phase with Chern number C = 1. This phase, however, is not present in the MF variational method, and is a warning of the systematic finite-size effects that can affect conclusions obtained in small clusters.
We show that entanglement between two solitary qubits in quasi one-dimensional Bose-Einstein cond... more We show that entanglement between two solitary qubits in quasi one-dimensional Bose-Einstein condensates can be spontaneously generated due to quantum fluctuations. Recently, we have shown that dark solitons are an appealing platform for qubits thanks to their appreciable long lifetime. We investigate the spontaneous generation of entanglement between dark soliton qubits in the dissipative process of spontaneous emission. By driving the qubits with the help of oscillating magnetic field gradients, we observe the formation of long distance steady-state concurrence. Our results suggest that dark-soliton qubits are a good candidates for quantum information protocols based purely on matter-wave phononics.
We study the finite time entanglement dynamics between two dark soliton qubits due to quantum flu... more We study the finite time entanglement dynamics between two dark soliton qubits due to quantum fluctuations in a quasi one dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long life time. We explore the entanglement decay for an entangled state of two phonon coherences and the qubits to be in the diagonal basis of so called Dicke states. We observe the collapse and revival of the entanglement, depending critically on the collective damping term but independent of the qubit-qubit interaction for both the initial states. The collective behavior of the dark soliton qubits demonstrate the dependence of entanglement evolution on the interatomic distance.
Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in ato... more Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in atomically thin materials and thus to unlock the much sought-after topological insulating phases in two dimensions. However, the observation of an Anderson topological transition induced by heavy adatoms has proved extremely challenging despite substantial experimental efforts. Here, we present a multi-scale approach combining advanced first-principles methods and accurate singleelectron descriptions of adatom-host interactions using graphene as a prototypical system. Our study reveals a surprisingly complex structure in the interactions mediated by random adatoms, including hitherto neglected hopping processes leading to strong valley mixing. We argue that the unexpected intervalley scattering strongly impacts the ground state at low adatom coverage, which would provide a compelling explanation for the absence of a topological gap in recent experimental reports on graphene. Our conjecture is confirmed by real-space Chern number calculations and largescale quantum transport simulations in disordered samples. This resolves an important controversy and suggests that a detectable topological gap can be achieved by increasing the spatial range of the induced spin-orbit interactions on graphene, e.g., using nanoparticles.
We study the possibility of using dark-solitons in quasi one dimensional Bose-Einstein condensate... more We study the possibility of using dark-solitons in quasi one dimensional Bose-Einstein condensates to produce two-level systems (qubits) by exploiting the intrinsic nonlinear and the coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the solitons and investigate the emission rate of the qubit in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being only limited by the dark-soliton "death" due to quantum evaporation.
The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced... more The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal 3-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive-in which case a small built in strain is enough to destroy the topological phase-to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing in particular how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multi-band Berry phase, which serves as a topological invariant of this system.
It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in... more It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in the presence of a critical in-plane electric field. We extend this mechanism to the three dimensional Weyl semimetals and analyze the physical consequences for the cases of both, real and pseudo Landau levels arising form strain-induced elastic magnetic fields.
We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple latti... more We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple lattice models based on enlarging the unit cell. As an example we study the Honeycomb lattice with nearest neighbors hopping and a local nearest neighbor Coulomb interaction V. We show that when the unit cell is enlarged to host six atoms that permits Kekulé distortions, self-consistent currents spontaneously form creating non trivial magnetic configurations with total zero flux at high electron densities. A very rich phase diagram is obtained within a variational mean field approach that includes metallic phases with broken time reversal symmetry (T). The predominant (T) breaking configuration is an anomalous Hall phase, a realization of a topological Fermi liquid.
We present a model for a Chern insulator on the square lattice with complex first and second neig... more We present a model for a Chern insulator on the square lattice with complex first and second neighbor hoppings and a sublattice potential which displays an unexpectedly rich physics. Similarly to the celebrated Haldane model, the proposed Chern insulator has two topologically non-trivial phases with Chern numbers ±1. As a distinctive feature of the present model, phase transitions are associated to Dirac points that can move, merge and split in momentum space, at odds with Haldane's Chern insulator where Dirac points are bound to the corners of the hexagonal Brillouin zone. Additionally, the obtained phase diagram reveals a peculiar phase transition line between two distinct topological phases, in contrast to the Haldane model where such transition is reduced to a point with zero sublattice potential. The model is amenable to be simulated in optical lattices, facilitating the study of phase transitions between two distinct topological phases and the experimental analysis of Dirac points merging and wandering.
Searching for triplet superconductivity has been pursued intensively in a broad field of material... more Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model, we reveal a spin triplet pairing in doped MoS2 by employing both the finite temperature determinant quantum Monte Carlo approach and the ground state constrained-phase quantum Monte Carlo method. In a wide filling region of n = 0.60−0.80 around charge neutrality n = 2/3, the f-wave pairing dominates over other symmetries. The pairing susceptibility strongly increases as the on-site Coulomb interaction increases, and it is insensitive to spin-orbit coupling.
Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Bu... more Multilayered van der Waals structures often lack periodicity, which difficults their modeling. Building on previous work for bilayers, we develop a tight-binding based, momentum space formalism capable of describing incommensurate multilayered van der Waals structures for arbitrary lattice mismatch and/or misalignment between different layers. We demonstrate how the developed formalism can be used to model angle-resolved photoemission spectroscopy measurements, and scanning tunnelling spectroscopy which can probe the local and total density of states. The general method is then applied to incommensurate twisted trilayer graphene structures. It is found that the coupling between the three layers can significantly affect the low energy spectral properties, which cannot be simply attributed to the pairwise hybridization between the layers.
We find that quasiperiodicity-induced transitions between extended and localized phases in generi... more We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-André model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously stu...
Edge-magnetism in zigzag transition-metal dichalcogenide nanoribbons is studied using a threeband... more Edge-magnetism in zigzag transition-metal dichalcogenide nanoribbons is studied using a threeband tight-binding model with local electron-electron interactions. Both mean field theory and the unbiased, numerically exact determinant quantum Monte Carlo method are applied. Depending on the edge filling, mean field theory predicts different phases: gapped spin dimer and antiferromagnetic phases appear for two specific fillings, with a tendency towards metallic edge-ferromagnetism away from those fillings. Determinant quantum Monte Carlo simulations confirm the stability of the antiferromagnetic gapped phase at the same edge filling as mean field theory, despite being sign-problematic for other fillings. The obtained results point to edge filling as yet another key ingredient to understand the observed magnetism in nanosheets. Moreover, the filling dependent edge-magnetism gives rise to spin-polarized edge currents in zigzag nanoribbons which could be tuned through a back gate voltage, with possible applications to spintronics.
We study the localization properties of electrons in incommensurate twisted bilayer graphene for ... more We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance of samples with fixed width decreases with the system size in the longitudinal direction for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability/quasiperiodicity effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.
We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on th... more We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using exact diagonalization (ED) and a mean-field (MF) variational approach. This model, governed by both onsite and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. Besides, a third one, a topologically non-trivial insulator with non-local order is manifest. We test expectations of previous analyses in spinless versions asserting that once a local order parameter is formed, the topological characteristics of the ground-state, associated with a finite Chern number, are no longer present, resulting on a topologically trivial wave-function. Here, at the largest cluster accessible to ED, we unveil a regime displaying both charge density ordering accompanied by an SU(2) symmetry broken phase with Chern number C = 1. This phase, however, is not present in the MF variational method, and is a warning of the systematic finite-size effects that can affect conclusions obtained in small clusters.
We show that entanglement between two solitary qubits in quasi one-dimensional Bose-Einstein cond... more We show that entanglement between two solitary qubits in quasi one-dimensional Bose-Einstein condensates can be spontaneously generated due to quantum fluctuations. Recently, we have shown that dark solitons are an appealing platform for qubits thanks to their appreciable long lifetime. We investigate the spontaneous generation of entanglement between dark soliton qubits in the dissipative process of spontaneous emission. By driving the qubits with the help of oscillating magnetic field gradients, we observe the formation of long distance steady-state concurrence. Our results suggest that dark-soliton qubits are a good candidates for quantum information protocols based purely on matter-wave phononics.
We study the finite time entanglement dynamics between two dark soliton qubits due to quantum flu... more We study the finite time entanglement dynamics between two dark soliton qubits due to quantum fluctuations in a quasi one dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long life time. We explore the entanglement decay for an entangled state of two phonon coherences and the qubits to be in the diagonal basis of so called Dicke states. We observe the collapse and revival of the entanglement, depending critically on the collective damping term but independent of the qubit-qubit interaction for both the initial states. The collective behavior of the dark soliton qubits demonstrate the dependence of entanglement evolution on the interatomic distance.
Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in ato... more Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in atomically thin materials and thus to unlock the much sought-after topological insulating phases in two dimensions. However, the observation of an Anderson topological transition induced by heavy adatoms has proved extremely challenging despite substantial experimental efforts. Here, we present a multi-scale approach combining advanced first-principles methods and accurate singleelectron descriptions of adatom-host interactions using graphene as a prototypical system. Our study reveals a surprisingly complex structure in the interactions mediated by random adatoms, including hitherto neglected hopping processes leading to strong valley mixing. We argue that the unexpected intervalley scattering strongly impacts the ground state at low adatom coverage, which would provide a compelling explanation for the absence of a topological gap in recent experimental reports on graphene. Our conjecture is confirmed by real-space Chern number calculations and largescale quantum transport simulations in disordered samples. This resolves an important controversy and suggests that a detectable topological gap can be achieved by increasing the spatial range of the induced spin-orbit interactions on graphene, e.g., using nanoparticles.
We study the possibility of using dark-solitons in quasi one dimensional Bose-Einstein condensate... more We study the possibility of using dark-solitons in quasi one dimensional Bose-Einstein condensates to produce two-level systems (qubits) by exploiting the intrinsic nonlinear and the coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the solitons and investigate the emission rate of the qubit in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being only limited by the dark-soliton "death" due to quantum evaporation.
The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced... more The effect of strain in zigzag ribbons of monolayer transition-metal dichalcogenides with induced superconductivity is studied using a minimal 3-band tight-binding model. The unstrained system shows a topological phase with Majorana zero modes localized at the boundaries of the one-dimensional (1D) zigzag edges. By direct inspection of the spectrum and wave functions we examine the evolution of the topological phase as an in-plane, uniaxial deformation is imposed. It is found that strain shifts the energy of 1D edge states, thus causing a topological phase transition which eliminates the Majorana modes. For realistic parameter values, we show that the effect of strain can be changed from completely destructive-in which case a small built in strain is enough to destroy the topological phase-to a situation where strain becomes an effective tuning parameter which can be used to manipulate Majorana zero modes. These two regimes are accessible by increasing the value of the applied Zeeman field within realistic values. We also study how strain effects are affected by the chemical potential, showing in particular how unwanted effects can be minimized. Finally, as a cross-check of the obtained results, we reveal the connection between 1D Majorana zero modes in the zigzag edge and the multi-band Berry phase, which serves as a topological invariant of this system.
It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in... more It is known that in two dimensional relativistic Dirac systems, the Landau levels can collapse in the presence of a critical in-plane electric field. We extend this mechanism to the three dimensional Weyl semimetals and analyze the physical consequences for the cases of both, real and pseudo Landau levels arising form strain-induced elastic magnetic fields.
We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple latti... more We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple lattice models based on enlarging the unit cell. As an example we study the Honeycomb lattice with nearest neighbors hopping and a local nearest neighbor Coulomb interaction V. We show that when the unit cell is enlarged to host six atoms that permits Kekulé distortions, self-consistent currents spontaneously form creating non trivial magnetic configurations with total zero flux at high electron densities. A very rich phase diagram is obtained within a variational mean field approach that includes metallic phases with broken time reversal symmetry (T). The predominant (T) breaking configuration is an anomalous Hall phase, a realization of a topological Fermi liquid.
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Papers by Eduardo Castro