Pierre Anthony Pantaleon Peralta

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• Doctor of Philosophy
• Researcher at Madrid Institute for Advanced Studies

Moiré materials represent strongly interacting electron systems bridging topological and correlated physics. Despite notable advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging its sen...

Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been observed in rhombohedral tetralayer graphene. To explain this finding, we study the role of electron-electron interactions in determining flavor symmetry breaking, using the Hartree Fock (HF) approximation, and also superconductivity driven by repul...

We investigate the electronic structure of graphene monolayers subjected to patterned dielectricsuperlattices. Through a quantum capacitance model approach, we simulate realistic devices capable of imposing periodic potentials on graphene. By means of both tight-binding and continuummodels, we analyze the electronic structure across varied patterni...

Since its discovery, graphene has been one of the most prominent 2D materials due to its unique properties and broad range of possible applications. In particular, the half-integer Quantum Hall Effect (HI-QHE) characterized by the quantization of Hall resistivity as a function of applied magnetic field, offers opportunities for advancements in quan...

The existence of superconductivity (SC) appears to be established in both twisted and nontwisted graphene multilayers. However, whether their building block, single-layer graphene (SLG), can also host SC remains an open question. Earlier theoretical works predicted that SLG could become a chiral d-wave superconductor driven by electronic interactio...

We investigate the electronic properties of two-dimensional electron gases (2DEGs) subjected to a periodic patterned gate. By incorporating the superlattice potential (SL) induced by patterning into the Schrodinger equation, we develop a methodology for obtaining exact analytical solutions. These solutions enable us to construct a comprehensive pha...

For the unconventional superconducting phases in moire materials, a critical question is the role played by electronic interactions in the formation of Cooper pairs. In twisted bilayer graphene (tBLG), the strength of electronic interactions can be reduced by increasing the twist angle or screening provided by the dielectric medium. In this work, w...

Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly t...

The existence of superconductivity (SC) in graphene appears to be established in both twisted and non-twisted multilayers. However, whether their building block, single-layer graphene (SLG), can also host SC remains an open question. Earlier theoretical works predicted that SLG could become a chiral d-wave superconductor driven by electronic intera...

We investigate the electronic structure of graphene monolayers subjected to patterned dielectric superlattices. Through a quantum capacitance model approach, we simulate realistic devices capable of imposing periodic potentials on graphene. By means of both tight-binding and continuum models, we analyze the electronic structure across varied patter...

The relentless pursuit of band structure engineering continues to be a fundamental aspect in solid-state research. Here, we meticulously construct an artificial kagome potential to generate and control multiple Dirac bands of graphene. This unique high-order potential harbors natural multiperiodic components, enabling the reconstruction of band str...

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers as well as untwisted stacks. We analyze here the contribution of long-range charge fluctuations in the superconductivity of twisted double bilayers and helical trilayers, and compare the results to twisted bilayer graphene. A diagrammatic...

Moir\'e materials represent strongly interacting electron systems bridging topological and correlated physics. Despite significant advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here, we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging...

Experiments conducted on two-dimensional twisted materials have revealed a plethora of moiré patterns with different forms and shapes. The formation of these patterns is usually attributed to the presence of small strains in the samples, which typically arise during their fabrication. In this paper we find that the superlattice structure of such sy...

Twist-controlled moiré superlattices (MSs) have emerged as a versatile platform for realizing artificial systems with complex electronic spectra. The combination of Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) can give rise to an interesting MS, which has recently featured a set of unexpected behaviors, such as unconventi...

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system owed to its unique flat electronic bands. However, understanding the single-particle band structure alone has been challenging due to complex lattice reconstruction effects and a lack of spectroscopic measurements over a broad energy range. Here, we prob...

The group of moiré graphene superconductors keeps growing, and by now it contains twisted graphene multilayers and twisted double bilayers. We analyze the contribution of long range charge fluctuations in the superconductivity of twisted double graphene bilayers and helical trilayers, and compare the results to twisted bilayer graphene. We apply a...

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review...

Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlatedquantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly t...

We analyze the electronic structure of twisted bilayer graphene (TBG) nanoribbons close to the magic angle. We describe a transition from an incomplete to a complete moiré structure. By considering zigzag and armchair edge terminations, the low-energy bands are strongly modified, and thus, the edge flat-band localization is sensitive to the type of...

Twist-controlled moire superlattices (MS) have emerged as a versatile platform in which to realize artificial systems with complex electronic spectra. Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) form an interesting example of the MS that has recently featured a set of unexpected behaviors, such as unconventional ferroele...

Motivated by a recent experiment [Kapfer et. al., Science 381, 677 (2023)], we analyze the low-energy physics of a bent nanoribbon placed on top of graphene, which creates a gradually changing moiré pattern. By means of a classical elastic model we derive the strains in the ribbon and we obtain its spectrum with a scaled tight-binding model. In a n...

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criter...

We analyze the electronic structure of twisted bilayer graphene (TBG) nanoribbons close to the magic angle. We describe a transition from an incomplete to a complete moiré structure. By considering zigzag and armchair edge terminations, the low-energy bands are strongly modified, and thus, the edge flat-band localization is sensitive to the type of...

Experiments conducted on two-dimensional twisted materials have revealed a plethora of moiré patterns with different forms and shapes. The formation of these patterns is usually attributed to the presence of small strains in the samples, which typically arise during their fabrication. In this work we find that the superlattice structure of such sys...

This study discusses the effect of long‐range interactions within the self‐consistent Hartree‐Fock (HF) approximation in comparison to short‐range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, it determines the quasi‐particle b...

Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. We analyze junctions between a scanning tunneling microscope (STM) tip and superconducting twisted bilayer graphene (TBG) and TBG Josephson junctions (JJs). We compare superconducting phases that are even or odd under valley exchange (s- or f-wave)....

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a tra...

Twisted bilayer graphene has a rich phase diagram, including superconductivity. Recently, an unexpected discovery has been the observation of superconductivity in non-twisted graphene bilayers and trilayers. In this Perspective, we give an overview of the search for uncommon phases in non-twisted graphene systems. We first contextualize these recen...

We discuss a Kohn-Luttinger-like mechanism for superconductivity in Bernal bilayer graphene and rhombohedral trilayer graphene. Working within the continuum model description without free parameters, we find that the screened long-range Coulomb interaction alone gives rise to superconductivity with critical temperatures that agree with experiments....

We discuss the effect of long-range interactions within the self-consistent Hartree-Fock (HF) approximation in comparison to short-range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, we determine the quasi-particle band structu...

The recent observed anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a platform to tune the correlated properties in graphene systems. In these graphene-based moiré superlattices, the aligned hBN subst...

Magnetic topological insulators (MTI) constitute a novel class of materials where the topologically protected band structure coexists with long-range ferromagnetic order, which can lead to the breaking of time-reversal symmetry (TRS), introducing a bandgap in the Dirac cone-shaped topological surface state (TSS). The gap opening in MITs has been pr...

The recent observed anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a new platform to tune the correlated properties in graphene systems. In these graphene-based moir\'e superlattices, the aligned hBN...

Junctions provide a wealth of information on the symmetry of the order parameter of superconductors. We analyze here normal-superconducting and Josephson junctions involving twisted bilayer graphene (TBG) and related systems. The first junctions describe the coupling between the tip and superconducting TBG samples in scanning tunneling microscope (...

The discovery of a very rich phase diagram in twisted bilayer graphene [1,2] renewed the interest into the properties of other systems based on graphene. An unexpected finding has been the observation of superconductivity in non-twisted graphene bilayers and trilayers [3-5]. In this perspective, we give an overview of the search for uncommon phases...

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criter...

We discuss a Kohn-Luttinger-like mechanism for superconductivity in Bernal bilayer graphene and rhombohedral trilayer graphene. Working within the continuum model description, we find that the screened long-range Coulomb interaction alone gives rise to superconductivity with critical temperatures that agree with experiments. We observe that the ord...

We analyze the effects of the long-range Coulomb interaction on the distribution of Berry curvature among the bands near charge neutrality of twisted bilayer graphene (TBG) closely aligned with hexagonal boron nitride (hBN). Due to the suppressed dispersion of the narrow bands, the band structure is strongly renormalized by electron-electron intera...

In this work, we study heterostructures of TBG and hexagonal boron nitride (hBN) using an atomistic tight-binding model together with semi-classical molecular dynamics to consider relaxation effects. The hBN substrate has significant effects on the band structure of TBG even in the case where TBG and hBN are not aligned. Specifically, the substrate...

We analyze the effects of the long-range Coulomb interaction on the distribution of Berry curvature among the bands near charge neutrality of twisted bilayer graphene (TBG) closely aligned with hexagonal boron nitride (hBN). Due to the suppressed dispersion of the narrow bands, the band structure is strongly renormalized by electron-electron intera...

Supplementary Material: Low energy models

We study the emergence of superconductivity in rhombohedral trilayer graphene due purely to the long-range Coulomb repulsion. This repulsive-interaction-driven phase in rhombohedral trilayer graphene is significantly different from those found in twisted bilayer and trilayer graphenes. In the latter case, the nontrivial momentum-space geometry of t...

Twisted bilayer graphene (TBG) has taken the spotlight in the condensed matter community since the discovery of correlated phases at the so-called magic angle. Interestingly, the role of a substrate on the electronic properties of TBG has not been completely elucidated. Up to now, most of the theoretical works carried out in order to understand thi...

The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sub-lattice symm...

We study the symmetries of twisted trilayer graphene's band structure under various extrinsic perturbations, and analyze the role of long-range electron-electron interactions near the first magic angle. The electronic structure is modified by these interactions in a similar way to twisted bilayer graphene. We analyze electron pairing due to long-wa...

The effects of the long range electrostatic interaction in twisted bilayer graphene are Described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symme...

We study the emergence of superconductivity in rhombohedral trilayer graphene due purely to the long-range Coulomb repulsion. This repulsive-interaction-driven phase in rhombohedral trilayer graphene is significantly different from those found in twisted bilayer and trilayer graphenes. In the latter case, the nontrivial momentum-space geometry of t...

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, and they have also been reported in other arrangements of graphene layers. We investigate three such arrangements: untwisted AB bilayer graphene on an hBN substrate, two graphene bilayers twisted with respect to each other, and a single ABC sta...

Angle disorder is an intrinsic feature of twisted bilayer graphene and other moiré materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-Büttiker transmission through an angle disorder barrier with a width comparable to the moiré period,...

Low Energy Model with strain, topological phases and additional results.

We study the symmetries of twisted trilayer graphene's band structure under various extrinsic perturbations, and analyze the role of long-range electron-electron interactions near the first magic angle. The electronic structure is modified by these interactions in a similar way to twisted bilayer graphene. We analyze electron pairing due to long-wa...

The occurrence of superconducting and insulating phases is well-established in twisted graphene bilayers, and they have also been reported in other arrangements of graphene layers. We investigate three such arrangements: untwisted AB bilayer graphene on an hBN substrate, two graphene bilayers twisted with respect to each other, and a single ABC sta...

Angle disorder is an important feature of twisted bilayer graphene and other moiré materials. In this work we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-Büttiker transmission through an angle disorder barrier of width comparable to the moiré perio...

Twisted bilayer graphene is highly sensitive to external perturbations. Strains, and the presence of the substrate, break the symmetries of the central bands. The resulting changes in the Berry curvature lead to valley currents and to a nonlinear Hall effect. We show that these effects, described by a Berry dipole, can be very significant, such tha...

The effect of an hexagonal boron nitride (hBN) layer close aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, θhBN≲2∘, the graphene electronic structure is strongly disturbed. The width of the low energy peak in the density of states changes from W∼5−10 meV for a decoupled sy...

Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transve...

The effect of an hexagonal boron nitride (hBN) layer close aligned with twisted bilayer graphene (TBG) is studied. At sufficiently low angles between twisted bilayer graphene and hBN, $\theta_{hBN} \lesssim 2^\circ$, the graphene electronic structure is strongly disturbed. The width of the low energy peak in the density of states changes from $W \s...

The formation of a superlattice in graphene can serve as a way to modify its electronic band structure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a copper substrate, leading to the breaking of the valley degeneracy while preserving the highly de...

The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekulé bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly des...

Since the discovery of the long-range ferromagnetic order in two-dimensional and multi-layered van der Waals crystals, and the observation of a nontrivial topology of the magnon bulk bands in the chromium trihalides, the bosonic honeycomb lattices have drawn significant attention within the condensed matter community. In this thesis, we employ a He...

We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekule-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal...

We have investigated the thermal Hall effect of magnons in a ferromagnetic honeycomb lattice with a Kekulé-O coupling (KOC) modulation and Dzyaloshinskii-Moriya interaction (DMI). By considering a strain-based mechanism for the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the therm...

We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magno...

We examine the combined effects of a Kekulé coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magno...

While the deviation of the edge on-site potential from the bulk values in a magnonic topological honeycomb lattice leads to the formation of edge states in a bearded boundary, this is not the case for a zigzag termination, where no edge state is found. In a semi-infinite lattice, the intrinsic on-site interactions along the boundary sites generate...

The difference between the edge on-site potential and the bulk values in a magnonic topological honeycomb lattice leads to the formation of edge states in a bearded boundary, and the same difference is found to be the responsible for the absence of edge states in a zig-zag termination. In a finite lattice, the intrinsic on-site interactions along t...

We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states...

We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states...

We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzialozinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the b...

We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the...

The visualization of propagation of quantum waves in space and time constitutes a valuable instrument to understand the main features of the dynamics of quantum electron transport, a phenomenon of great interest in basic and applied research in the context of the physics of low-dimensional systems. In this work, we analyze the dynamical behavior of...

Se obtienen soluciones analíticas exactas de la ecuación de Schrodinger dependiente del tiempo con condición inicial de obturador de Moshonsky bidimensional, para analizar el comportamiento dinámico del transporte electrónico en guias de onda cuánticas. Los canales de propagacion permitidos dependen de la energía de los electrones incidences y del...

Se realizó un estudio de las propiedades del transporte electrónico en guías de onda cuánticas con potenciales dispersores mediante dos formalismos distintos, el método de acoplamiento de modos y el método integral de Lippmann-Schwinger. Con el fin de disponer de una herramienta más versátil, se realizó una adaptación del formalismo de acoplamiento...