Papers by Cristiane Morais Smith
Physical Review Research
Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena aris... more Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would manifest at noninteger dimension. Here, we report on the appearance of fractal eigenvalue degeneracies and Fermi surfaces in Hermitian and non-Hermitian topological band structures. This might have profound implications on the physics of black holes and Fermi surface instability driven phenomena, such as superconductivity and charge density waves.
Bulletin of the American Physical Society, 2016
Recent works demonstrate that 2D singlecrystalline sheets of semiconductors forming a honeycomb l... more Recent works demonstrate that 2D singlecrystalline sheets of semiconductors forming a honeycomb lattice can be synthesized by oriented attachment of semiconductor nanocrystals. Inspired by these results, we have performed atomistic tight-binding calculations of the band structure of CdSe [1] and HgTe [2] sheets with honeycomb nano-geometry. In the case of CdSe [1], we predict that their conduction band exhibits Dirac cones at two distinct energies. The lowest one has s-orbital character. The bands higher in energy present a Dirac cone and nontrivial flat bands because of their p-orbital character. We show that lattices of HgTe [2] combine the effects of the honeycomb geometry and strong spinorbit coupling. The conduction bands can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin-orbit coupling. This results in very large topological gaps and a flattened band detached from the others. Honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase. [1] E.
Crossover from rigid to elastic vortex creep in thin layered superconductors with columnar defects
Physical Review Letters, 2016
Topological states of matter are peculiar quantum phases showing different edge and bulk transpor... more Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a tenfold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.
The European Physical Journal B, 2016
The experimental observation of the renormalization of the Fermi velocity vF as a function of dop... more The experimental observation of the renormalization of the Fermi velocity vF as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field B, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in B, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.
Fractal Nodal Band Structures
arXiv (Cornell University), Apr 18, 2023
Physical Review B
Non-Hermitian systems have provided a rich platform to study unconventional topological phases. T... more Non-Hermitian systems have provided a rich platform to study unconventional topological phases. These phases are usually robust against external perturbations that respect certain symmetries of the system. In this work, we provide a new method to analytically study the effect of disorder, using tools from quantum field theory applied to discrete models around phase-transition points. We investigate two different one-dimensional models, the paradigmatic non-Hermitian SSH model and a s-wave superconductor with imbalanced pairing. These analytic results are compared to numerical simulations in the discrete models. An universal behavior is found for the two investigated models, namely that the systems are driven from a topological to a trivial phase for disorder strengths equal to about four times the energy scale of the model.
Physical Review B
The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocitydepe... more The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocitydependent coupling. That leads to the description of a set of models able to capture Markovian and non-Markovian versions of Brownian and Lévy statistics, depending on the functional form of the coupling and on the spectral function of the reservoir. One specific coupling force is found that establishes a connection with Lévy statistics of cold atoms in Sisyphus laser cooling. In the low-velocity limit, this also gives rise to additional inertia of the Brownian particle, reproducing the Abraham-Lorentz equation from first principles for a superohmic bath. Through path-integral quantization in Euclidean time, the environment is integrated out, leaving a set of non-local effective actions. These results further serve as starting points for several numerical calculations, particularly decoherence properties of non-ohmic baths.
arXiv e-prints, Mar 1, 2020
The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocitydepe... more The Caldeira-Leggett model of quantum Brownian motion is generalized using a generic velocitydependent coupling. That leads to the description of a set of models able to capture Markovian and non-Markovian versions of Brownian and Lévy statistics, depending on the functional form of the coupling and on the spectral function of the reservoir. One specific coupling force is found that establishes a connection with Lévy statistics of cold atoms in Sisyphus laser cooling. In the low-velocity limit, this also gives rise to additional inertia of the Brownian particle, reproducing the Abraham-Lorentz equation from first principles for a superohmic bath. Through path-integral quantization in Euclidean time, the environment is integrated out, leaving a set of non-local effective actions. These results further serve as starting points for several numerical calculations, particularly decoherence properties of non-ohmic baths.
Preparation and study of semiconductors with a honeycomb nanogeometry
International Conference on Fundamental Processes in Semiconductor Nanocrystals, FQDots14, Sep 8, 2014
Physical review, May 3, 2022
We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a... more We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce dual free bosonic fields, with a propagator corresponding to an effective (renormalized) interaction with Maki-Thompson and Aslamazov-Larkin type corrections and beyond, and demonstrate that the superconducting pairing originates as an instability of the effective interaction. We derive the corresponding Bethe-Salpeter equation (instability criterion) and show that the interaction enters the equation only in its effective form to all orders, including the exchange part of the self-energy. An important implication of this result is that the effective interaction always remains finite, even at phase-transition points, directly contradicting the often used assumption of linear relationship between the interaction and susceptibility, established within the random-phase approximation. By analyzing the Bethe-Salpeter equation in the context of unconventional superconductivity, we find that the presence of a flat band close the Fermi level, found in materials such as twisted bilayer graphene, has a twofold favorable impact persisting beyond the weak-coupling approximation: a reduced kinetic energy cost of the gap formation and an increased anisotropy of the effective interaction, favoring a momentum dependent order parameter.
arXiv: Statistical Mechanics, 2020
We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is foun... more We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is found that the critical point of the topological phase transition coincides with the maxima of the efficiency and work output of the total Otto engine. Finite size effects are taken into account using the method of Hill's nanothermodynamics, as well as using the method of temperature-dependent energy levels. We identify the bulk and boundary thermal cycles of the Kitaev chain engine and find that they are non-ideal Otto cycles. The physics of deviation from ideal Otto cycle is identified as a finite size effect, which we dub as "topological friction", leading to heat transfer from the bulk to the boundary during adiabatic transformation of the whole system. Besides, we have determined the regimes allowing for independently running an ideal Otto refrigerator at the boundary and ideal Otto engines in the bulk and in the whole system. Furthermore, we show that the first-order phas...
Physical Review Research, 2021
One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge... more One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge modes. Their existence is a consequence of the bulk-boundary correspondence and their stability guarantees the quantization of the transverse conductance. In this work, we study two microscopic models, the Hofstadter lattice model and an extended version of Haldane's Chern insulator. Both models host Quantum Hall phases in two dimensions. We transfer them to lattice implementations of fractals with a dimension between one and two and study the existence and robustness of their edge states. Our main observation is that, contrary to their two-dimensional counterpart, there is no universal behavior of the edge modes in fractals. Instead, their presence and stability critically depends on details of the models and the lattice realization of the fractal.
Physical Review B, 2020
We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is foun... more We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is found that the critical point of the topological phase transition coincides with the maxima of the efficiency and work output of the total Otto engine. Finite-size effects are taken into account using the method of Hill's nanothermodynamics, as well as using the method of temperature-dependent energy levels. We identify the bulk and boundary thermal cycles of the Kitaev chain engine and find that they are non-ideal Otto cycles. The physics of deviation from ideal Otto cycle is identified as a finite size effect, which we dub as "internal geometric friction", leading to heat transfer from the bulk to the boundary during the adiabatic transformation of the whole system. Besides, we determine the regimes allowing for independently running an ideal Otto refrigerator at the boundary and ideal Otto engines in the bulk and in the whole system. Furthermore, we show that the first-order phase transition in the boundary and the second-order phase transition in the bulk can be identified through their respective contributions to the engine work output.
Theory anticipates that the in-plane p x , p y orbitals in a honeycomb lattice lead to potentiall... more Theory anticipates that the in-plane p x , p y orbitals in a honeycomb lattice lead to potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and excitonpolaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s−p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orbital bands, including the p orbital flat band and Dirac cone.
Physical Review Research, 2020
Journal of Physics: Conference Series, 2019
Electron pumping in topological materials has attracted a lot of attention recently. Even in the ... more Electron pumping in topological materials has attracted a lot of attention recently. Even in the most intensely studied example, the integer quantum Hall cylinder, the detailed dynamics of topological charge transport remains difficult to visualize, due to the presence of gauge symmetry. Here, we exploit the absence of gauge freedom in one-dimensional charge ordered systems subject to an external driving force, to demonstrate details of their topological pumping. Inspection of the instantaneous eigenstates of a particular mean-field charge ordered model reveals an interplay between topological edge states and the mobility edge. The results also allow us to visualize adiabatic (Thouless) pumping in general charge ordered materials and other topological systems.
Physical Review B, 2019
The ability to pump quantised amounts of charge is one of the hallmarks of topological materials.... more The ability to pump quantised amounts of charge is one of the hallmarks of topological materials. An archetypical example is Laughlin's gauge argument for transporting an integer number of electrons between the edges of a quantum Hall cylinder upon insertion of a magnetic flux quantum. This is mathematically equivalent to the equally famous suggestion of Thouless' that an integer number of electrons are pumped between two ends of a one-dimensional quantum wire upon sliding a charge-density wave over a single wave length. We use the correspondence between these descriptions to visualise the detailed dynamics of the electron flow during a single pumping cycle, which is difficult to do directly in the quantum Hall setup, because of the gauge freedom inherent to its description. We find a close correspondence between topological edge states and the mobility edges in charge-density wave, quantum Hall, and other topological systems. We illustrate this connection by describing an alternative, non-adiabatic mode of topological transport that displaces precisely the opposite amount of charge as compared to the adiabatic pump. We discuss possible experimental realisations in the context of ultracold atoms and photonic waveguide experiments.
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Papers by Cristiane Morais Smith