UMR 8502 Université Paris Sud

Bat 510, 91405 Orsay cedex

2020

V. F. D. Peters, Vis, M., Wensink, H. H., and Tuinier, R., “Algebraic equations of state for the liquid crystalline phase behavior of hard rods”, Phys. Rev. E, vol. 101, p. 062707, 2020. Website

S. Kwok, Botet, R., Sharpnack, L., and Cabane, B., “Apollonian packing in polydisperse emulsions”, Soft Matter, vol. 16, p. 2426-2430, 2020. Website

L. Privitera, Ziani, N. T., Safi, I., and Trauzettel, B., “Backscattering off a driven Rashba impurity at the helical edge”, Phys. Rev. B, vol. 102, p. 195413, 2020. Website

P. Stoliar, Schneegans, O., and Rozenberg, M. J., “Biologically Relevant Dynamical Behaviors Realized in an Ultra-Compact Neuron Model”, Frontiers in Neuroscience, vol. 14, p. 421, 2020. WebsiteAbstract

We demonstrate a variety of biologically relevant dynamical behaviors building on a recently introduced ultra-compact neuron (UCN) model. We provide the detailed circuits which all share a common basic block that realizes the leaky-integrate-and-fire (LIF) spiking behavior. All circuits have a small number of active components and the basic block has only three, two transistors and a silicon controlled rectifier (SCR). We also demonstrate that numerical simulations can faithfully represent the variety of spiking behavior and can be used for further exploration of dynamical behaviors. Taking Izhikevich’s set of biologically relevant behaviors as a reference, our work demonstrates that a circuit of a LIF neuron model can be used as a basis to implement a large variety of relevant spiking patterns. These behaviors may be useful to construct neural networks that can capture complex brain dynamics or may also be useful for artificial intelligence applications. Our UCN model can therefore be considered the electronic circuit counterpart of Izhikevich’s (2003) mathematical neuron model, sharing its two seemingly contradicting features, extreme simplicity and rich dynamical behavior.

K. Yang, Goerbig, M. O., and Douıfmmode \mboxç\else ç\fi{}ot, B. \^ıt, “Collective excitations of quantum Hall states under tilted magnetic field”, Phys. Rev. B, vol. 102, p. 045145, 2020. Website

V. F. D. Peters, Vis, M., Garc\'ıa, G. Á., Wensink, H. H., and Tuinier, R., “Defying the Gibbs Phase Rule: Evidence for an Entropy-Driven Quintuple Point in Colloid-Polymer Mixtures”, Phys. Rev. Lett., vol. 125, p. 127803, 2020. Website

X. Lu and Goerbig, M. O., “Dirac quantum well engineering on the surface of a topological insulator”, Phys. Rev. B, vol. 102, p. 155311, 2020. Website

I. Safi, “Fluctuation-dissipation relations for strongly correlated out-of-equilibrium circuits”, Phys. Rev. B, vol. 102, p. 041113, 2020. Website

B. van der Meer, Smallenburg, F., Dijkstra, M., and Filion, L., “High antisite defect concentrations in hard-sphere colloidal Laves phases”, Soft matter, vol. 16, p. 4155—4161, 2020. Website

G. Abramovici, “Incompatible Coulomb hamiltonian extensions”, vol. 10, no. 1, p. 7280, 2020. WebsiteAbstract

We revisit the resolution of the one-dimensional Schrödinger hamiltonian with a Coulomb λ/|x| potential. We examine among its self-adjoint extensions those which are compatible with physical conservation laws. In the one-dimensional semi-infinite case, we show that they are classified on a U(1) circle in the attractive case and on $${\boldsymbol{(}}{\mathbb{R}},{\boldsymbol{+}}{\boldsymbol{\infty }}{\boldsymbol{)}}$$(R,+∞) in the repulsive one. In the one-dimensional infinite case, we find a specific and original classification by studying the continuity of eigenfunctions. In all cases, different extensions are incompatible one with the other. For an actual experiment with an attractive potential, the bound spectrum can be used to discriminate which extension is the correct one.

J. Trastoy, et al., “Magnetic field frustration of the metal-insulator transition in ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$”, Phys. Rev. B, vol. 101, p. 245109, 2020. Website

S. Polatkan, et al., “Magneto-Optics of a Weyl Semimetal beyond the Conical Band Approximation: Case Study of TaP”, Phys. Rev. Lett., vol. 124, p. 176402, 2020. Website

C. Ferreiro-Córdova, Del Gado, E., Foffi, G., and Bouzid, M., “Multi-component colloidal gels: interplay between structure and mechanical properties”, Soft Matter, vol. 16, p. 4414-4421, 2020. Website

G. M. Thurston, Hayden, D. L., Foffi, G., Ross, D. S., and Hamilton, J. F., “On Non-Monotonic Dependence of Phase Separation Properties on Molecular Interaction Parameters”, Biophysical JournalBiophysical Journal, vol. 118, no. 3, p. 517a, 2020. Website

Y. Kalcheim, Camjayi, A., del Valle, J., Salev, P., Rozenberg, M., and Schuller, I. K., “Non-thermal resistive switching in Mott insulator nanowires”, vol. 11, no. 1, p. 2985, 2020. WebsiteAbstract

Resistive switching can be achieved in a Mott insulator by applying current/voltage, which triggers an insulator-metal transition (IMT). This phenomenon is key for understanding IMT physics and developing novel memory elements and brain-inspired technology. Despite this, the roles of electric field and Joule heating in the switching process remain controversial. Using nanowires of two archetypal Mott insulators—VO2 and V2O3 we unequivocally show that a purely non-thermal electrical IMT can occur in both materials. The mechanism behind this effect is identified as field-assisted carrier generation leading to a doping driven IMT. This effect can be controlled by similar means in both VO2 and V2O3, suggesting that the proposed mechanism is generally applicable to Mott insulators. The energy consumption associated with the non-thermal IMT is extremely low, rivaling that of state-of-the-art electronics and biological neurons. These findings pave the way towards highly energy-efficient applications of Mott insulators.

N. Ehlen, et al., “Origin of the Flat Band in Heavily Cs-Doped Graphene”, ACS Nano, vol. 14, p. 1055-1069, 2020. Website

G. Bareigts, et al., “Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters”, Phys. Rev. Lett., vol. 124, p. 058003, 2020. Website

J. - N. Fuchs, Patil, S., and Vidal, J., “Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way”, Phys. Rev. B, vol. 102, p. 115130, 2020. Website

A. F. Santander-Syro, et al., “Quantum interference effects of out-of-plane confinement on two-dimensional electron systems in oxides”, Phys. Rev. B, vol. 102, p. 075101, 2020. Website

A. } {Jagannathan and {Tarzia, M. }, “Re-entrance and localization phenomena in disordered Fibonacci chains - Disorder induced crossover from critical states to Anderson localized states”, Eur. Phys. J. B, vol. 93, p. 46, 2020. Website

B. Real, et al., “Semi-Dirac Transport and Anisotropic Localization in Polariton Honeycomb Lattices”, Phys. Rev. Lett., vol. 125, p. 186601, 2020. Website

P. Bruneel and Gabay, M., “Spin texture driven spintronic enhancement at the $\mathrm{La}\mathrm{Al}{\mathrm{O}}_{3}/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ interface”, Phys. Rev. B, vol. 102, p. 144407, 2020. Website

G. Rai, Haas, S., and Jagannathan, A., “Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems”, Phys. Rev. B, vol. 102, p. 134211, 2020. Website

S. Mar\'ın-Aguilar, Wensink, H. H., Foffi, G., and Smallenburg, F., “Tetrahedrality Dictates Dynamics in Hard Sphere Mixtures”, Phys. Rev. Lett., vol. 124, p. 208005, 2020. Website

B. Loret, et al., “Universal relationship between the energy scales of the pseudogap phase, the superconducting state, and the charge-density-wave order in copper oxide superconductors”, Phys. Rev. B, vol. 101, p. 214520, 2020. Website

V. Perrin, et al., “Unveiling Odd-Frequency Pairing around a Magnetic Impurity in a Superconductor”, Phys. Rev. Lett., vol. 125, p. 117003, 2020. Website

2019

A. M. R. V. L. Monteiro, et al., “Band inversion driven by electronic correlations at the (111) ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface”, Phys. Rev. B, vol. 99, p. 201102, 2019. Website

N. Manca, et al., “Bimodal Phase Diagram of the Superfluid Density in LaAlO3/SrTiO3 Revealed by an Interfacial Waveguide Resonator”, PHYSICAL REVIEW LETTERS, vol. 122, p. 036801, 2019.Abstract

We explore the superconducting phase diagram of the two-dimensional electron system at the LaAlO3/SrTiO3 interface by monitoring the frequencies of the cavity modes of a coplanar waveguide resonator fabricated in the interface itself. We determine the phase diagram of the superconducting transition as a function of the temperature and electrostatic gating, finding that both the superfluid density and the transition temperature follow a dome shape but that the two are not monotonically related. The ground state of this two-dimensional electron system is interpreted as a Josephson junction array, where a transition from long-to short-range order occurs as a function of the electronic doping. The synergy between correlated oxides and superconducting circuits is revealed to be a promising route to investigate these exotic compounds, complementary to standard magnetotransport measurements.

M. Trif and Simon, P., “Braiding of Majorana Fermions in a Cavity”, Phys. Rev. Lett., vol. 122, p. 236803, 2019. Website

A. Hichri, Jaziri, S., and Goerbig, M. O., “Charged excitons in two-dimensional transition metal dichalcogenides: Semiclassical calculation of Berry curvature effects”, Phys. Rev. B, vol. 100, p. 115426, 2019. Website

S. Chen, et al., “Competing Fractional Quantum Hall and Electron Solid Phases in Graphene”, PHYSICAL REVIEW LETTERS, vol. 122, p. 026802, 2019.Abstract

We report experimental observation of the reentrant integer quantum Hall effect in graphene, appearing in the N = 2 Landau level. Similar to high-mobility GaAs/AlGaAs heterostructures, the effect is due to a competition between incompressible fractional quantum Hall states, and electron solid phases. The tunability of graphene allows us to measure the B-T phase diagram of the electron solid phase. The hierarchy of reentrant states suggests spin and valley degrees of freedom play a role in determining the ground state energy. We find that the melting temperature scales with magnetic field, and construct a phase diagram of the electron liquid-solid transition.

A. Borin, Safi, I., and Sukhorukov, E., “Coulomb drag effect induced by the third cumulant of current”, Phys. Rev. B, vol. 99, p. 165404, 2019. Website

B. Sung, Wensink, H. H., and Grelet, E., “Depletion-driven morphological transitions in hexagonal crystallites of virus rods”, Soft Matter, vol. 15, p. 9520-9527, 2019. WebsiteAbstract

The assembly of nanometer-sized building blocks into complex morphologies is not only of fundamental interest but also plays a key role in material science and nanotechnology. We show that the shape of self-assembled superstructures formed by rod-like viruses can be controlled by tuning the attraction via the depletion interaction between the rods. Using non-adsorbing polymers as a depleting agent{,} we demonstrate that a hierarchical unidimensional self-organization into crystalline clusters emerges progressively upon increasing depletion attraction and enhanced growth kinetics. We observe a polymorphic change proceeding from two-dimensional (2D) crystalline monolayers at weak depletion to one-dimensional (1D) columnar fibers at strong depletion{,} via the formation of smectic fibrils at intermediate depletion strength. A simple theory for reversible polymerization enables us to determine the typical bond energy between monomeric units making up the smectic fibrils. We also demonstrate that gentle flow-assistance can be used to template filament-like structures into highly aligned supported films. Our results showcase a generic bottom-up approach for tuning the morphology of crystalline superstructures through modification of the interaction between non-spherical building blocks. This provides a convenient pathway for controlling self-organization{,} dimensionality and structure-formation of anisotropic nanoparticles for use in nanotechnology and functional materials.

A. A. Zyuzin and Simon, P., “Disorder-induced exceptional points and nodal lines in Dirac superconductors”, Phys. Rev. B, vol. 99, p. 165145, 2019. Website

I. Safi, “Driven quantum circuits and conductors: A unifying perturbative approach”, PHYSICAL REVIEW B, vol. 99, p. 045101, 2019.Abstract

We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is nonperturbative with respect to strong coupling to an electromagnetic environment or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage V-dc, and the out-of-equilibrium dc current which encodes the effects of interactions. We extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge q free from unknown parameters through the robustness of the Josephson-like frequency. We have derived similar relations for noise (I. Safi, arXiv:1401.5950) which have been exploited, recently, to determine the fractional charge in the fractional quantum Hall effect (FQHE) within the Jain series {[}M. Kapfer et al., Science (to be published)]. The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates rectification exploited here to propose methods to measure the charge q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-Gaussian source of noise. We also apply the theory to the Tomonaga-Luttinger liquid (TLL), showing a counterintuitive feature: A Lorentzian pulse superimposed on V-dc can reduce the current compared to its dc value, at the same V-dc, questioning the terminology ``photoassisted.{''} Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect or voltage drop across a phase-slip Josephson junction.

R. Botet and Kuratsuji, H., “The duality between a non-Hermitian two-state quantum system and a massless charged particle”, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 52, p. 035303, 2019.Abstract

We show that the equations for the dynamics of a non-Hermitian two-state quantum system arc the same as the equations of motion for a massless charged particle in an electromagnetic field. Using simple analytical arguments to prove this unexpected duality between two very different domains in physics, we further exemplify it through a case-study of polarization of light propagating in a dichroic medium with magneto-optic activity.

H. H. Wensink, “Effect of Size Polydispersity on the Pitch of Nanorod Cholesterics”, Crystals, vol. 9, 2019. WebsiteAbstract

Many nanoparticle-based chiral liquid crystals are composed of polydisperse rod-shaped particles with considerable spread in size or shape, affecting the mesoscale chiral properties in, as yet, unknown ways. Using an algebraic interpretation of Onsager-Straley theory for twisted nematics, we investigate the role of length polydispersity on the pitch of nanorod-based cholesterics with a continuous length polydispersity, and find that polydispersity enhances the twist elastic modulus, K 2 , of the cholesteric material without affecting the effective helical amplitude, K t . In addition, for the infinitely large average aspect ratios considered here, the dependence of the pitch on the overall rod concentration is completely unaffected by polydispersity. For a given concentration, the increase in twist elastic modulus (and reduction of the helical twist) may be up to 50% for strong size polydispersity, irrespective of the shape of the unimodal length distribution. We also demonstrate that the twist reduction is reinforced in bimodal distributions, obtained by doping a polydisperse cholesteric with very long rods. Finally, we identify a subtle, non-monotonic change of the pitch across the isotropic-cholesteric biphasic region.

S. Brazovskii and Kirova, N., “From chiral anomaly to two-fluid hydrodynamics for electronic vortices”, Annals of Physics, vol. 403, p. 184 - 197, 2019. WebsiteAbstract

Many recent experiments addressed manifestations of electronic crystals, particularly the charge density waves, in nano-junctions, under electric field effect, at high magnetic fields, together with real space visualizations by STM and micro X-ray diffraction. This activity returns the interest to stationary or transient states with static and dynamic topologically nontrivial configurations: electronic vortices as dislocations, instantons as phase slip centers, and ensembles of microscopic solitons. Describing and modeling these states and processes calls for an efficient phenomenological theory which should take into account the degenerate order parameter, various kinds of normal carriers and the electric field. Here we notice that the commonly employed time-depend Ginzburg–Landau approach suffers with violation of the charge conservation law resulting in unphysical generation of particles which is particularly strong for nucleating or moving electronic vortices. We present a consistent theory which exploits the chiral transformations taking into account the principle contribution of the fermionic chiral anomaly to the effective action. The resulting equations clarify partitions of charges, currents and rigidity among subsystems of the condensate and normal carriers. On this basis we perform the numerical modeling of a spontaneously generated coherent sequence of phase slips – the spacetime vortices – serving for the conversion among the injected normal current and the collective one.

B. Loret, et al., “Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates”, Nature Physics, vol. 15, p. 771-775, 2019. WebsiteAbstract

The cuprate high-temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature TCDW and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases1,2. To address this issue, it is important to extract the energy scale DCDW associated with the CDW order, and to compare it with the pseudogap DPG and with the superconducting gap DSC. However, while TCDW is well characterized from earlier work3, little is currently known about DCDW. Here, we report the extraction of DCDW for several cuprates using electronic Raman spectroscopy. We find that on approaching the parent Mott state by lowering p, DCDW increases in a manner similar to the doping dependence of DPG and DSC. This reveals that these three phases have a common microscopic origin. In addition, we find that DCDW [?] DSC over a substantial doping range, which suggests that CDW and superconducting phases are intimately related; for example, they may be intertwined or connected by an emergent symmetry1,4-9.

G. C. Ménard, et al., “Isolated pairs of Majorana zero modes in a disordered superconducting lead monolayer”, Nature Communications, vol. 10, p. 2587, 2019. WebsiteAbstract

Majorana zero modes are fractional quantum excitations appearing in pairs, each pair being a building block for quantum computation. Some signatures of Majorana zero modes have been reported at endpoints of one-dimensional systems, which are however required to be extremely clean. An alternative are two-dimensional topological superconductors, such as the Pb/Co/Si(111) system shown recently to be immune to local disorder. Here, we use scanning tunneling spectroscopy to characterize a disordered superconducting monolayer of Pb coupled to underlying Co-Si magnetic islands. We show that pairs of zero modes are stabilized: one zero mode positioned in the middle of the magnetic domain and its partner extended all around the domain. The zero mode pair is remarkably robust, isolated within a hard superconducting gap. Our theoretical scenario supports the protected Majorana nature of this zero mode pair, highlighting the role of magnetic or spin-orbit coupling textures.

J. - N. Fuchs, Mosseri, R., and Vidal, J., “Landau level broadening, hyperuniformity, and discrete scale invariance”, Phys. Rev. B, vol. 100, p. 125118, 2019. Website

S. Rostamzadeh, Adagideli, ıfmmode \dot{I. }\else İ. \fi{}nanıfmmode \mboxç\else ç\fi{}, and Goerbig, M. O., “Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response”, Phys. Rev. B, vol. 100, p. 075438, 2019. Website

Y. Zhang, et al., “Machine learning in electronic-quantum-matter imaging experiments”, Nature, vol. 570, p. 484-490, 2019. WebsiteAbstract

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena1. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science2-5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)6-16, the next challenge is to apply this approach to experimental data–for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals18,19 are consistent with these observations.

X. Lu and Goerbig, M. O., “Magneto-optical signatures of Volkov-Pankratov states in topological insulators”, {EPL} (Europhysics Letters), vol. 126, p. 67004, 2019. WebsiteAbstract

In addition to the usual chiral surface states, massive surface states can arise at a smooth interface between a topological and a trivial bulk insulator. While not subject to topological protection as the chiral states, these massive states, theorized by Volkov and Pankratov in the 1980s, reflect nevertheless emergent Dirac physics at the interface. We study theoretically the magneto-optical response of these surface states, which is strikingly different from that of the bulk states. Most saliently, we show that these states can be identified clearly in the presence of a magnetic field and its orientation with respect to the interface.

X. } {Lu and {Goerbig, M. O. }, “Magneto-optical signatures of Volkov-Pankratov states in topological insulators”, EPL, vol. 126, p. 67004, 2019. Website

D. C. Vaz, et al., “Mapping spin–charge conversion to the band structure in a topological oxide two-dimensional electron gas”, vol. 18, no. 11, p. 1187 - 1193, 2019. WebsiteAbstract

While spintronics has traditionally relied on ferromagnetic metals as spin generators and detectors, spin–orbitronics exploits the efficient spin–charge interconversion enabled by spin–orbit coupling in non-magnetic systems. Although the Rashba picture of split parabolic bands is often used to interpret such experiments, it fails to explain the largest conversion effects and their relationship with the electronic structure. Here, we demonstrate a very large spin-to-charge conversion effect in an interface-engineered, high-carrier-density SrTiO3 two-dimensional electron gas and map its gate dependence on the band structure. We show that the conversion process is amplified by enhanced Rashba-like splitting due to orbital mixing and in the vicinity of avoided band crossings with topologically non-trivial order. Our results indicate that oxide two-dimensional electron gases are strong candidates for spin-based information readout in new memory and transistor designs. Our results also emphasize the promise of topology as a new ingredient to expand the scope of complex oxides for spintronics.

R. Bisognin, et al., “Microwave photons emitted by fractionally charged quasiparticles”, Nature Communications, vol. 10, p. 1708, 2019. WebsiteAbstract

Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.

R. Bisognin, et al., “Microwave photons emitted by fractionally charged quasiparticles”, Nature Communications, vol. 10, no. 1, p. 1708, 2019. WebsiteAbstract

Strongly correlated low-dimensional systems can host exotic elementary excitations carrying a fractional charge q and potentially obeying anyonic statistics. In the fractional quantum Hall effect, their fractional charge has been successfully determined owing to low frequency shot noise measurements. However, a universal method for sensing them unambiguously and unraveling their intricate dynamics was still lacking. Here, we demonstrate that this can be achieved by measuring the microwave photons emitted by such excitations when they are transferred through a potential barrier biased with a dc voltage Vdc. We observe that only photons at frequencies f below qVdc/h are emitted. This threshold provides a direct and unambiguous determination of the charge q, and a signature of exclusion statistics. Derived initially within the Luttinger model, this feature is also predicted by universal non-equilibrium fluctuation relations which agree fully with our measurements. Our work paves the way for further exploration of anyonic statistics using microwave measurements.

A. Jagannathan, Jeena, P., and Tarzia, M., “Nonmonotonic crossover and scaling behavior in a disordered one-dimensional quasicrystal”, PHYSICAL REVIEW B, vol. 99, p. 054203, 2019.Abstract

We consider a noninteracting disordered 1D quasicrystal in the weak-disorder regime. We show that the critical states of the pure model approach strong localization in strikingly different ways, depending on their renormalization properties. A finite-size scaling analysis of the inverse participation ratios of states (IPR) of the quasicrystal shows that they are described by several kinds of scaling functions. While most states show a progressively increasing IPR as a function of the scaling variable, other states exhibit a nonmonotonic ``reentrant{''} behavior wherein the IPR first decreases, and passes through a minimum, before increasing. This surprising behavior is explained in the framework of perturbation renormalization group treatment, where wave functions can be computed analytically as a function of the hopping amplitude ratio and the disorder, however it is not specific to this model. Our results should help to clarify results of recent studies of localization due to random and quasiperiodic potentials.

H. H. Wensink, “Polymeric Nematics of Associating Rods: Phase Behavior, Chiral Propagation, and Elasticity”, MacromoleculesMacromolecules, vol. 52, no. 21, p. 7994 - 8005, 2019. Website

1. S. Sakai and Civelli, M., “Doping evolution of the electron-hole asymmetric s-wave pseudogap in underdoped high-Tc cuprate superconductors”, JPS Conf. Proc. 2014. Website

2. M. O. Goerbig, Montambaux, G., and Piéchon, F., “Measure of Diracness in two-dimensional semiconductors”, 2014. Website

3. P. Stoliar, Rozenberg, M., and et al., “Non-volatile multilevel resistive switching memory cell: A transition metal oxide-based circuit”, IEEE Transactions on CAS II , 2014. Website

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5. A. Jagannathan and Duneau, M., “Tight-binding models in a quasiperiodic optical lattice”, International Conference on Quasicrystals CQ12 (Kracow, Poland) . 2014. Website

6. H. H. Wensink and et al., “Differently Shaped Hard Body Colloids in Confinement: From passive to active particles ”, Eur. Phys. J. Special Topics, no. 222, p. 3023, 2013. Website

7. C. P. Moca, Simon, P., and et al., “Finite-frequency-dependent noise of a quantum dot in a magnetic field”, 2013. Website

8. N. Thiebaut, Regnault, N., and Goerbig, M. O., “Fractional quantum Hall states in charge-imbalanced bilayer systems ”, J. Phys.: Conf. Ser. , no. 456, p. 012036 , 2013. Website