Massimo Rontani

National Research Council, Roma, Latium, Italy

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Publications (84)283.77 Total impact

  • Pino D'Amico, Massimo Rontani
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    ABSTRACT: We study a few Fermi atoms interacting through attractive contact forces in a one-dimensional trap by means of numerical exact diagonalization. From the combined analysis of energies and wave functions of correlated ground and excited states we find evidence of BCS-like pairing even for very few atoms. For moderate interaction strength, we reproduce the even-odd oscillation of the separation energy observed in [G. Zuern, A. N. Wenz, S. Murmann, A. Bergschneider, T. Lompe, and S. Jochim, Phys. Rev. Lett. 111, 175302 (2013)]. For stronger interactions nonlinear, co-operative effects emerge, including non trivial spatial arrangement of atomic Cooper pairs in the trap.
    04/2014;
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    Pino D'Amico, Massimo Rontani
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    ABSTRACT: We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a one-dimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark for exact-diagonalization technique (also known as full configuration interaction), which is found to slowly converge in the case of strong interatomic attraction.
    Journal of Physics B Atomic Molecular and Optical Physics 10/2013; 47(6). · 2.03 Impact Factor
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    Massimo Rontani
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    ABSTRACT: A simple theory for the tunneling of two cold atoms out of a trap in the presence of an attractive contact force is developed. Two competing decay channels, respectively for single-atom and bound-pair tunneling, contribute independently to the decay law of the mean atom number in the trap. The single-atom tunneling rate is obtained through the quasiparticle wave function formalism. For pair tunneling an effective equation for the center-of-mass motion is derived, so the calculation of the corresponding tunneling rate is again reduced to a simpler one-body problem. The predicted dependence of tunneling rates on the interaction strength qualitatively agrees with a recent measurement of the two-atom decay time [G. Zuern, A. N. Wenz, S. Murmann, T. Lompe, and S. Jochim, arXiv:1307.5153].
    Physical Review A 08/2013; 88(4). · 3.04 Impact Factor
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    ABSTRACT: Two electrons on a string form a simple model system where Coulomb interactions are expected to play an interesting role. In the presence of strong interactions, these electrons are predicted to form a Wigner molecule, separating to the ends of the string. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet so far a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultraclean carbon nanotube to realize this system in a tunable potential. Using tunnelling spectroscopy we measure the addition spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their exchange symmetries. The formation of a Wigner molecule is evident from a tenfold quenching of the fundamental excitation energy as compared with the non-interacting value. Our ability to tune the two-carrier state in space and to study it for both electrons and holes provides an unambiguous demonstration of this strongly interacting quantum ground state. O ne of the simplest realizations of an interacting quantum-mechanical system is that of two electrons on a string. The behavior of this system is governed by the bal-ance between kinetic and interaction energies. When kinetic energy dominates, the electrons occupy particle-in-a-box levels along the string. In contrast, when interactions dominate, a Wigner-molecule ground state is formed, in which the repulsion of the two electrons drives them to localize at the two sides of the string 1,2 . Owing to the fermionic nature of the two particles their total wavefunction is anti-symmetric with respect to electron exchange, leading to an intimate connection between their real-space and spin-space behaviours. Consequently, the real-space charge separation in a Wigner molecule goes hand in hand with a spin-space signature, namely a pronounced quenching of its spin excitation energies 3 . A carbon nanotube is an excellent system to search for the existence of a Wigner-molecule ground state. This system is known to have strong electron–electron interactions 4–8 , and can be clean enough to allow measurements down to the single-carrier limit 9,10 , made more accessible by recent technological breakthroughs 11–14 . Some of these measurements showed unexplained deviations from the expected shell-filling model, which hinted that interesting physics occur at low electronic numbers 9,11,12 . Compared with iii–v semiconductor systems 15–18 in which Wigner-molecule formation has been explored previously, in suspended nanotubes the screening of Coulomb interactions is strongly reduced and the one-dimensional confinement potential for electrons or holes can be shaped with gate electrodes. This ability to control the confining potential is critical because it allows one to distinguish between extrinsic electrostatic effects that spatially separate the two electrons and intrinsic separation driven by their repulsion. Furthermore, in addition to the conventional twofold spin degeneracy in other semiconductors, electrons in nanotubes possess a twofold orbital degeneracy (isospin), forming a fourfold spin–isospin subspace. Recent experiments 12 have shown that the electrons'
    Nature Physics 07/2013; 9:576-581. · 19.35 Impact Factor
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    Andrea Secchi, Massimo Rontani
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    ABSTRACT: We develop a theory of inter-valley Coulomb scattering in semiconducting carbon-nanotube quantum dots, taking into account the effects of curvature and chirality. Starting from the effective-mass description of single-particle states, we study the two-electron system by fully including Coulomb interaction, spin-orbit coupling, and short-range disorder. We find that the energy level splittings associated with inter-valley scattering are nearly independent of the chiral angle and, while smaller than those due to spin-orbit interaction, large enough to be measurable.
    Physical Review B 06/2013; 88(12). · 3.66 Impact Factor
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    Massimo Rontani, L. J. Sham
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    ABSTRACT: We review the topic of Bose-Einstein condensation of excitons in semiconductors, focusing on the signatures of the macroscopic order of the exciton condensate.
    01/2013;
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    Dimitrios Toroz, Massimo Rontani, Stefano Corni
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    ABSTRACT: Scanning tunneling spectroscopy (STS) allows us to image single molecules decoupled from the supporting substrate. The obtained images are routinely interpreted as the square moduli of molecular orbitals, dressed by the mean-field electron-electron interaction. Here we demonstrate that the effect of electron correlation beyond the mean field qualitatively alters the uncorrelated STS images. Our evidence is based on the ab initio many-body calculation of STS images of planar molecules with metal centers. We find that many-body correlations alter significantly the image spectral weight close to the metal center of the molecules. This change is large enough to be accessed experimentally, surviving to molecule-substrate interactions.
    Physical Review Letters 01/2013; 110(1):018305. · 7.73 Impact Factor
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    Massimo Rontani
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    ABSTRACT: A theory for the tunneling of one atom out of a trap containing two interacting cold atoms is developed. The quasiparticle wave function, dressed by the interaction with the companion atom in the trap, replaces the noninteracting orbital at resonance in the tunneling matrix element. The computed decay time for two ^{6}Li atoms agrees with recent experimental results [G. Zürn, F. Serwane, T. Lompe, A. N. Wenz, M. G. Ries, J. E. Bohn, and S. Jochim, Phys. Rev. Lett. 108, 075303 (2012)], unveiling the "fermionization" of the wave function and a novel two-body effect.
    Physical Review Letters 03/2012; 108(11):115302. · 7.73 Impact Factor
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    ABSTRACT: We study by means of exact-diagonalization techniques the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays at strong coupling very well pronounced Friedel oscillations with a `4k_F periodicity', the pair correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.
    Physical review. B, Condensed matter 02/2012; 86(7). · 3.77 Impact Factor
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    ABSTRACT: We observe a low-lying sharp spin mode of three interacting electrons in an array of nanofabricated AlGaAs/GaAs quantum dots by means of resonant inelastic light scattering. The finding is enabled by a suppression of the inhomogeneous contribution to the excitation spectra obtained by reducing the number of optically probed quantum dots. Supported by configuration-interaction calculations we argue that the observed spin mode offers a direct probe of Stoner ferromagnetism in the simplest case of three interacting spin one-half fermions.
    Physical review. B, Condensed matter 09/2011; 85(3). · 3.77 Impact Factor
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    Andrea Secchi, Massimo Rontani
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    ABSTRACT: We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub-) Kelvin range.
    Physical review. B, Condensed matter 09/2011; · 3.77 Impact Factor
  • Massimo Rontani
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    ABSTRACT: Tunnelling and capacitance spectroscopies are able to image the wavefunctions of electrons in atom-like solid-state systems as they are shaped by an external magnetic field.
    Nature Material 03/2011; 10(3):173-5. · 35.75 Impact Factor
  • Massimo Rontani, Dimitrios Toroz, Stefano Corni
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    ABSTRACT: Scanning tunnelling spectroscopy (STS) visualizes electron states in both extended systems and nano-objects, as quantum dots and molecules. Whereas bulk quantum states are insensitive to electron number fluctuations, an energy gap opens each time a new electron is injected by the STS tip into a sufficiently small system. This gap originates from the interaction of the next incoming electron with the others already present in the system. In this Coulomb blockade regime a fundamental question is whether the wave function of the "quasi-particle" added to the system -imaged by the STS tip- is sensitive to electron-electron interaction. Here we show that the STS images of single planar molecules with metal centres predicted by ab initio many-body calculations differ qualitatively from their uncorrelated counterparts. We find in the maps resolved at the Fermi energy that correlation significantly removes spectral weight from the metal atom, as well as the overall weight is remarkably reduced. This change may be measured and compared with STS images of molecules without the metal center, whose many-body and uncorrelated versions are alike.
    03/2011;
  • Andrea Secchi, Massimo Rontani
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    ABSTRACT: The paradigm of few-electron complexes in quantum dots (QDs) relies on the idea that the lowest quantized levels are filled according to Pauli's exclusion principle. If Coulomb repulsion is sufficiently strong to overcome the kinetic energy cost of localization, a different scenario is predicted: a "Wigner" molecule (WM) forms, made of electrons frozen in space according to a geometrical pattern. Despite considerable experimental effort, evidence of the WM in semiconductor QDs has been elusive so far. Here we demonstrate theoretically that WMs occur in gate-defined QDs embedded in typical semiconducting carbon nanotubes (CNTs). The unambiguous signatures of the WM state must be searched in the scanning tunneling microscopy (STM) images of the electrons. Through exact diagonalisation (ED) calculations, we unveil the inherent features of the electron molecular states. We show that, like nuclei in a usual molecule, electrons have localized wave functions and hence negligible exchange interactions. ED results for single and double QDs provide a simple interpretation for transport experiments in ultraclean CNTs.
    03/2011;
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    Dimitrios Toroz, Massimo Rontani, Stefano Corni
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    ABSTRACT: Scanning tunneling microscopy (STM) has been a fundamental tool to characterize many-body effects in condensed matter systems, from extended solids to quantum dots. STM of molecules decoupled from the supporting conductive substrate has the potential to extend STM characterization of many-body effects to the molecular world as well. In this paper, we describe a many-body tunneling theory for molecules decoupled from the STM substrate, and we report on the use of standard quantum chemical methods to calculate the quantities necessary to provide the "correlated" STM molecular image. The developed approach has been applied to 18 different molecules to explore the effects of their chemical nature and of their substituents, as well as to verify the possible contribution by transition metal centers. Whereas the bulk of calculations has been performed with the configuration interaction method with single and double excitations (CISD), because of the computational cost some tests have been also performed with the more accurate coupled cluster with single and double excitations (CCSD) method to quantify the importance of the computational level on many-body STM images. We have found that correlation induces a remarkable squeezing of the images, and that correlated images are not derived from Hartree-Fock HOMO or LUMO alone, but include contributions from other orbitals as well. Although correlation effects are too small to be resolved by present STM experiments for the studied molecules, our results provide hints for seeking out other species with larger, and possibly experimentally detectable, correlation effects.
    The Journal of Chemical Physics 01/2011; 134(2):024104. · 3.12 Impact Factor
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    Massimo Rontani
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    ABSTRACT: The transmission phase through a quantum dot with few electrons shows a complex, non-universal behavior. Here we combine configuration-interaction calculations ---treating rigorously Coulomb interaction--- and the Friedel sum rule to provide a rationale for the experimental findings. The phase evolution for more than two electrons is found to strongly depend on dot's shape and electron density, whereas from one to two the phase never lapses. In the Coulomb (Kondo) regime the phase shifts are significant fractions of pi (pi/2) for the second and subsequent charge addition if the dot is strongly correlated. These results are explained by the proper inclusion in the theory of Coulomb interaction, spin, and orbital degrees of freedom. Comment: RevTeX 4.0, 6 pages, 3 b/w figures. Physical Review B (2010), in press
    Physical review. B, Condensed matter 07/2010; · 3.77 Impact Factor
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    ABSTRACT: We observe the low-lying excitations of a molecular dimer formed by two electrons in a GaAs semiconductor quantum dot in which the number of confined electrons is tuned by optical illumination. By employing inelastic light scattering we identify the intershell excitations in the one-electron regime and the distinct spin and charge modes in the interacting few-body configuration. In the case of two electrons, a comparison with configuration-interaction calculations allows us to link the observed excitations with the breathing mode of the molecular dimer and to determine the singlet-triplet energy splitting.
    Physical Review Letters 06/2010; 104(24):246802. · 7.73 Impact Factor
  • Stefano Corni, Dimitrios Toroz, Massimo Rontani
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    ABSTRACT: Single molecular orbitals are nowadays imaged in real space by both scanning tunnelling (STM) and photoemission spectroscopies. The key quantity provided by these techniques is the density of states --an intrinsically many-body observable. For extended systems, its energy and momentum dependence signals intriguing phenomena like non-Fermi liquid behavior, electron pairing, Kondo effect, Fermi edge singularity. For isolated molecules, the space-resolved spectral density of states reduces to the wave function square modulus of the ``quasi-particle'' added to the system. The latter is sensitive to both correlation effects and changes of the electron number. Here we predict, on the basis of ab-initio many-body calculations, that the orbital images of certain planar conjugated molecules are significantly modified by electron correlation. We find differences in the nodal plane orientations of HOMO and LUMO correlated orbitals with respect to the Hartree-Fock results, as well as spectral weight rearrangements all over the molecule. These features may be detected experimentally, providing an accessible signature of correlation effects in simple molecules.
    03/2010;
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    Andrea Secchi, Massimo Rontani
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    ABSTRACT: We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy -indeed some of them have already been observed by Deshpande and Bockrath [Nature Phys. 4, 314 (2008)]. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions. Comment: 12 pages (6 color figures, 3 b/w figures, 3 tables). This paper has been extensively revised, including more theoretical material, the discussion of experiments by Deshpande and Bockrath (Nature Phys. 2008) and Kuemmeth et al. (Nature 2008), the location of their quantum-dot devices in the proposed theoretical phase diagram. To appear in Physical Review B
    Physical review. B, Condensed matter 08/2009; · 3.77 Impact Factor

Publication Stats

701 Citations
283.77 Total Impact Points

Institutions

  • 2011–2012
    • National Research Council
      Roma, Latium, Italy
  • 2010
    • Scuola Normale Superiore di Pisa
      • Laboratory NEST: National Enterprise for Nano-Science and Nano-Technology
      Pisa, Tuscany, Italy
  • 2009
    • Michigan State University
      East Lansing, Michigan, United States
  • 1998–2009
    • Università degli Studi di Modena e Reggio Emilia
      • Department of Engineering "Enzo Ferrari"
      Modène, Emilia-Romagna, Italy
  • 2007
    • University of Hamburg
      • Institute of Applied Physics
      Hamburg, Hamburg, Germany
  • 2006
    • Nippon Telegraph and Telephone
      Edo, Tōkyō, Japan
  • 2005
    • Cineca
      Casalecchio di Reno, Emilia-Romagna, Italy