Correlation Effects in low-dimensional systems
In collaboration with H. Grabert (Freiburg, DE), B. Trauzettel (Wuerzburg, DE) and I. Safi (Orsay, FR), we have investigated electron transport properties of 1D interacting quantum wires (Luttinger liquids). The idea underlying our study is to account for some aspects that are present in any realistic experimental setup but that theoretical models often neglect, such as the finite length of the wire, the contacts with the metallic electrodes, and the presence of impurities in the wire. We have investigated both the electronic current and its fluctuations (noise) in the quantum regime, in both two-terminal and three-terminals setups.
➤ Electron Transport in Luttinger liquids
A low-dimensional system is a physical system that exhibits a quantum confinement along some space directions, due to material engineering, chemical structure or geometrical effects. Under these conditions, the physical properties are well described in terms of a system with a reduced number of space coordinates, and are typically quite different with respect to the ordinary three-dimensional (3D) case.
A so-called zero-dimensional (0D) system corresponds to the extreme limit, where a spatial confinement is realized along all three directions, giving rise to discrete energy spectra. For these reasons 0D nanostructures are usually referred to as semiconductor macroatoms. Thanks to this three-dimensional spatial confinement, the charge and spin carriers experience small dissipation/decoherence effects, making semiconductor macroatoms an ideal solid-state hardware for quantum information processing and for the realization of all-optical read-out devices.
Similarly, 1D systems are realized in semiconductor quantum wires, in carbon nanotubes, at the edge states of quantum Hall bars or of Topological insulators.
In low-dimensional systems, electron-electron interaction strongly affects both the optical response and the electronic transport of these systems, making their microscopic description a highly non trivial problem.
In low-dimensional nanostructures, for instance, electrons and holes, typically generated via a properly tailored optical excitation, attract each other via interband Coulomb interaction and form stable electron-hole complexes called excitons. This effect leads to significant modifications of the optical response of the system, and their investigation is crucial for the design and optimization of new-generation optoelectronic devices.
In 1D systems electronic correlations are so strong that the usual Fermi liquid description of interacting electrons breaks down. In 1D there is simply no room for one electron to tackle the other ones, so that any small interaction always gives rise to collective excitations. The eigenstates of a 1D interacting electron system are thus intrinsically correlated, causing spectacular effects such as spin-charge separation, charge fractionalization and non linear current voltage characteristics in transport properties.
This type of behavior is well described by the Luttinger Liquid Theory.
➤ Semiconductor macroatoms as building blocks for new-generation quantum devices
➤ Excitonic effects in the optical spectra of nanostructures
We have predicted the following effects
Interaction-induced oscillations: the current-voltage characteristics exhibits oscillations as a function of applied bias, due to the combined effect of the impurity, the finite length of the wire and electron interaction in the wire.
charge fractionalization: while the zero frequency noise only yields the bare electron charge, the analysis of the finite frequency noise gives access to the fractional charge of the elementary excitations of the interacting wire.
3-terminal transport: electron tunneling from a third terminal into the interacting wire: due to the presence of the leads, the (interaction-induced) current partitioning predicted by the standard Luttinger liquid theory is suppressed. Nevertheless, interaction signatures do appear in the non linear tunneling conductance.
References
J.C. Budich, F. Dolcini, P. Recher, B. Trauzettel, Phonon-Induced backscattering in Helical Edge States, Phys. Rev. Lett. 108, 086602 (2012).
S. Pugnetti, F. Dolcini, D. Bercioux, H. Grabert, Electron tunneling into a quantum wire in the Fabry-Perot regime, Phys. Rev. B 79, 035121 (2009).
F. Dolcini, B. Trauzettel, I. Safi, H. Grabert, Negativity of the excess noise in a quantum wire capacitively coupled to a gate, Phys. Rev. B 75, 45332 (2007).
S. Pugnetti, F. Dolcini, and R. Fazio, dc Josephson Effect in Metallic Single-Walled Carbon Nanotubes, Solid State Communications 144, 551 (2007).
F. Dolcini, B. Trauzettel, I. Safi, H. Grabert, Transport properties of single channel quantum wires with an impurity: Influence of finite length and temperature on average current and noise, Phys. Rev. B 71, 165309 (2005).
B. Trauzettel, I. Safi, F. Dolcini, and H. Grabert, Appearance of fractional charge in the noise of non-chiral Luttinger liquids , Phys. Rev. Lett. 92, 226405 (2004)
F. Dolcini, H. Grabert, I. Safi, and B. Trauzettel, Oscillatory nonlinear conductance of an interacting quantum wire with an impurity , Phys. Rev. Lett. 91, 266402 (2003).
In low-dimensional nanostructures, the interband Coulomb correlation, together with the presence of carrier quantum confinement, strongly affects the optical response of the system. In particular, the pioneering work by F. Rossi and E. Molinari, has shown that electron-hole Coulomb correlation in semiconductor quantum wires leads to a suppression of the well-known Van Hove singularity, thus modifying the performances of one-dimensional semiconductor-based laser sources. The analysis, based on a set of generalized semiconductor Bloch equations, allows a multisubband description of electron-hole correlation for any confinement profile, and permits a direct comparison with experiments for available quantum-wire structures.
Quasi zero-dimensional systems have an extremely high potential in the topical quest for semiconductor-based quantum processors. In this respect, our group investigated the feasibility of employing suitably arranged arrays of semiconductor quantum dots as quantum
register for noiseless information encoding. Several fundamental issues have been addressed in the past years. It turned out that, in addition to the suppression of phase-breaking processes due to the well-known phonon bottleneck, a proper quantum encoding would allow for a decoherence-free evolution on a time scale long compared to the femtosecond scale of modern ultrafast laser technology. Moreover, in some systems -such as GaN-based heterostructures- the existence of a strong built-in electric field induced by the spontaneous polarization and by the piezoelectricity can be exploited to generate entangled few-exciton states in coupled quantum dots without resorting to external fields. The resulting intrinsic exciton-exciton coupling is the key ingredient to realize basic quantum information encoding and manipulation in an ultrafast optically driven scheme.
References
Semiconductor Macroatoms: Basic Physics and Quantum-Device Applications, ed. by F. Rossi (Imperial College Press, London, 2005).
P. Zanardi and F. Rossi, Quantum Information in Semiconductors: Noiseless Encoding in a quantum-dot array, Phys. Rev. Lett. 81, 4752 (1998)
S. De Rinaldis, I. D'Amico, E. Biolatti, R. Rinaldi, R. Cingolani, and F. Rossi, Intrinsic exciton-exciton coupling in GaN-based quantum dots: Application to solid-state quantum computing, Phys. Rev. B 65, 081309(R) (2002).
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Theory of addition spectra in double quantum dots: Single-particle tunneling vs. Coulomb interactions, in Mat. Res. Soc. Symposium Proceedings, edited by S.C. Moss, vol. 571, p. 179 (1999).
G. Goldoni, F. Rossi, A. Orlandi, M. Rontani, F. Manghi, and E. Molinari, Enhancement of Coulomb interactions in semiconductor nanostructures by dielectric confinement, Physica E 6, 482 (2000).
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality, Phys. Rev. B 59, 10165 (1999).
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Multiple quantum phases in artificial double-dot molecules, Solid State Commun. 112, 151 (1999).
References
F. Rossi, Theory of Semiconductor Quantum Devices (Springer, Berlin Heidelberg, 2011).
O. Mauritz, G. Goldoni, F. Rossi, and E. Molinari, Local Optical Spectroscopy in Quantum Confined Systems: A Theoretical Description, Phys. Rev. Lett. 82, 847 (1999).
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality, Phys. Rev. B 59, 10165 (1999).
M. Rontani, F. Rossi, F. Manghi, and E. Molinari, Multiple quantum phases in artificial double-dot molecules, Solid State Commun. 112, 151 (1999).
U. Hohenester, R. Di Felice, E. Molinari, and F. Rossi, Optical spectra of nitride quantum dots: Quantum confinement and electron-hole coupling, Appl. Phys. Lett. 75, 3449 (1999).
U. Hohenester, F. Rossi, and E. Molinari, Excitonic and biexcitonic effects in the coherent optical response of semiconductor quantum dots, Physica B 272, 1 (1999).
F. Rossi and E. Molinari, Coulomb-Induced Suppression of Band-Edge Singularities in the Optical Spectra of Realistic Quantum-Wire Structures, Phys. Rev. Lett. 76, 3642 (1996).
F. Rossi and E. Molinari, Linear and nonlinear optical properties of realistic quantum-wire structures: The dominant role of Coulomb correlation, Phys. Rev. B 53, 16462 (1996).
➤ Extended Hubbard models
There are various situations of great physical interest where band theory fails by construction. A spectacular example are Mott insulators: solids that have an odd number of valence electrons per elementary cell and yet are insulating. The Hubbard model is the simplest generalization beyond the band theory description of solids which explicitly includes the on-site electron-electron Coulomb repulsion. Yet it still appears to capture the basic physical features of many real systems.
There are many cases in which it is fruitful to consider models that are extensions of it. The extensions mainly consist in either taking into account further terms in the expansion of the Coulomb interaction or to consider terms of interactions which involve more than two bodies. Several extensions have been proposed by considering more than one orbital per site. Furthermore, there are materials or regimes of external parameters (fields, temperature, pressure) in which these physical processes become important.
We are particularly interested in the investigation of the extensions of the Hubbard Hamiltonian that allow for physical phenomena relevant within the context of high-Tc superconductivity, such as, for instance, pairing mechanisms, superconducting correlations and phase separation, superconductor to insulator transition. We have shown for instance that the inclusion of the bond-charge interaction induces all of the above properties
References
A. Anfossi, C. Degli Esposti Boschi, and A. Montorsi, Fulde-Ferrell-Larkin-Ovchinnikov oscillations and magnetic domains in the Hubbard model with off-diagonal Coulomb repulsion, J. Stat. Mech. P12014 (2011).
A. Anfossi, L. Barbiero, and A. Montorsi, Detecting the tunneling rates for strongly interacting fermions on optical lattices, Phys. Rev. A 81, 043630 (2010).
M. Roncaglia, C. Degli Esposti Boschi, and A. Montorsi, Hidden XY structure of the bond-charge Hubbard model, Phys. Rev. B 82, 233105 (2010).
A. Anfossi, C. Degli Esposti Boschi, and A. Montorsi, Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model, Phys. Rev. B 79, 235117 (2009).
A.A. Aligia, A. Anfossi, L. Arrachea, C. Degli Esposti Boschi, A.O. Dobry, C. Gazza, A. Montorsi, F. Ortolani, M.E. Torio, Incommensurability and unconventional superconductor to insulator transistion in the Hubbard model with bond-charge interaction, Phys. Rev. Lett. 99, 296401 (2007)
F. Dolcini and A. Montorsi, Finite-temperature properties of the Hubbard chain with bond- charge interaction, Phys. Rev. B 66, 75112 (2002).
F. Dolcini, A. Montorsi, Exact thermodynamics of an Extended Hubbard Model of single and paired carriers, Phys. Rev. B 65, 155105 (2002).
F. Dolcini, and A. Montorsi, Band and filling controlled transitions in exactly solved electronic models, Phys. Rev. B 63, 121103(R) (2001).
➤ Exact solutions and Integrability in strongly correlated systems
The failure of many conventional approaches to capture correlation effects in low-dimensional quantum systems emphasize the importance of finding, at least in some cases, exact solutions for quantum models. In turn, this is strictly connected with the notion of integrability of their Hamiltonian H.
Integrability actually consists in the possibility of finding a complete set of commuting observables, so that the eigenstates of H can be uniquely characterized by the values of the quantum numbers. Within this subject, the Quantum Inverse Scattering Method is a very powerful tool in one dimension, providing sets of commuting operators. It is based on the Yang-Baxter Equation (YBE), a functional equation for a C-number matrix (the R-matrix), which can be thought of as a factorizability condition for the scattering matrix. In case of fermionic systems, the QISM has to face with their anticommutation properties, which is done either by mapping them into spin systems through a Jordan-Wigner transformation or by working with operator valued R-matrices.
We have developed a constructive method, the Polynomial R-matrix Technique (PRT), allowing to look for solutions of the YBE starting with a given fermionic Hamiltonian of interest. Such a method, when applied for instance to the class of extended Hubbard models, produces 96 different integrable cases. A quite important related problem is concerned with the symmetries. The investigation of symmetries is very useful to determine the physical features of a given model: indeed one can derive exact phase diagrams of interacting fermionic models (in some cases even in dimension greater than one) just by exploiting their symmetry properties.
References
A. Montorsi, Phase separation in fermionic systems with particle-hole asymmetry, J. Stat. Mech, L09001 (2008)
A. Anfossi and A. Montorsi, Spin-fermion mappings for even Hamiltonian operators, J. Phys. A: Math and Gen. 38, 4519 (2005)
F. Dolcini, A. Montorsi, Exact thermodynamics of an Extended Hubbard Model of single and paired carriers, Phys. Rev. B 65, 155105 (2002).
F. Dolcini, and A. Montorsi, Band and filling controlled transitions in exactly solved electronic models, Phys. Rev. B 63, 121103(R) (2001).
F. Dolcini and A. Montorsi, Results on the symmetries of integrable fermionic models on chains, Nucl. Phys. B592, 563 (2001).
F. Dolcini and A. Montorsi, Integrable Extended Hubbard Hamiltonians from Symmetric Group solutions, Int. J. Mod. Phys. B13, 2953 (2000).
F. Dolcini and A. Montorsi, Extended Hubbard Hamiltonian with (super)symmetries: Additive polynomial R-matrix for some integrable cases, Int. J. Mod. Phys. B13, 2953 (1999).
Nanophysics and Quantum Systems