Chemistry (all); Biochemistry, Genetics and Molecular Biology (all); Physics and Astronomy (all)
Abstract :
[en] Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons-electron-hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators.
Disciplines :
Physics
Author, co-author :
Varsano, Daniele ; CNR-NANO, Via Campi 213a, 41125, Modena, Italy
Sangalli, Davide ; CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, 00016, Monterotondo Scalo, Italy
BARBORINI, Matteo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > HPC Platform ; CNR-NANO, Via Campi 213a, 41125, Modena, Italy
Corni, Stefano ; CNR-NANO, Via Campi 213a, 41125, Modena, Italy ; Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Marzolo 1, 35131, Padova, Italy
Molinari, Elisa; CNR-NANO, Via Campi 213a, 41125, Modena, Italy ; Dipartimento di Scienze Fisiche, Informatiche e Matematiche (FIM), Università degli Studi di Modena e Reggio Emilia, 41125, Modena, Italy
This work was supported in part by European Union H2020-EINFRA-2015-1 program under grant agreement No. 676598 project \u201CMaX\u2013Materials Design at the Exascale\u201D. S.S. acknowledges computational resouces provided through the HPCI System Research Project No. hp160126 on the K computer at RIKEN Advanced Institute for Computational Science. D.V., E.M. & M.R. acknowledge PRACE for awarding them access to the Marconi system based in Italy at CINECA (Grant No. Pra14_3622).
Sherrington, D., & Kohn, W. Speculations about gray tin. Rev. Mod. Phys. 40, 767-769 (1968
Keldysh, L. V., & Kopaev, Y. V. Possible instability of the semimetallic state against Coulomb interaction. Fiz. Tverd. Tela 6, 2791-2798 (1964) [Sov. Phys. Solid State 6, 2219-2224 (1965)].
des Cloizeaux, J. Excitonic instability and crystallographic anomalies in semiconductors. J. Phys. Chem. Solids 26, 259-266 (1965
Jèrome, D., Rice, T. M., & Kohn, W. Excitonic insulator. Phys. Rev. 158, 462-475 (1967
Halperin, B. I., & Rice, T. M. The excitonic state at the semiconductorsemimetal transition. Solid State Phys. 21, 115-192 (1968
Lozovik, Y. E., & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Zh. Eksp. i Teor. Fiz. 71, 738-753 (1976) [Sov. Phys.-JETP 44, 389-397 (1976)].
Portengen, T., Östreich, T., & Sham, L. J. Theory of electronic ferroelectricity. Phys. Rev. B 54, 17452-17463 (1996
Balatsky, A. V., Joglekar, Y. N., & Littlewood, P. B. Dipolar superfluidity in electron-hole bilayer systems. Phys. Rev. Lett. 93, 266801 (2004
Rontani, M., & Sham, L. J. Coherent transport in a homojunction between an excitonic insulator and semimetal. Phys. Rev. Lett. 94, 186404 (2005
Su, J., & MacDonald, A. H. How to make a bilayer exciton condensate flow. Nat. Phys. 4, 799-802 (2008
Littlewood, P. B. in Problems of Condensed Matter Physics, vol. 139 of International Series of Monographs on Physics (eds Ivanov, A. L., & Tikhodeev, S. G) Ch. 11 163-181 (Oxford University Press, Oxford, 2008
Bucher, B., Steiner, P., & Wachter, P. Excitonic insulator phase in TmSe0.45Te0.55. Phys. Rev. Lett. 67, 2717-2720 (1991
Rontani, M., & Sham, L. J. in Novel Superfluids Volume 2, vol. 157 of International Series of Monographs on Physics (eds Bennemann, K. H., & Ketterson, J. B) Ch. 19 423-474 (Oxford University Press, Oxford, 2014
Salvo, F. J. D., Moncton, D. E., & Waszczak, J. V. Electronic properties and superlattice formation in the semimetal TiSe2. Phys. Rev. B 14, 4321-4328 (1976
Rossnagel, K. On the origin of charge-density waves in select layered transitionmetal dichalcogenides. J. Phys. Condens. Matter 23, 213001 (2011
Rice, T. M. The electron-hole liquid in semiconductors: theoretical aspects. Solid State Phys. 32, 1-86 (1977
Keldysh, L. V. in Bose-Einstein Condensation (eds Griffin, A., Snoke, D. W., & Stringari, S) Ch. 12 246-280 (Cambridge University Press, Cambridge, 1995
Ikeda, N., et al. Ferroelectricity from iron valence ordering in the chargefrustrated system LuFe2O4. Nature 436, 1136-1138 (2005
Spielman, I. B., Eisenstein, J. P., Pfeiffer, L. N., & West, K. W. Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet. Phys. Rev. Lett. 84, 5808-5811 (2000
Nandi, A., Finck, A. D. K., Eisenstein, J. P., Pfeiffer, L. N., & West, K. W. Exciton condensation and perfect Coulomb drag. Nature 488, 481-484 (2012
Palo, S. D., Rapisarda, F., & Senatore, G. Exciton condensation in a symmetric electron-hole bilayer. Phys. Rev. Lett. 88, 206401 (2002
Kuneš, J. Excitonic condensation in systems of strongly correlated electrons. J. Phys. Condens. Matter 27, 333201 (2015
Khveshchenko, D. V. Ghost excitonic insulator transition in layered graphite. Phys. Rev. Lett. 87, 246802 (2001
Vafek, O., & Case, M. J. Renormalization group approach to two-dimensional Coulomb interacting Dirac fermions with random gauge potential. Phys. Rev. B 77, 033410 (2008
Drut, J. E., & Lände, T. A. Is graphene in vacuum an insulator?. Phys. Rev. Lett. 102, 026802 (2009
Gamayun, O. V., Gorbar, E. V., & Gusynin, V. P. Supercritical Coulomb center and excitonic instability in graphene. Phys. Rev. B 80, 165429 (2009
Lozovik, Y. E., & Sokolik, A. A. Electron-hole pair condensation in a graphene bilayer. JETP Lett. 87, 55-59 (2008
Dillenschneider, R., & Han, J. H. Exciton formation in graphene bilayer. Phys. Rev. B 78, 045401 (2008
Min, H., Bistritzer, R., Su, J., & MacDonald, A. H. Room-Temperature superfluidity in graphene bilayers. Phys. Rev. B 78, 121401(R) (2008
Zhang, C., & Joglekar, Y. N. Excitonic condensation of massless fermions in graphene bilayers. Phys. Rev. B 77, 233405 (2008
Rodin, A. S., & Castro Neto, A. H. Excitonic collapse in semiconducting transition-metal dichalcogenides. Phys. Rev. B 88, 195437 (2013
Fogler, M. M., Butov, L. V., & Novoselov, K. S. High-Temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014
Stroucken, T., & Koch, S. W. Optically bright p-excitons indicating strong Coulomb coupling in transition-metal dichalcogenides. J. Phys: Condens. Matter 27, 345003 (2015
Saito, R., Dresselhaus, G., & Dresselhaus, M. S. Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998
Ilani, S., & McEuen, P. L. Electron transport in carbon nanotubes. Annu. Rev. Condens. Matter Phys. 1, 1-25 (2010
Ando, T. Excitons in carbon nanotubes. J. Phys. Soc. Jpn 66, 1066-1073 (1997
Maultzsch, J., et al. Exciton binding energies in carbon nanotubes from twophoton photoluminescence. Phys. Rev. B 72, 241402(R) (2005
Wang, F., Dukovic, G., Brus, L. E., & Heinz, T. The optical resonances in carbon nanotubes arise from excitons. Science 308, 838-841 (2005
Wang, F., et al. Observation of excitons in one-dimensional metallic singlewalled carbon nanotubes. Phys. Rev. Lett. 99, 227401 (2007
Waissman, J., et al. Realization of pristine and locally tunable one-dimensional electron systems in carbon nanotubes. Nat. Nanotechnol. 8, 569-574 (2013
Laird, E. A., et al. Quantum transport in carbon nanotubes. Rev. Mod. Phys. 87, 703-764 (2015
Aspitarte, L., et al. Giant modulation of the electronic band gap of carbon nanotubes by dielectric screening. Sci. Rep. 7, 8828 (2017
Charlier, J., Blase, X., & Roche, S. Electronic and transport properties of nanotubes. Rev. Mod. Phys. 79, 677-732 (2007
Onida, G., Reining, L., & Rubio, A. Electronic excitations: density-functional versus many-body Green?s function approaches. Rev. Mod. Phys. 74, 601-659 (2002
Foulkes, W. M. C., Mitas, L., Needs, R. J., & Rajagopal, G. Quantum Monte Carlo simulations of solids. Rev. Mod. Phys. 73, 33-83 (2001
Balents, L., & Fisher, M. P. A. Correlation effects in carbon nanotubes. Phys. Rev. B 55, R11973-R11976 (1997
Kane, C. L., Balents, L., & Fisher, M. Coulomb interaction and mesoscopic effects in carbon nanotubes. Phys. Rev. Lett. 79, 5086-5089 (1997
Egger, R., & Gogolin, A. O. Effective low-energy theory for correlated carbon nanotubes. Phys. Rev. Lett. 79, 5082-5085 (1997
Krotov, Y. A., Lee, D., & Louie, S. G. Low energy properties of (n, n) carbon nanotubes. Phys. Rev. Lett. 78, 4245-4248 (1997
Yoshioka, H., & Odintsov, A. A. Electronic properties of armchair carbon nanotubes: Bosonization approach. Phys. Rev. Lett. 82, 374-377 (1999
Nersesyan, A. A., & Tsvelik, A. M. Coulomb blockade regime of a single-wall carbon nanotube. Phys. Rev. B 68, 235419 (2003
Chen, W., Andreev, A. V., Tsvelik, A. M., & Orgad, D. Twist instability in strongly correlated carbon nanotubes. Phys. Rev. Lett. 101, 246802 (2008
Liu, H. J., & Chan, C. T. Properties of 4 Å carbon nanotubes from firstprinciples calculations. Phys. Rev. B 66, 115416 (2002
Machón, M., Reich, S., Thomsen, C., Sánchez-Portal, D., & Ordejón, P. Ab initio calculations of the optical properties of 4 Å-diameter single-walled carbon nanotubes. Phys. Rev. B 66, 155410 (2002
Cabria, I., Mintmire, J. W., & White, C. T. Metallic and semiconducting narrow carbon nanotubes. Phys. Rev. B 67, 121406(R) (2003
Spataru, C. D., Ismail-Beigi, S., Benedict, L. X., & Louie, S. G. Excitonic effects and optical spectra of single-walled carbon nanotubes. Phys. Rev. Lett. 92, 077402 (2004
Bohnen, K., Heid, R., Liu, H. J., & Chan, C. T. Lattice dynamics and electronphonon interaction in (3, 3) carbon nanotubes. Phys. Rev. Lett. 93, 245501 (2004
Connétable, D., Rignanese, G., Charlier, J., & Blase, X. Room temperature Peierls distortion in small diameter nanotubes. Phys. Rev. Lett. 94, 015503 (2005
Dumont, G., Boulanger, P., Côté, M., & Ernzerhof, M. Peierls instability in carbon nanotubes: a first-principles study. Phys. Rev. B 82, 035419 (2010
Lu, H., Wu, J., & Zhang, W. Corrugation-induced metal-semiconductor transition in single-wall carbon nanotubes with a small radius. Phys. Rev. B 88, 035423 (2013
Ando, T., Nakanishi, T., & Saito, R. Berry?s phase and absence of backscattering in carbon nanotubes. J. Phys. Soc. Jpn. 67, 2857-2862 (1998
Kuemmeth, F., Ilani, S., Ralph, D. C., & McEuen, P. L. Coupling of spin and orbital motion of electrons in carbon nanotubes. Nature 452, 448-452 (2008
Steele, G. A., et al. Large spin-orbit coupling in carbon nanotubes. Nat. Commun. 4, 1573 (2013
Capello, M., Becca, F., Fabrizio, M., Sorella, S., & Tosatti, E. Variational description of Mott insulators. Phys. Rev. Lett. 94, 026406 (2005
Deshpande, V. V., et al. Mott insulating state in ultraclean carbon nanotubes. Science 323, 106-110 (2009
Ajiki, H., & Ando, T. Electronic states of carbon nanotubes. J. Phys. Soc. Jpn. 62, 1255-1266 (1993
Sangalli, D., & Marini, A. Anomalous Aharonov-Bohm gap oscillations in carbon nanotubes. Nano Lett. 11, 4052-4057 (2011
Schulz, H. J. Wigner crystal in one dimension. Phys. Rev. Lett. 71, 1864-1867 (1993
Zittartz, J. Transport properties of the excitonic insulator: electrical conductivity. Phys. Rev. 165, 605-611 (1968
Kohn, W., & Sherrington, D. Two kinds of bosons and Bose condensates. Rev. Mod. Phys. 42, 1-11 (1970
Guseinov, R. R., & Keldysh, L. V. Nature of the phase transition under the condition of an excitonic instability in the electronic spectrum of a crystal. Zh. Eksp. i Teor. Fiz. 63, 2255-2263 (1972) [Sov. Phys.-JETP 36, 1193-1197 (1973)].
Giannozzi, P., et al. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009
Perdew, J. P., et al. Atoms, molecules, solid, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671-6687 (1992
Marini, A., Hogan, C., Grüning, M., & Varsano, D. Yambo: an ab initio tool for excited state calculations. Comput. Phys. Commun. 180, 1392-1403 (2009
Burkatzki, M., Filippi, C., & Dolg, M. Energy-consistent pseudopotentials for quantum Monte Carlo calculations. J. Chem. Phys. 126, 234105 (2007
Sorella, S., Devaux, N., Dagrada, M., Mazzola, G., & Casula, M. Geminal embedding scheme for optimal atomic basis set construction in correlated calculations. J. Chem. Phys. 143, 244112 (2015
Dagrada, M., Karakuzu, S., Vildosola, V. L., Casula, M., & Sorella, S. Exact special twist method for quantum Monte Carlo simulations. Phys. Rev. B 94, 245108 (2016
Umrigar, C. J., Toulouse, J., Filippi, C., Sorella, S., & Rhenning, H. Alleviation of the fermion-sign problem by optimization of many-body wave functions. Phys. Rev. Lett. 98, 110201 (2007
Calandra Buonaura, M., & Sorella, S. Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers. Phys. Rev. B 57, 11446-11456 (1998
Rontani, M. Anomalous magnetization of a carbon nanotube as an excitonic insulator. Phys. Rev. B 90, 195415 (2014
