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Baghdasaryan DA, Harutyunyan VA, Kazaryan EM, Sarkisyan HA, Petrosyan LS, Shahbazyan TV. Possibility of Exciton Bose-Einstein Condensation in CdSe Nanoplatelets. Nanomaterials (Basel) 2023; 13:2734. [PMID: 37836375 PMCID: PMC10574473 DOI: 10.3390/nano13192734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Revised: 10/01/2023] [Accepted: 10/06/2023] [Indexed: 10/15/2023]
Abstract
The quasi-two-dimensional exciton subsystem in CdSe nanoplatelets is considered. It is theoretically shown that Bose-Einstein condensation (BEC) of excitons is possible at a nonzero temperature in the approximation of an ideal Bose gas and in the presence of an "energy gap" between the ground and the first excited states of the two-dimensional exciton center of inertia of the translational motion. The condensation temperature (Tc) increases with the width of the "gap" between the ground and the first excited levels of size quantization. It is shown that when the screening effect of free electrons and holes on bound excitons is considered, the BEC temperature of the exciton subsystem increases as compared to the case where this effect is absent. The energy spectrum of the exciton condensate in a CdSe nanoplate is calculated within the framework of the weakly nonideal Bose gas approximation, considering the specifics of two-dimensional Born scattering.
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Affiliation(s)
- Davit A. Baghdasaryan
- Institute of Engineering and Physics, Russian-Armenian University, H. Emin 123, Yerevan 0051, Armenia; (D.A.B.); (V.A.H.); (E.M.K.)
| | - Volodya A. Harutyunyan
- Institute of Engineering and Physics, Russian-Armenian University, H. Emin 123, Yerevan 0051, Armenia; (D.A.B.); (V.A.H.); (E.M.K.)
| | - Eduard M. Kazaryan
- Institute of Engineering and Physics, Russian-Armenian University, H. Emin 123, Yerevan 0051, Armenia; (D.A.B.); (V.A.H.); (E.M.K.)
| | - Hayk A. Sarkisyan
- Institute of Engineering and Physics, Russian-Armenian University, H. Emin 123, Yerevan 0051, Armenia; (D.A.B.); (V.A.H.); (E.M.K.)
- Institute of Electronics and Telecommunications, Peter the Great Saint-Petersburg Polytechnical University, 195251 Saint-Petersburg, Russia
| | - Lyudvig S. Petrosyan
- Department of Physics, Jackson State University, Jackson, MS 39217, USA; (L.S.P.); (T.V.S.)
| | - Tigran V. Shahbazyan
- Department of Physics, Jackson State University, Jackson, MS 39217, USA; (L.S.P.); (T.V.S.)
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Scott Z, Muhammad S, Shahbazyan TV. Plasmon-induced coherence, exciton-induced transparency, and Fano interference for hybrid plasmonic systems in strong coupling regime. J Chem Phys 2022; 156:194702. [PMID: 35597643 DOI: 10.1063/5.0083197] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
We present an analytical model describing the transition to a strong coupling regime for an ensemble of emitters resonantly coupled to a localized surface plasmon in a metal-dielectric structure. The response of a hybrid system to an external field is determined by two distinct mechanisms involving collective states of emitters interacting with the plasmon mode. The first mechanism is the near-field coupling between the bright collective state and the plasmon mode, which underpins the energy exchange between the system components and gives rise to exciton-induced transparency minimum in scattering spectra in the weak coupling regime and to emergence of polaritonic bands as the system transitions to the strong coupling regime. The second mechanism is the Fano interference between the plasmon dipole moment and the plasmon-induced dipole moment of the bright collective state as the hybrid system interacts with the radiation field. The latter mechanism is greatly facilitated by plasmon-induced coherence in a system with the characteristic size below the diffraction limit as the individual emitters comprising the collective state are driven by the same alternating plasmon near field and, therefore, all oscillate in phase. This cooperative effect leads to scaling of the Fano asymmetry parameter and of the Fano function amplitude with the ensemble size, and therefore, it strongly affects the shape of scattering spectra for large ensembles. Specifically, with increasing emitter numbers, the Fano interference leads to a spectral weight shift toward the lower energy polaritonic band.
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Affiliation(s)
- Zoe Scott
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
| | - Shafi Muhammad
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
| | - Tigran V Shahbazyan
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
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ElKabbash M, Miele E, Fumani AK, Wolf MS, Bozzola A, Haber E, Shahbazyan TV, Berezovsky J, De Angelis F, Strangi G. Cooperative Energy Transfer Controls the Spontaneous Emission Rate Beyond Field Enhancement Limits. Phys Rev Lett 2019; 122:203901. [PMID: 31172774 DOI: 10.1103/physrevlett.122.203901] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Indexed: 06/09/2023]
Abstract
Quantum emitters located in proximity to a metal nanostructure individually transfer their energy via near-field excitation of surface plasmons. The energy transfer process increases the spontaneous emission (SE) rate due to plasmon-enhanced local field. Here, we demonstrate a significant acceleration of the quantum emitter SE rate in a plasmonic nanocavity due to cooperative energy transfer (CET) from plasmon-correlated emitters. Using an integrated plasmonic nanocavity, we realize up to sixfold enhancement in the emission rate of emitters coupled to the same nanocavity on top of the plasmonic enhancement of the local density of states. The radiated power spectrum retains the plasmon resonance central frequency and line shape, with the peak amplitude proportional to the number of excited emitters indicating that the observed cooperative SE is distinct from superradiance. Plasmon-assisted CET offers unprecedented control over the SE rate and allows us to dynamically control the spontaneous emission rate at room temperature which can enable SE rate based optical modulators.
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Affiliation(s)
- Mohamed ElKabbash
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
| | - Ermanno Miele
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
- IIT-Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy
| | - Ahmad K Fumani
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
| | - Michael S Wolf
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
| | - Angelo Bozzola
- IIT-Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy
| | - Elisha Haber
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
| | - Tigran V Shahbazyan
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
| | - Jesse Berezovsky
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
| | | | - Giuseppe Strangi
- Department of Physics, Case Western Reserve University, 10600 Euclid Avenue, Cleveland, Ohio 44106, USA
- IIT-Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy
- CNR-NANOTEC Istituto di Nanotecnologia and Department of Physics, University of Calabria, 87036-Rende, Italy
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Abstract
We present a model for exciton-plasmon coupling based on an energy exchange mechanism between quantum emitters (QE) and localized surface plasmons in metal-dielectric structures. Plasmonic correlations between QEs give rise to a collective state exchanging its energy cooperatively with a resonant plasmon mode. By defining carefully the plasmon mode volume for a QE ensemble, we obtain a relation between QE-plasmon coupling and a cooperative energy transfer rate that is expressed in terms of local fields. For a single QE near a sharp metal tip, we find analytically the enhancement factor for QE-plasmon coupling relative to QE coupling to a cavity mode. For QEs distributed in an extended region enclosing a plasmonic structure, we find that the ensemble QE-plasmon coupling saturates to a universal value independent of system size and shape, consistent with the experiment.
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Affiliation(s)
- Tigran V Shahbazyan
- Department of Physics , Jackson State University , Jackson , Mississippi 39217 , United States
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Abstract
We obtain the local density of states (LDOS) for any nanoplasmonic system in the frequency range dominated by a localized surface plasmon. By including the Ohmic losses in a consistent way, we show that the plasmon LDOS is proportional to the local field intensity normalized by the absorbed power. We obtain explicit formulas for the energy transfer (ET) between quantum emitters and plasmons as well as between donors and acceptors situated near a plasmonic structure. In the latter case, we find that the plasmon-assisted ET rate is proportional to the LDOS product at the donor and acceptor positions, obtain, in a general form, the plasmon ET enhancement factor, and establish the transition onset between Förster-dominated and plasmon-dominated ET regimes.
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Affiliation(s)
- Tigran V Shahbazyan
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
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Abstract
Metal photoluminescence (MPL) originates from radiative recombination of photoexcited core holes and conduction band electrons. In metal nanostructures, MPL is enhanced due to the surface plasmon local field effect. We identify another essential process in plasmon-assisted MPL-excitation of Auger plasmons by core holes-that hinders MPL from small nanostructures. We develop a microscopic theory of plasmon-enhanced MPL that incorporates both plasmon-assisted enhancement and suppression mechanisms and derive the enhancement factor for MPL quantum efficiency. Our numerical calculations of MPL from Au nanoparticles are in excellent agreement with the experiment.
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Affiliation(s)
- Tigran V Shahbazyan
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA.
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Petrosyan LS, Kirakosyan AS, Shahbazyan TV. Extraordinary electron transmission through a periodic array of quantum dots. Phys Rev Lett 2011; 107:196802. [PMID: 22181631 DOI: 10.1103/physrevlett.107.196802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2011] [Indexed: 05/31/2023]
Abstract
We study electron transmission through a periodic array of quantum dots (QD) sandwiched between doped semiconductor leads. When the Fermi wavelength of tunneling electron exceeds the array lattice constant, the off-resonant per QD conductance is enhanced by several orders of magnitude relative to the single-QD conductance. The physical mechanism of the enhancement is delocalization of a small fraction of system eigenstates caused by coherent coupling of QDs via the electron continuum in the leads.
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Affiliation(s)
- L S Petrosyan
- Department of Medical Physics, Yerevan State Medical University, 2 Koryun Street, Yerevan, 0025, Armenia and Department of Physics, Jackson State University, Jackson, Mississippi 39217 USA
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Pustovit VN, Shahbazyan TV. Cooperative emission of light by an ensemble of dipoles near a metal nanoparticle: the plasmonic Dicke effect. Phys Rev Lett 2009; 102:077401. [PMID: 19257713 DOI: 10.1103/physrevlett.102.077401] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2008] [Indexed: 05/02/2023]
Abstract
We identify a new mechanism for cooperative emission of light by an ensemble of N dipoles near a metal nanostructure supporting a surface plasmon. The cross talk between emitters due to the virtual plasmon exchange leads to the formation of three plasmonic superradiant modes whose radiative decay rates scale with N, while the total radiated energy is thrice that of a single emitter. Our numerical simulations indicate that the plasmonic Dicke effect survives nonradiative losses in the metal.
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Affiliation(s)
- Vitaliy N Pustovit
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
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Abstract
We theoretically study the spectrum of radial vibrational modes in composite metal nanostructures such as bimetallic core-shell particles and metal nanoshells with dielectric core in an environment. We calculate frequencies and damping rates of fundamental (breathing) modes for these nanostructures along with those of two higher-order modes. For metal nanoshells, we find that the breathing mode frequency is always lower than the one for solid particles of the same size, while the damping is higher and increases with a reduction in the shell thickness. We identify two regimes that can be characterized as weakly damped and overdamped vibrations in the presence of external medium. For bimetallic particles, we find periodic dependence of frequency and damping rate on the shell thickness with period being determined by the mode number. For both types of nanostructures, the frequency of higher modes is nearly independent of the environment, while the damping rate shows a strong sensitivity to the outside medium.
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Affiliation(s)
- Arman S Kirakosyan
- Department of Physics, Jackson State University, Jackson, Mississippi 39217, USA
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Tong M, Kirakosyan AS, Shahbazyan TV, Vardeny ZV. Ultrafast response of surface electromagnetic waves in an aluminum film perforated with subwavelength hole arrays. Phys Rev Lett 2008; 100:056808. [PMID: 18352413 DOI: 10.1103/physrevlett.100.056808] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2007] [Revised: 10/09/2007] [Indexed: 05/26/2023]
Abstract
The ultrafast dynamics of surface electromagnetic waves photogenerated on aluminum film perforated with subwavelength arrays of holes was studied in the visible spectral range by the technique of transient photomodulation with approximately 100 fs time resolution. We observed a pronounced blueshift of the resonant transmission band that reveals the important role of plasma attenuation in the optical response of nanohole arrays. The blueshift is inconsistent with plasmonic mechanism of extraordinary transmission and points to the crucial role of interference in the formation of transmission bands. The transient photomodulation spectra were successfully modeled within the Boltzmann equation approach for the electron-phonon relaxation dynamics, involving nonequilibrium hot electrons and quasiequilibrium phonons.
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Affiliation(s)
- M Tong
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
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Guillon C, Langot P, Del Fatti N, Vallée F, Kirakosyan AS, Shahbazyan TV, Cardinal T, Treguer M. Coherent acoustic vibration of metal nanoshells. Nano Lett 2007; 7:138-42. [PMID: 17212453 DOI: 10.1021/nl062380d] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Using time-resolved pump-probe spectroscopy, we have performed the first investigation of the vibrational modes of gold nanoshells. The fundamental isotropic mode launched by a femtosecond pump pulse manifests itself in a pronounced time-domain modulation of the differential transmission probed at the frequency of nanoshell surface plasmon resonance. The modulation amplitude is significantly stronger, and the period is longer than that in a gold nanoparticle of the same overall size, in agreement with theoretical calculations. This distinct acoustical signature of nanoshells provides a new and efficient method for identifying these versatile nanostructures and for studying their mechanical and structural properties.
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Affiliation(s)
- C Guillon
- Centre de Physique Moléculaire Optique et Hertzienne CNRS and Université Bordeaux I, 351 cours de la Libération, 33405 Talence, France
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Pustovit VN, Shahbazyan TV. Finite-size effects in surface-enhanced Raman scattering in noble-metal nanoparticles: a semiclassical approach. J Opt Soc Am A Opt Image Sci Vis 2006; 23:1369-74. [PMID: 16715155 DOI: 10.1364/josaa.23.001369] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
We study finite-size effects in surface-enhanced Raman scattering (SERS) from molecules adsorbed on small metal particles. Within an electromagnetic description of SERS, the enhancement of the Raman signal originates from the local field of the surface plasmon resonance in a nanoparticle. With decreasing particle sizes, this enhancement is reduced due to the size-dependent Landau damping of the surface plasmon. We show that, in small noble-metal particles, the reduction of interband screening in the surface layer leads to an additional increase in the local field acting on a molecule close to the metal surface. The overall size dependence of Raman signal enhancement is determined by the interplay between Landau damping and underscreening effects. Our calculations, based on a two-region model, show that the role of the surface layer increases for smaller nanoparticle sizes due to a larger volume fraction of the underscreened region.
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Affiliation(s)
- Vitaliy N Pustovit
- Department of Physics and Computational Center for Molecular Structure and Interactions, Jackson State University, Mississippi 39217, USA
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Dai J, Raikh ME, Shahbazyan TV. Two-electron linear intersubband light absorption in a biased quantum well. Phys Rev Lett 2006; 96:066803. [PMID: 16606029 DOI: 10.1103/physrevlett.96.066803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2005] [Indexed: 05/08/2023]
Abstract
We point out a novel manifestation of many-body correlations in the linear optical response of electrons confined in a quantum well. Namely, we demonstrate that along with the conventional absorption peak at a frequency omega close to the intersubband energy delta, there exists an additional peak at frequency h omega approximately = 2delta. This new peak is solely due to electron-electron interactions, and can be understood as excitation of two electrons by a single photon. The actual peak line shape is comprised of a sharp feature, due to excitation of pairs of intersubband plasmons, on top of a broader band due to absorption by two single-particle excitations. The two-plasmon contribution allows us to infer intersubband plasmon dispersion from linear absorption experiments.
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Affiliation(s)
- J Dai
- Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
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Shahbazyan TV, Perakis IE, Raikh ME. Spin correlations in nonlinear optical response: light-induced Kondo effect. Phys Rev Lett 2000; 84:5896-5899. [PMID: 10991082 DOI: 10.1103/physrevlett.84.5896] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/1999] [Indexed: 05/23/2023]
Abstract
We study the role of spin correlations in nonlinear absorption due to transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons at the impurity leads to a logarithmic divergence in chi(3) at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump.
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Affiliation(s)
- T V Shahbazyan
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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Shahbazyan TV, Primozich N, Perakis IE, Chemla DS. Femtosecond coherent dynamics of the fermi-edge singularity and exciton hybrid. Phys Rev Lett 2000; 84:2006-2009. [PMID: 11017682 DOI: 10.1103/physrevlett.84.2006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/1999] [Indexed: 05/23/2023]
Abstract
We study theoretically the coherent nonlinear optical response of doped quantum wells with several subbands. When the Fermi energy approaches the exciton level of an upper subband, the absorption spectrum acquires a characteristic double-peak shape originating from the interference between the Fermi-edge singularity and the exciton resonance. We demonstrate that, for off-resonant pump excitation, the pump-probe spectrum undergoes a striking transformation, with a time-dependent exchange of oscillator strength between the Fermi-edge singularity and exciton peaks. This effect originates from the many-body electron-hole correlations which determine the dynamical response of the Fermi sea.
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Affiliation(s)
- T V Shahbazyan
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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Shahbazyan TV, Raikh ME. Exact Shape of the Lowest Landau Level in a Double-Layer System and a Superlattice with Uncorrelated Disorder. Phys Rev Lett 1996; 77:5106-5109. [PMID: 10062715 DOI: 10.1103/physrevlett.77.5106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Shahbazyan TV, Ulloa SE. Far-infrared absorption in parallel quantum wires with weak tunneling. Phys Rev B Condens Matter 1996; 54:16749-16756. [PMID: 9985805 DOI: 10.1103/physrevb.54.16749] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Shahbazyan TV, Raikh ME. Surface plasmon in a two-dimensional Anderson insulator with interactions. Phys Rev B Condens Matter 1996; 53:7299-7307. [PMID: 9982177 DOI: 10.1103/physrevb.53.7299] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Raikh ME, Shahbazyan TV. Anomalous tunneling in a strong magnetic field and smooth random potential: The universal distribution of the localization lengths. Phys Rev B Condens Matter 1995; 51:9682-9695. [PMID: 9977634 DOI: 10.1103/physrevb.51.9682] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Hajdu J, Raikh ME, Shahbazyan TV. Anomalous tunneling in a strong magnetic field and a smooth potential. Phys Rev B Condens Matter 1994; 50:17625-17627. [PMID: 9976175 DOI: 10.1103/physrevb.50.17625] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Shahbazyan TV, Raikh ME. Low-field anomaly in 2D hopping magnetoresistance caused by spin-orbit term in the energy spectrum. Phys Rev Lett 1994; 73:1408-1411. [PMID: 10056785 DOI: 10.1103/physrevlett.73.1408] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Raikh ME, Shahbazyan TV. Magnetocapacitance oscillations in a periodically modulated two-dimensional electron gas in the presence of a smooth random potential. Phys Rev B Condens Matter 1994; 49:1935-1942. [PMID: 10010993 DOI: 10.1103/physrevb.49.1935] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Raikh ME, Shahbazyan TV. High Landau levels in a smooth random potential for two-dimensional electrons. Phys Rev B Condens Matter 1993; 47:1522-1531. [PMID: 10006168 DOI: 10.1103/physrevb.47.1522] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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