The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Roald Hoffmann - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Interference graphs walks and polynomials
Chemical Reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley–Hamilton theorem for characteristic polynomials and the Coulson–Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green’s function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Huckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For nonalternant hydrocarbons, the finite Green’s function expansion may include...
-
Quantum Interference, Graphs, Walks, and Polynomials
Chemical reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or H{\"u}ckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For non-alternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for non-alternants, from the cancellation of odd and even-length walk terms. We report some progress, but not a complete resolution of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. And we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.
-
Quantum Interference in polyenes
The Journal of chemical physics, 2014Co-Authors: Yuta Tsuji, Ramis Movassagh, Roald Hoffmann, Supriyo DattaAbstract:The explicit form of the zeroth Green's function in the Huckel model, approximated by the negative of the inverse of the Huckel matrix, has direct Quantum Interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of Quantum Interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments – if coherence in probe connections can be arranged – in some cases new destructive Interference results, while in others one may have constructive Interference. One such case may already exist in the literature.
Yuta Tsuji - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Interference graphs walks and polynomials
Chemical Reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley–Hamilton theorem for characteristic polynomials and the Coulson–Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green’s function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Huckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For nonalternant hydrocarbons, the finite Green’s function expansion may include...
-
Quantum Interference, Graphs, Walks, and Polynomials
Chemical reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or H{\"u}ckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For non-alternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for non-alternants, from the cancellation of odd and even-length walk terms. We report some progress, but not a complete resolution of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. And we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.
-
Quantum Interference in polyenes
The Journal of chemical physics, 2014Co-Authors: Yuta Tsuji, Ramis Movassagh, Roald Hoffmann, Supriyo DattaAbstract:The explicit form of the zeroth Green's function in the Huckel model, approximated by the negative of the inverse of the Huckel matrix, has direct Quantum Interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of Quantum Interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments – if coherence in probe connections can be arranged – in some cases new destructive Interference results, while in others one may have constructive Interference. One such case may already exist in the literature.
Ramis Movassagh - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Interference graphs walks and polynomials
Chemical Reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley–Hamilton theorem for characteristic polynomials and the Coulson–Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green’s function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Huckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For nonalternant hydrocarbons, the finite Green’s function expansion may include...
-
Quantum Interference, Graphs, Walks, and Polynomials
Chemical reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or H{\"u}ckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For non-alternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for non-alternants, from the cancellation of odd and even-length walk terms. We report some progress, but not a complete resolution of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. And we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.
-
Quantum Interference in polyenes
The Journal of chemical physics, 2014Co-Authors: Yuta Tsuji, Ramis Movassagh, Roald Hoffmann, Supriyo DattaAbstract:The explicit form of the zeroth Green's function in the Huckel model, approximated by the negative of the inverse of the Huckel matrix, has direct Quantum Interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of Quantum Interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Green's function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments – if coherence in probe connections can be arranged – in some cases new destructive Interference results, while in others one may have constructive Interference. One such case may already exist in the literature.
Ernesto Estrada - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Interference graphs walks and polynomials
Chemical Reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley–Hamilton theorem for characteristic polynomials and the Coulson–Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green’s function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Huckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For nonalternant hydrocarbons, the finite Green’s function expansion may include...
-
Quantum Interference, Graphs, Walks, and Polynomials
Chemical reviews, 2018Co-Authors: Yuta Tsuji, Ernesto Estrada, Ramis Movassagh, Roald HoffmannAbstract:In this paper, we explore Quantum Interference in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Green's function for electron transmission in terms of the odd powers of the vertex adjacency matrix or H{\"u}ckel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, Quantum Interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of Quantum Interference. For non-alternant hydrocarbons, the finite Green's function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for non-alternants, from the cancellation of odd and even-length walk terms. We report some progress, but not a complete resolution of the problem of understanding the coefficients in the expansion of the Green's function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. And we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Green's function.
Colin J. Lambert - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Interference in Graphene Nanoconstrictions
Nano letters, 2016Co-Authors: Pascal Gehring, Hatef Sadeghi, Sara Sangtarash, Chit Siong Lau, Junjie Liu, Arzhang Ardavan, Jamie H. Warner, Colin J. Lambert, G. Andrew D. Briggs, Jan A. MolAbstract:We report Quantum Interference effects in the electrical conductance of chemical vapor deposited graphene nanoconstrictions fabricated using feedback controlled electroburning. The observed multimode Fabry–Perot Interferences can be attributed to reflections at potential steps inside the channel. Sharp antiresonance features with a Fano line shape are observed. Theoretical modeling reveals that these Fano resonances are due to localized states inside the constriction, which couple to the delocalized states that also give rise to the Fabry–Perot Interference patterns. This study provides new insight into the interplay between two fundamental forms of Quantum Interference in graphene nanoconstrictions.
-
Quantum Interference in single molecule electronic systems
Physical Review B, 2011Co-Authors: Rachel Sparks, Víctor M. García-suárez, D. Zs. Manrique, Colin J. LambertAbstract:We present a general analytical formula and an ab initio study of Quantum Interference in multibranch molecules. Ab initio calculations are used to investigate Quantum Interference in a benzene-1,2-dithiolate (BDT) molecule sandwiched between gold electrodes and through oligoynes of various lengths. We show that when a point charge is located in the plane of a BDT molecule and its position varied, the electrical conductance exhibits a clear Interference effect, whereas when the charge approaches a BDT molecule along a line normal to the plane of the molecule and passing through the center of the phenyl ring, Interference effects are negligible. In the case of oligoynes, Quantum Interference leads to the appearance of a critical energy E-c at which the electron transmission coefficient T (E) of chains with even or odd numbers of atoms is independent of length. To illustrate the underlying physics, we derive a general analytical formula for electron transport through multibranch structures and demonstrate the versatility of the formula by comparing it with the above ab initio simulations. We also employ the analytical formula to investigate the current inside the molecule and demonstrate that large countercurrents can occur within a ringlike molecule such as BDT, when the point charge is located in the plane of the molecule. The formula can be used to describe Quantum Interference and Fano resonances in structures with branches containing arbitrary elastic scattering regions connecting nodal sites.
