arXiv subjects

Roald Hoffmann

Publications and source records attributed to Roald Hoffmann.

4 recordsLinked to original sources

arXiv2021

Superconductivity in SrB3C3 clathrate

We predict superconductivity for the carbon-boron clathrate SrB3C3 at 27-43 K for Coulomb pseudopotential (mu*) values between 0.17 and 0.10 using first-principles calculations with conventional electron-phonon coupling. Electrical transport measurements, facilitated by a novel in situ experimental design compatible with extreme synthesis conditions (>3000 K at 50 GPa), show non-hysteretic resistivity drops that track the calculated magnitude and pressure dependence of superconductivity for mu*=0.15, and transport measurements collected under applied magnetic fields confirm superconductivity with an onset Tc of approximately 20 K at 40 GPa. Carbon-based clathrates thus represent a new class of superconductors similar to other covalent metals like MgB2 and doped fullerenes. Carbon clathrates share structures similar to superconducting superhydrides, but covalent C-B bonds allow metastable persistence at ambient conditions.

cond-mat.mtrl-sci↗

arXiv2019

High-pressure lithium as an elemental topological semimetal

Topological semimetals generally contain heavy elements. Using density-functional theoretic calculations, we predict that three dense lithium polymorphs in the pressure range 200--360 GPa display nontrivial semimetallic electronic structure. Specifically, these high-pressure phases exhibit Fermi pockets which are degenerate over a loop in $\boldsymbol{k}$-space, around which an encircling $\bm k$-space path is threaded by $\pm π$ Berry phase. Accordingly, these dense lithium phases are topological nodal loop semimetals involving a single light element.

cond-mat.mtrl-sci↗

arXiv2018

Quantum Interference, Graphs, Walks, and Polynomials

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{ü}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.

physics.chem-ph↗

arXiv2017

The Green's Function for the Hückel (Tight Binding) Model

Applications of the Hückel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is also the Laplacian matrix plus twice the identity. In this paper, we analytically calculate the determinant and, when it exists, the inverse of this matrix in connection with the Green's function, $\mathbf{G}$, of the $N\times N$ Hückel matrix. A corollary is a closed form expression for a Harmonic sum (Eq. 12). We then extend the results to $d-$dimensional lattices, whose linear size is $N$. The existence of the inverse becomes a question of number theory. We prove a new theorem in number theory pertaining to vanishing sums of cosines and use it to prove that the inverse exists if and only if $N+1$ and $d$ are odd and $d$ is smaller than the smallest divisor of $N+1$. We corroborate our results by demonstrating the entry patterns of the Green's function and discuss applications related to transport and conductivity.

math-ph↗