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Let $\{C_i\}_{i\in \Gamma_1},$ and $\{D_j\}_{j\in \Gamma_2},$ be two families of Cartan factors such that all of them have dimension at least $2$, and consider the atomic JBW$^*$-triples $A=\bigoplus\limits_{i\in \Gamma_1}^{\ell_{\infty}} C_i$ and $B=\bigoplus\limits_{j\in \Gamma_2}^{\ell_{\infty}} D_j$. Let $\Delta :A \to B$ be a {\rm(}non-necessarily linear nor continuous{\rm)} bijection preserving the truncation of triple products in both directions, that is, $$\begin{aligned} \boxed{a \mbox{ is a truncation of } \{b,c,b\}} \Leftrightarrow \boxed{\Delta(a) \mbox{ is a truncation of } \{\Delta(b),\Delta(c),\Delta(b)\}} \end{aligned}$$ Assume additionally that the restriction of $\Delta$ to each rank-one Cartan factor in $A$, if any, is a continuous mapping. Then we show that $\Delta$ is an isometric real linear triple isomorphism. We also study some general properties of bijections preserving the truncation of triple products in both directions between general JB$^*$-triples.

In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs, correspond to norm-closed triple ideals. In the present paper we extend this result to (possibly non-selfadjoint) real operator algebras and Jordan operator algebras, where the argument is necessarily different. We also give simple characterizations of one-sided M-ideals in real operator algebras, and give some applications to that theory., Comment: 17 pages

Let $\mathcal{M}$ be a Banach bimodule over an associative Banach algebra $\mathcal{A}$, and let $F: \mathcal{A}\to \mathcal{M}$ be a linear mapping. Three main uses of the term \emph{generalized derivation} are identified in the available literature, namely, ($\checkmark$) $F$ is a generalized derivation of the first type if there exists a derivation $ d : \mathcal{A}\to \mathcal{M}^{**}$ satisfying $F(a b ) = F(a) b + a d(b),$ for all $a,b\in \mathcal{A}$. ($\checkmark$) $F$ is a generalized derivation of the second type if there exists an element $\xi\in \mathcal{M}^{**}$ satisfying $F(a b ) = F(a) b + a F(b) - a \xi b,$ for all $a,b\in \mathcal{A}$. ($\checkmark$) $F$ is a generalized derivation of the third type if there exist two (non-necessarily linear) mappings $G,H : \mathcal{A}\to \mathcal{M}$ satisfying $F(a b ) = G(a) b + a H(b),$ for all $a,b\in \mathcal{A}$. These three types of maps are not, in general, equivalent. Although the first two notions are well studied when $\mathcal{A}$ is a C$^*$-algebra, their connections with the third one have not yet been explored. In this note we prove that every generalized derivation of the third type from a C$^*$-algebra $\mathcal{A}$ to a Banach $\mathcal{A}$-bimodule $\mathcal{M}$ is automatically continuous. We also show that every (continuous) generalized derivation of the third type from $\mathcal{A}$ to $\mathcal{M}$ is a generalized derivation of the first and second type. Consequently, the three notions coincide in this case. We also explore some concepts of generalized Jordan derivations on a C$^*$-algebra and establish some continuity properties for them.

We prove that a subspace of a real JBW$^*$-triple is an $M$-summand if and only if it is a weak$^*$-closed triple ideal. As a consequence, $M$-ideals of real JB$^*$-triples correspond to norm-closed triple ideals. As in the setting of complex JB$^*$-triples, a geometric property is characterized in purely algebraic terms. This is a newfangled treatment of the classical notion of $M$-ideal in the real setting by a fully new approach due to the unfeasibility of the known arguments in the setting of complex C$^*$-algebras and JB$^*$-triples. The results in this note also provide a full characterization of all $M$-ideals in real C$^*$-algebras, real JB$^*$-algebras and real TROs.

Let $\mathcal{L}$ be a completely distributive commutative subspace lattice or a subspace lattice with two atoms, we use a unified approach to study the derivations, homomorphisms on $\mathrm{Alg} \mathcal{L}$. We verify that the multiplier algebra of $\mathrm{Alg} \mathcal{L}\cap \mathcal{K}(\mathcal{H})$ is isomorphic to $\mathrm{Alg} \mathcal{L}$ and $\mathrm{Alg} \mathcal{L}$ is zero product determined. For $T$ in $M_{n}(\mathbb{C})$, $n\geq 2$, we show that $\mathcal{A}_{T}$ is zero product determined if and only if every local derivation from $\mathcal{A}_{T}$ into any Banach $\mathcal{A}_{T}$-bimodule is a derivation. In addition, we establish some equivalent conditions for an algebra to be zero product determined. For countable dimensional locally matrix algebras and triangular UHF algebras, we also show that they are zero Lie product determined.

We reveal stacking-induced strong coupling between atomic motion and interlayer excitons through photocurrent measurements of WSe$_2$/MoSe$_2$ heterojunction photodiodes. Strong coupling manifests as pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances. The sidebands, which repeat over large swathes of the interlayer exciton photocurrent spectrum, occur in energy increments corresponding directly to a prominent vibrational mode of the heterojunction. Such periodic patterns, together with interlayer photoconductance oscillations, vividly demonstrate the emergence of extraordinarily strong exciton-phonon coupling - and its impact on interlayer excitations - in stack-engineered van der Waals heterostructure devices. Our results establish photocurrent spectroscopy as a powerful tool for interrogating vibrational coupling to interlayer excitons and suggest an emerging strategy to control vibronic physics in the solid-state.

Placing graphene on SnS2 results in significant charge transfer, on the order of 10^13/cm^2, from the graphene to the SnS2, and the charge transfer results in a negative Schottky barrier contact for electron injection from the graphene into the SnS2 conduction band. However, due to the s-px,y composition of the SnS2 conduction band, the coupling between the SnS2 and the graphene is relatively weak. A third layer, HfSe2, placed between the SnS2 and the graphene, serves as a matrix element matching layer, since it has strong coupling to both the graphene and the SnS2. It increases the coupling to the graphene by a factor of 10, and it has little effect on the negative Schottky barrier height, since the conduction band wavefucntion of the SnS2 / HfSe2 is a coherent superposition of the orbitals from the two individual layers, such that there is no energy barrier for an electron to move between the two layers. This paper first investigates the electronic properties of the heterostructure bilayer SnS2 / HfSe2 in the presence of an applied vertical electric field, and then it investigates the trilayer systems of BN / SnS2 / HfSe2 and graphene / SnS2 / HfSe2. A tunneling Hamiltonian estimate of the the contact resistance of the graphene to the SnS2 / HfSe2 heterostructure indicates an excellent low-resistance contact., Comment: 21 pages, 8 figures

Interlayer misorientation in transition metal dichalcogenides alters the interlayer distance, the electronic band structure, and the vibrational modes, but, its effect on the interlayer resistance is not known. This work analyzes the coherent interlayer resistance of misoriented 2H-MoS2 for low energy electrons and holes as a function of the misorientation angle. The electronic interlayer resistance monotonically increases with the supercell lattice constant by several orders of magnitude similar to that of misoriented bilayer graphene. The large hole coupling gives low interlayer hole resistance that weakly depends on the misorientation angle. Interlayer rotation between an n-type region and a p-type region will suppress the electron current with little effect on the hole current. We estimate numerical bounds and explain the results in terms of the orbital composition of the bands at high symmetry points. Density functional theory calculations provide the interlayer coupling used in both a tunneling Hamiltonian and a non-equilibrium Green function calculation of the resistivity., Comment: 6 pages, 3 figures

In a heterostructure of graphene and the ferromagnetic insulator EuO, the Eu atoms induce proximity exchange and inter-valley interactions in the graphene layer. Constrained by the lattice symmetries, and guided by ab initio calculations, a model Hamiltonian is constructed that describes the low-energy bands. Band parameters such as proximity induced exchange splitting, spin orbit coupling, and inter-valley interaction are determined. Calculations of the Chern number identify the conditions under which the hetero-structures exhibit topologically non-trivial bands that give rise to the quantum anomalous Hall effect with a Hall conductivity of $\sigma_{xy} = 2 e^2/h$., Comment: 8 pages, 7 figures