We resolve two long-standing and closely related problems concerning stably free $mathbb{Z} G$-modules and the homotopy type of finite 2-complexes. In particular, for all $k ge 1$, we show that there exists a group $G$ and a non-free stably free $mat
hbb{Z} G$-module of rank $k$. We use this to show that, for all $k ge 0$, there exists homotopically distinct finite 2-complexes with fundamental group $G$ and with Euler characteristic $k$ greater than the minimal value over $G$. This provides a solution to Problem D5 in the 1979 Problems List of C. T. C. Wall.
We show that the homotopy type of a finite oriented Poincar{e} 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck and Bauer, this
applies in the case of smooth oriented 4-manifolds whose fundamental group is a finite subgroup of SO(3). An important class of examples are elliptic surfaces with finite fundamental group.
If $G$ has $4$-periodic cohomology, then D2 complexes over $G$ are determined up to polarised homotopy by their Euler characteristic if and only if $G$ has at most two one-dimensional quaternionic representations. We use this to solve Walls D2 proble
m for several infinite families of non-abelian groups and, in these cases, also show that any finite Poincar{e} $3$-complex $X$ with $pi_1(X)=G$ admits a cell structure with a single $3$-cell. The proof involves cancellation theorems for $mathbb{Z} G$ modules where $G$ has periodic cohomology.
A long standing problem, which has its roots in low-dimensional homotopy theory, is to classify all finite groups $G$ for which the integral group ring $mathbb{Z}G$ has stably free cancellation (SFC). We extend results of R. G. Swan by giving a condi
tion for SFC and use this to show that $mathbb{Z}G$ has SFC provided at most one copy of the quaternions $mathbb{H}$ occurs in the Wedderburn decomposition of the real group ring $mathbb{R}G$. This generalises the Eichler condition in the case of integral group rings.
Charge transfer in superlattices consisting of SrIrO$_3$ and SrMnO$_3$ is investigated using density functional theory. Despite the nearly identical work function and non-polar interfaces between SrIrO$_3$ and SrMnO$_3$, rather large charge transfer
was experimentally reported at the interface between them. Here, we report a microscopic model that captures the mechanism behind this phenomenon, providing a qualitative understanding of the experimental observation. This leads to unique strain dependence of such charge transfer in iridate-manganite superlattices. The predicted behavior is consistently verified by experiment with soft x-ray and optical spectroscopy. Our work thus demonstrates a new route to control electronic states in non-polar oxide heterostructures.
Strong interplay of fundamental order parameters in complex oxides are known to give rise to exotic physical phenomena. The 4d transition metal oxide SrRhO3 has generated much interest, but advances have been hindered by difficulties in preparing sin
gle crystalline phases. Here, we have epitaxially stabilized high quality single crystalline SrRhO3 films and investigated their structural, electronic, and magnetic properties. We determine that their properties significantly differ from the paramagnetic metallic ground state that governs bulk samples and are strongly related to rotations of the RhO6 octahedra.
Direct observations using scanning transmission electron microscopy unveil an intriguing interfacial bi-layer that enables epitaxial growth of a strain-free, monoclinic, bronze-phase VO2(B) thin film on a perovskite SrTiO3 (STO) substrate. We observe
an ultrathin (2-3 unit cells) interlayer best described as highly strained VO2(B) nanodomains combined with an extra (Ti,V)O2 layer on the TiO2 terminated STO (001) surface. By forming a fully coherent interface with the STO substrate and a semi-coherent interface with the strain-free epitaxial VO2(B) film above, the interfacial bi-layer enables the epitaxial connection of the two materials despite their large symmetry and lattice mismatch.
Strong Coulomb repulsion and spin-orbit coupling are known to give rise to exotic physical phenomena in transition metal oxides. Initial attempts to investigate systems where both of these fundamental interactions are comparably strong, such as 3d an
d 5d complex oxide superlattices, have revealed properties that only slightly differ from the bulk ones of the constituent materials. Here, we observe that the interfacial coupling between the 3d antiferromagnetic insulator SrMnO3 and the 5d paramagnetic metal SrIrO3 is enormously strong, yielding an anomalous Hall response as the result of charge transfer driven interfacial ferromagnetism. These findings show that low dimensional spin-orbit entangled 3d-5d interfaces provide an avenue to uncover technologically relevant physical phenomena unattainable in bulk materials.
