We construct and characterize tight-binding Hamiltonians which contain a completely flat topological band made of continuum lowest Landau-level wave functions sampled on a lattice. We find an infinite family of such Hamiltonians, with simple analytic descriptions. These provide a valuable tool for constructing exactly solvable models. We also implement a numerical algorithm for finding the most local Hamiltonian with a flat Landau level. We find intriguing structures in the spatial dependence of the matrix elements for this optimized model.

We describe a method for computing near-exact energies for correlated systems with large Hilbert spaces. The method efficiently identifies the most important basis states (Slater determinants) and performs a variational calculation in the subspace spanned by these determinants. A semistochastic approach is then used to add a perturbative correction to the variational energy to compute the total energy. The size of the variational space is progressively increased until the total energy converges to within the desired tolerance.

Validated formative assessment tools provide a reliable way to compare student learning across variables such as pedagogy and curricula, or demographics. Such assessments typically employ a closed-response format developed from student responses to open-response questions and interviews with students and experts. The validity and reliability of these assessments is usually evaluated using statistical tools such as classical test theory or item response theory.

Recent research in introductory physics labs suggests that most students judge the quality of a measurement based on a comparison with theory. To probe this dimension of students’ judgments based on authority, we sought to evaluate whether students’ responses about evaluations of measurement depended on contextual cues. We asked students which measurement of the acceleration due to gravity was ‘better:’ (1) one given with uncertainty and found by ‘you and your friend’ or ‘you and your research group’ or (2) a textbook value with no reported uncertainty but more significant figures.

We explore generic "unnecessary" quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions.

Measurements in quantum mechanics are often taught in an abstract, theoretical context. Compared to what is known about student understanding of experimental data in classical mechanics, it is unclear how students think about measurement and uncertainty in the context of experimental data from quantum mechanical systems. In this paper, we tested how students interpret the variability in data from hypothetical experiments in classical and quantum mechanics.

We developed perovskite solar cells (PSCs) with a ZnO electron-Transporting layer (ETL) of which the surface was passivated with methoxybenzoic acid self-Assembled monolayers (SAMs). The self-Assembled monolayer (SAM) simultaneously improved the photovoltaic performance and device stability.

Memristive devices whose resistance can be hysteretically switched by electric field or current are intensely pursued both for fundamental interest as well as potential applications in neuromorphic computing and phase-change memory. When the underlying material exhibits additional charge or spin order, the resistive states can be directly coupled, further allowing electrical control of the collective phases. The observation of abrupt, memristive switching of tunneling current in nanoscale junctions of ultrathin CrI3, a natural layer antiferromagnet, is reported here.

Science is, at its core, an empirical discipline: Theories must coordinate with evidence obtained through systematic, scientific investigations. Learning science involves learning how science is done, not just what science has found, and so nearly every introductory college science course has an associated laboratory component. The value of these labs, however, has often been called into question, particularly when considering concerns about the associated space, time, equipment, and personnel needs.