Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

Abstract: Atomic engineering in a solid-state material has the potential to functionalize the host with novel phenomena. STM-based lithographic techniques have enabled the placement of individual phosphorus atoms at selective lattice sites of silicon with atomic precision. Here, we show that by placing four phosphorus donors spaced 10-15 nm apart from their neighbours in a linear chain, it is possible to realize coherent spin coupling between the end dopants of the chain, analogous to the superexchange interaction in magnetic materials. Since phosphorus atoms are a promising building block of a silicon quantum computer, this enables spin coupling between their bound electrons beyond nearest neighbours, allowing the qubits to be spaced out by 30-45 nm. The added flexibility in architecture brought about by this long-range coupling not only reduces gate densities but can also reduce correlated noise between qubits from local noise sources that are detrimental to error correction codes. We base our calculations on a full configuration interaction technique in the atomistic tight-binding basis, solving the 4-electron problem exactly, over a domain of a million silicon atoms. Our calculations show that superexchange can be tuned electrically through gate voltages where it is less sensitive to charge noise and donor placement errors.

Abstract: We employ a tight-binding model to calculate the optical selection rules of gold-terminated carbyne chains in the presence of an applied electric field. We show that both the magnitude of the edge-state gap and the strength of optical transitions across it can be tuned via the Stark effect. In the case of sufficiently long carbyne chains, the dipole transitions between edge states occur within the THz frequency range.

Abstract: The theory of composite fermions consists of two complementary parts: a standard ansatz for constructing many-body wave-functions of various fractional quantum Hall states, and an effective theory (the HLR theory) for predicting responses of these states to external perturbations. Conventionally, both the ansatz and the HLR theory are justified by Lopez-Fradkin's theory based on the singular Chern-Simons transformation. In this work, we aim to provide an alternative basis and unify the two parts into a coherent theory by developing quantum mechanics of composite fermions based on the dipole picture. We argue that states of a composite fermion in the dipole picture are naturally described by bivariate wave functions which are holomorphic (anti-holomorphic) in the coordinate of its constituent electron (vortex), defined in a Bergman space with its weight determined by the spatial profiles of the physical and the emergent Chern-Simons magnetic fields. Based on a semi-classical phenomenological model and the quantization rules of the Bergman space, we establish general wave equations for composite fermions. The wave equations resemble the ordinary Schr\"odinger equation but have drift velocity corrections not present in the HLR theory. Using Pasquier-Haldane's interpretation of the dipole picture, we develop a general wave-function ansatz for constructing many-body wave functions of electrons by projecting states of composite fermions solved from the wave equation into a half-filled bosonic Laughlin state of vortices. It turns out that for ideal fractional quantum Hall states the general ansatz and the standard ansatz are equivalent, albeit using different wave-function representations for composite fermions. To justify the phenomenological model, we derive it from the microscopic Hamiltonian and the general variational principle of quantum mechanics.

Abstract: We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. Our design consists of quantum dots tunnel coupled by a hybrid superconducting island together with a tunable capacitive coupling between the dots. We show that coherent control of Cooper pair splitting, elastic cotunneling, and Coulomb interactions allows us to implement the universal set of quantum gates defined by Bravyi and Kitaev. Finally, we discuss possible limitations of the device and list necessary experimental efforts to overcome them.

Abstract: Observations of the anomalous Hall effect in RuO$_2$ and MnTe have demonstrated unconventional time-reversal symmetry breaking in the electronic structure of a recently identified new class of compensated collinear magnets, dubbed altermagnets. While in MnTe the unconventional anomalous Hall signal accompanied by a vanishing magnetization is observable at remanence, the anomalous Hall effect in RuO$_2$ is excluded by symmetry for the N\'eel vector pointing along the zero-field [001] easy-axis. Guided by a symmetry analysis and ab initio calculations, a field-induced reorientation of the N\'eel vector from the easy-axis towards the [110] hard-axis was used to demonstrate the anomalous Hall signal in this altermagnet. We confirm the existence of an anomalous Hall effect in our RuO$_2$ thin-film samples whose set of magnetic and magneto-transport characteristics is consistent with the earlier report. By performing our measurements at extreme magnetic fields up to 68 T, we reach saturation of the anomalous Hall signal at a field $H_{\rm c} \simeq$ 55 T that was inaccessible in earlier studies, but is consistent with the expected N\'eel-vector reorientation field.