Important note To cite this publication, please use the final published version (if applicable). Please check the document version above.

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

The structure of Cd3As2, a high-mobility semimetal reported to host electrons that act as Dirac particles, is reinvestigated by single-crystal X-ray diffraction. It is found to be centrosymmetric rather than noncentrosymmetric as previously reported. It has a distorted superstructure of the antifluorite (M2X) structure type with a tetragonal unit cell of a = 12.633(3) and c = 25.427(7) Å in the centrosymmetric I41/acd space group. The antifluorite superstructure can be envisioned as consisting of distorted Cd6□2 cubes (where □ = an empty cube vertex) in parallel columns, stacked with opposing chirality. Electronic structure calculations performed using the experimentally determined centrosymmetric structure are similar to those performed with the inversion symmetry absent but with the important implication that Cd3As2 is a three-dimensional (3D)-Dirac semimetal with no spin splitting; all bands are spin degenerate and there is a 4-fold degenerate bulk Dirac point at the Fermi energy along Γ-Z in the Brillouin zone. This makes Cd3As2 a 3D electronic analogue of graphene. Scanning tunneling microscopy experiments identify a 2 × 2 surface reconstruction in the (112) cleavage plane of single crystals; needle crystals grow with a [110] long axis direction.

Understanding the origin of superconductivity in strongly correlated electron systems continues to be at the forefront of the unsolved problems of physics 1 . Among the heavy f-electron systems, CeCoIn 5 is one of the most fascinating, as it shares many of the characteristics of correlated d-electron high-T c cuprate and pnictide superconductors 2-4 , including competition between antiferromagnetism and superconductivity 5 . Although there has been evidence for unconventional pairing in this compound 6-11 , high-resolution spectroscopic measurements of the superconducting state have been lacking. Previously, we have used high-resolution scanning tunnelling microscopy (STM) techniques to visualize the emergence of heavy fermion excitations in CeCoIn 5 and demonstrate the composite nature of these excitations well above T c (ref. 12). Here we extend these techniques to much lower temperatures to investigate how superconductivity develops within a strongly correlated band of composite excitations. We find the spectrum of heavy excitations to be strongly modified just before the onset of superconductivity by a suppression of the spectral weight near the Fermi energy (E F ), reminiscent of the pseudogap state 13,14 in the cuprates. By measuring the response of superconductivity to various perturbations, through both quasiparticle interference (QPI) and local pair-breaking experiments, we demonstrate the nodal d-wave character of superconducting pairing in CeCoIn 5 .CeCoIn 5 undergoes a superconducting transition at 2.3 K. Despite evidence of unconventional pairing, consensus on the mechanism of pairing and direct experimental verification of the order parameter symmetry are still lacking [6][7][8][9]11 . Moreover, experiments have suggested that superconductivity in this compound emerges from a state of unconventional quasiparticle excitations with a pseudogap phase similar to that found in underdoped high-T c cuprates [15][16][17] . Previously, we demonstrated that scanning tunnelling spectroscopic techniques can be used to directly visualize the emergence of heavy fermion excitations in CeCoIn 5 and their quantum critical nature 12 . Through these measurements, we also demonstrated the composite nature of heavy quasiparticles and showed their band formation as the f -electrons hybridize with the spd-electrons starting at 70 K, well above T c (ref. 12). This previous breakthrough, together with our recent development of high-resolution millikelvin STM, offers a unique opportunity to measure how superconductivity emerges in a heavy electron system. Figure 1 shows STM topographs of the two commonly observed atomically ordered surfaces of CeCoIn 5 produced after the cleaving of single crystals in situ in the ultra-high vacuum environment 1 Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, New Jersey 08544, USA, 2 Condensed Matter and Magnet Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. † These authors contributed equally to this work. *e-mail: yazdani@pr...

Electronic states in disordered conductors on the verge of localization are predicted to exhibit critical spatial characteristics indicative of the proximity to a metal-insulator phase transition. We have used scanning tunneling microscopy to visualize electronic states in Ga 1-x Mn x As samples close to this transition. Our measurements show that doping-induced disorder produces strong spatial variations in the local tunneling conductance across a wide range of energies. Near the Fermi energy, where spectroscopic signatures of electron-electron interaction are the most prominent, the electronic states exhibit a diverging spatial correlation length. Power-law decay of the spatial correlations is accompanied by log-normal distributions of the local density of states and multifractal spatial characteristics. Our method can be used to explore critical correlations in other materials close to a quantum critical point.Since Anderson first proposed that disorder could localize electrons in solids fifty years ago (1), studies of the transition between extended and localized quantum states have been at the forefront of physics (2). Realizations of Anderson localization occur in a wide range of physical systems from seismic waves to ultracold atomic gases, in

No abstract

Although geometric phases in quantum evolution were historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of non-adiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.Besides its central role in the understanding of contemporary physics [1,2], the quantum geometric phase is gaining recognition as a powerful resource for practical applications using quantum systems [3][4][5]. The manipulation of nanoscale systems has progressed rapidly towards realizing quantum-enhanced information processing and sensing, but also revealed the necessity for new methods to combat noise and decoherence [6][7][8]. Due to their intrinsic tolerance to local fluctuations [9,10], geometric phases offer an attractive route for implementing high-fidelity quantum logic. This approach, termed holonomic quantum computation (HQC) [3,[11][12][13][14][15], employs the cyclic evolution of quantum states and derives its resilience from the global geometric structure of the evolution in Hilbert space. Arising both for adiabatic [16] and non-adiabatic [17] cycles, geometric phases can be either Abelian (phase shifts) or non-Abelian (matrix transformations) [18] by acting on a single state or a subspace of states, respectively.Recently, non-Abelian, non-adiabatic holonomic gates using three-level dynamics [19] were proposed to match the computational universality of earlier adiabatic schemes [3,[11][12][13], but also eliminate the restriction of slow evolution. By reducing the run-time of holonomic gates, and thus their exposure to decoherence, this advance enabled experimental demonstration of HQC in superconducting qubits [20], nuclear spin ensembles in liquid [21], and nitrogen-vacancy (NV) centers in diamond [22,23]. However, these initial demonstrations were limited to fixed rotation angles about arbitrary axes, and thus required two non-adiabatic loops of evolution, from two iterations of experimental control, to execute an arbitrary gate [20][21][22][23]. Alternatively, variable angle rotations from a single non-adiabatic loop can be achieved using Abelian geometric phases [14,24] or hyperbolic secant pulses [25][26][27], but these approaches are complicated by a concomitant dynamic phase. To address these shortcomings, non-Abelian, non-adiabatic single-loop schemes * awsch@uchicago.edu [28,29] were designed to allow purely geometric, arbitrary angle rotations about arbitrary axes with a single experimental iteration.In this Letter, we realize single-loop, single-qubit holonomic gates by implementing th...

No abstract