Brian B. Zhou

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2

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.

Visualizing Critical Correlations Near the Metal-Insulator Transition in Ga1-xMnxAs

Metal-Insulator Transition At near-zero temperatures, some materials undergo a metal-insulator transition and their electronic properties change from conducting to insulating. In the dilute magnetic semiconductor Ga1−xMnxAs, a promising spintronics material, the metal-insulator transition is driven by the substitution of Ga atoms with Mn. While disorder clearly plays a key role in this transition, the influence of electron-electron correlations has been far from clear. Richardella et al. (p. 665; see the Perspective by Fiete and de Lozanne) used scanning tunneling microscopy to study the electronic states of this system. The autocorrelation function of the local density of states exhibited a power law (rather than an exponential) decay at Fermi energy. Thus, electron-electron interactions are indeed crucial for understanding dilute magnetic semiconductors. Scanning tunneling microscopy reveals the import role of electron-electron interactions in a dilute magnetic semiconductor. 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 used scanning tunneling microscopy to visualize electronic states in Ga1-xMnxAs 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.

The Crystal and Electronic Structures of Cd3As2, the Three-Dimensional Electronic Analogue of Graphene

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.This is a revised version of a manuscript that was originally posted here in February of 2014. It has been accepted at the journal Inorganic Chemistry after reviews that included those of two crystallographers who made sure all the ts were crossed and the is were dotted. The old work (from 1968) that said that Cd3As2 was noncentrosymmetric was mistaken, with the authors of that study making a type of error that in the 1980s became infamous in crystallography. As a result of the increased scrutiny of the issue of centrosymmetricity of the 1980s, there are now much better analysis tools to resolve the issue fully, and its important to understand that not just our crystals are centrosymmetric, even the old guys crystals were centrosymmetric (and by implication everyones are). There is no shame in having made that error back in the day and those authors would not find the current centrosymmetric result controversial; their paper is excellent in all other aspects. This manuscript describes how the structure is determined, explains the structure schematically, calculates the electronic structure based on the correct centrosymmetric crystal structure, and gives the structural details that should be used for future analysis and modeling.

Visualizing nodal heavy fermion superconductivity in CeCoIn5

By means of low-temperature scanning tunnelling spectroscopy, a heavy fermion material in its superconducting and mixed states can be imaged. Besides probing the superconducting gap symmetry, the measurements also reveal a pseudogap.

Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system

Adiabatic processes are useful in quantum control, but they are slow. A way around this is to exploit shortcuts to adiabaticity, which can speed things up — for instance, by boosting stimulated Raman adiabatic passage. Adiabatic processes are useful for quantum technologies1,2,3 but, despite their robustness to experimental imperfections, they remain susceptible to decoherence due to their long evolution time. A general strategy termed shortcuts to adiabaticity4,5,6,7,8,9 (STA) aims to remedy this vulnerability by designing fast dynamics to reproduce the results of a slow, adiabatic evolution. Here, we implement an STA technique known as superadiabatic transitionless driving10 (SATD) to speed up stimulated Raman adiabatic passage1,11,12,13,14 in a solid-state lambda system. Using the optical transitions to a dissipative excited state in the nitrogen-vacancy centre in diamond, we demonstrate the accelerated performance of different shortcut trajectories for population transfer and for the initialization and transfer of coherent superpositions. We reveal that SATD protocols exhibit robustness to dissipation and experimental uncertainty, and can be optimized when these effects are present. These results suggest that STA could be effective for controlling a variety of solid-state open quantum systems11,12,13,14,15,16.

Design and performance of an ultra-high vacuum scanning tunneling microscope operating at dilution refrigerator temperatures and high magnetic fields

We describe the construction and performance of a scanning tunneling microscope capable of taking maps of the tunneling density of states with sub-atomic spatial resolution at dilution refrigerator temperatures and high (14 T) magnetic fields. The fully ultra-high vacuum system features visual access to a two-sample microscope stage at the end of a bottom-loading dilution refrigerator, which facilitates the transfer of in situ prepared tips and samples. The two-sample stage enables location of the best area of the sample under study and extends the experiment lifetime. The successful thermal anchoring of the microscope, described in detail, is confirmed through a base temperature reading of 20 mK, along with a measured electron temperature of 250 mK. Atomically resolved images, along with complementary vibration measurements, are presented to confirm the effectiveness of the vibration isolation scheme in this instrument. Finally, we demonstrate that the microscope is capable of the same level of performance as typical machines with more modest refrigeration by measuring spectroscopic maps at base temperature both at zero field and in an applied magnetic field.

Optical manipulation of the Berry phase in a solid-state spin qubit

Phase relations between quantum states represent a resource for storing and processing quantum information. Although quantum phases are commonly controlled dynamically by tuning energetic interactions, the use of geometric phases that accumulate during cyclic evolution may offer superior robustness to noise. To date, demonstrations of geometric phase in solid-state systems employ microwave fields that have limited spatial resolution. Here, we demonstrate an all-optical method to accumulate a geometric phase, the Berry phase, in an individual nitrogen–vacancy centre in diamond. Using stimulated Raman adiabatic passage controlled by diffraction-limited laser light, we loop the nitrogen–vacancy centres spin around the Bloch sphere to enclose an arbitrary Berry phase. We investigate the limits of this control due to the loss of adiabaticity and decoherence, as well as its robustness to noise introduced into the experimental control parameters. These techniques set the foundation for optical geometric manipulation in photonic networks of solid-state qubits linked and controlled by light. An all-optical manipulation of the Berry phase based on stimulated Raman adiabatic passage is demonstrated in an individual nitrogen–vacancy centre in diamond. The adiabatic control is 100 times faster than that demonstrated before in atomic systems.

Holonomic Quantum Control by Coherent Optical Excitation in Diamond

Although geometric phases in quantum evolution are 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 nonadiabatic 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.

Imaging electronic states on topological semimetals using scanning tunneling microscopy

Following the intense studies on topological insulators, significant efforts have recently been devoted to the search for gapless topological systems. These materials not only broaden the topological classification of matter but also provide a condensed matter realization of various relativistic particles and phenomena previously discussed mainly in high energy physics. Weyl semimetals host massless, chiral, low-energy excitations in the bulk electronic band structure, whereas a symmetry protected pair of Weyl fermions gives rise to massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy to explore the behavior of electronic states both on the surface and in the bulk of topological semimetal phases. By mapping the quasiparticle interference (QPI) and emerging Landau levels at high magnetic field in Dirac semimetals Cd3As2 and Na3Bi, we observed extended Dirac-like bulk electronic bands. QPI imaged on Weyl semimetal TaAs demonstrated the predicted momentum dependent delocalization of Fermi arc surface states in the vicinity of the surface-projected Weyl nodes.

Visualizing heavy fermion formation and their unconventional superconductivity in f-electron materials

In solids containing elements with f-orbitals, the interaction between f-electron spins and those of itinerant electrons leads to the development of low-energy fermionic excitations with a heavy effective mass. These excitations are fundamental to the appearance of unconventional superconductivity observed in actinide- and lanthanide-based compounds. We use spectroscopic mapping with the scanning tunneling microscope to detect the emergence of heavy excitations with lowering of temperature in Ce- and U-based heavy fermion compounds. We demonstrate the sensitivity of the tunneling process to the composite nature of these heavy quasiparticles, which arises from quantum entanglement of itinerant conduction and f-electrons. Scattering and interference of the composite quasiparticles is used in the Ce-based compounds to resolve their energy-momentum structure and to extract their mass enhancement, which develops with decreasing temperature. Finally, by extending these techniques to much lower temperatures, we ...