Session L15: Phenomena in Dirac Systems

Dirac Materials

Discoveries of superfluid phases in 3He, high Tc superconductors, graphene and topological insulators have brought into focus materials where quasiparticles are described by same Dirac and Weyl equation that governs behavior of relativistic particles. This class of materials, called Dirac materials [1], exhibits unusual universal features: Klein tunneling, chirality and impurity resonances.~ I will explore these similarities and discuss the unique role of symmetries that protect the Dirac spectrum. As an example of universal behavior of Dirac-Weyl materials I will consider impurity resonances, filling of the gap and gapless spectra in the magnetically doped topological insulators [2]. I will also discuss Dirac materials~quantum imaging~and how the ripples in the Dirac sea produced by defects can induce fascinating features in local magnetism and Kondo effect. At the end I will outline future opportunities to design Dirac materials that host bosonic Dirac excitations, something that would not be possible in particle physics [3].~Work supported by US DOE E304. [1] T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky (2014) Dirac materials,Advances in Physics, 63:1, 1-76. [2] A. M. Black-Schaffer, A. V. Balatsky, and J. Fransson, Phys. Rev. B~91, 201411(R) (2015). [3] S. Banerjee, A. M. Black-Schaffer, J. Fransson, H. Agren, A.V. Balatsky, Bosonic Dirac Materials in 2 Dimensions, preprint [2015], J. Fransson et.al, Dirac Magnons, preprint [2015].   

Artificial Graphene in Nano-patterned GaAs Quantum Wells

We report the realization of artificial graphene (AG) in a 2D electron gas in a highly tunable semiconductor quantum well system. Very short period (as small as 40 nm) honeycomb lattices were formed in a GaAs heterostructure by electron beam lithography followed by dry etching. Characterization of the AG samples by photoluminescence at low temperature (about 4K) indicates modulation of 2D electron states. Low-lying electron excitations observed by resonant inelastic light scattering and interpreted with a calculated AG band structure confirm the formation of AG bands with a well-defined Dirac cone, evidence for the presence of massless Dirac fermions. These results suggest that engineered semiconductor nano-scale structures can serve as advanced quantum simulators for probing novel electron behavior in low dimensional systems.   

Fabrication of artificial graphene in a GaAs heterostructure

Engineered honeycomb lattices, known as artificial graphene, constitute a platform for the exploration of graphene-like phenomena in a highly controllable and tunable manner, offering insight into a broader parameter range inaccessible to natural graphene. The electronic states of a 2D electron gas whose density is modulated by a potential with honeycomb topology have been predicted to generate massless Dirac fermions (MDFs) with tunable Fermi velocity. In this work we present the fabrication of artificial graphene in an ultrahigh quality GaAs/AlGaAs quantum well, with lattice period as small as 40nm, the smallest reported so far for this type of system. The combination of high precision electron-beam lithography, used to define an etch mask with honeycomb geometry on the surface of the sample, and precise anisotropic reactive ion etching allows to create artificial graphene with excellent uniformity and long range order. Different methodologies for preparation of the mask are compared and their limits are discussed. Thanks to the achievement of such high-resolution artificial graphene we expected to be able to observe, for the first time, MDFs in an engineered semiconductor and the possibility of access to novel topological phases.   

Berry's Phase and Giant Non-Reciprocity in Dirac Quantum Dots

Recently, nanoscale pn-junction rings have been introduced as a vehicle for coherent control of electronic states in Dirac materials [1]. Confined states in such ring-shaped electron resonators arise due to constructive interference of electronic waves incident at the pn junction at oblique angles and inward-reflected from the ring. Contrary to confined electronic states in conventional quantum dots, Dirac electrons are characterized by a non-trivial Berry's phase. Here we show [2] that the Dirac quantum dot energy levels are sensitive to the Berry's phase. In particular, we predict that the Berry's phase can induce a giant spectral non-reciprocity arising in weak magnetic fields. The effect is maximal for massless Dirac electrons, e.g. graphene, and is manifested in anomalously large splittings of the resonances which are degenerate at B=0 due to time reversal symmetry. This non-reciprocity effect overwhelms the conventional orbital and spin-induced non-reciprocity. The predicted giant non-reciprocity is readily accessible by Faraday and Kerr optical rotation measurements as well as by scanning tunneling spectroscopy. [1] Zhao, et al., Science 348, 672 (2015). [2] JRN, et al., arXiv:1508.06609.   

a universal regulation for the angle resolved transport properties of Dirac cones and beyond

A universal regulation for the angle resolved transport properties of two-dimensional (2D) Dirac cones, such as graphene, graphynes or even beyond, was established for the first time. The anisotropy and isotropy properties of 2D Dirac cones were investigated theoretically combining with first-principles calculation. It was found the moving direction of Dirac cones ($\theta_{\mathrm{move}})$ varies with the strain orientation ($\theta_{\mathrm{q}})$ can be approximately described by a linear law. Moreover, $\theta_{\mathrm{move}}$ is related the hopping (S$_{\mathrm{12}})$ between two bases with respective to the strain. The coefficients, a$_{\mathrm{x}}$, a$_{\mathrm{y}}$, a$_{\mathrm{\gamma ,\thinspace }}$in the taylor expansion formula of S$_{\mathrm{12}}$ and strain were determined with DFT calculations. Graphene and graphynes were calculated to check the universality of the theory, which turns out to be working well. This new regulation could also be recommended into semiconductive systems to predict their transport behaviors, such as phosphorene or MoS$_{\mathrm{2}}$, whose angle resolved transport properties have been widely investigated experimentally for comparison.   

Graphene quantum dots for high-performance THz hot electron bolometers

We study graphene quantum dots patterned from epitaxial graphene on SiC with a resistance strongly dependent on temperature. The combination of weak electron-phonon coupling and small electronic heat capacity in graphene makes these quantum dots ideal hot-electron bolometers. We characterize their response to THz radiation as a function of dot size, with sizes ranging from 30 to 700 nm and temperature, from 2.4K to 80K. We show that quantum dots exhibit a variation of resistance with temperature higher than 430 M$\Omega $/K below 6K, leading to electrical responsivities for an absorbed THz power above 1\texttimes 10$^{\mathrm{10}}$ V/W. The high responsivity, the potential for operation above 80 K and the process scalability show great promise towards practical applications of graphene quantum dot THz detectors. $^{\mathrm{1}}$A. El Fatimy, R.L.Myers-Ward, A.K. Boyd, K.M. Daniels, D. K. Gaskill, and P. Barbara, Nature Nanotechnology, Accepted (2015).   

Ballistic Transport in Graphene Antidot Lattices

We observed commensurability magnetoresistance arising from ballistic electron transport in the triangular antidot lattice of high-mobility graphene. For both the monolayer and bilayer, magnetoresistance peaks were observed at the commensurability magnetic elds of the cyclotron orbit with antidot lattice. This condition was approximately unchanged for massless and massive Dirac fermions. The peaks appeared when the carrier mean free path was roughly larger than the lattice constant of the antidot, which indicates that the effect stems from the short-range characteristics of the carrier's scattering with antidots. We also found that the magnitude of commensurability peak diminished with changing the gate voltages to the charge neutrality point. This arose from the screening of charged impurity in graphene, which is dependent on carrier density.   

Magneto Transport of Graphene Monolayer with Antidot Arrays

Graphene has a significant potential for electronics application as well as in high precision resistive metrological standard. Here we report magneto transport studies of monolayer graphene with antidot in hexagonal arrays on SiO2/Si substrate. The choice of antidot array was motivated by the potential to enhance quantum interference effect amongst charge carriers. The graphene-antidot arrays were fabricated by electron beam lithography followed by reactive ion etching. In our samples the dc magnetic field (B) was applied continuously up to 18 Tesla while the measurement temperature (T) was held steady at desired set points, ranging from 200 mK to 20 K. The effect of nanoarrays on the temperature and field dependence of the electrical properties (MR) and quantum hall effect with particular attention to Aharonov-Bohm oscillations will be reported.   

An Einzel lens apparatus for deposition of levitated graphene on a substrate in UHV

The goal of our research is to levitate a charged micron-scale graphene flake in an electrical AC quadrupole trap in ultra-high vacuum (UHV) in order to study its properties and dynamics while decoupled from any substrate [1,2]. As a complement to the optical measurements that can be performed on the levitated flake, we are developing a method of depositing the same flake on a substrate, which can be removed from the system for further study using such probes as atomic force microscopy (AFM) and scanning tunneling microscopy (STM). As the flake is released from the trap and propelled toward the substrate, its trajectory will be controlled by an Einzel (electrostatic) lens to achieve accurate positioning on the substrate. This talk will discuss the design of the lens as well as particle tracing simulations to determine the proper lens voltage to focus the particle's trajectory. In the future, deposited graphene may be used to passivate H-terminated silicon. The method is expected to be generalizable to achieve deposition of 2D materials on surfaces in a clean UHV environment. [1] Kane, B.E. \textit{Phys. Rev. B.}, \textbf{82}, 115441 (2010). [2] Nagornykh, P., et. al. \textit{Appl. Phys. Lett.} \textbf{106}, 244102 (2015).   

Rotational dynamics of levitated graphite flakes

Trapping of charged graphene multilayer flakes in a quadrupole ion trap provides a unique method of characterization of 2D materials via complete separation of the flake and the environment. As the ability to cool the center-of-mass temperature of the flakes levitated in high vacuum was shown in the previous work [1], in this talk we concentrate on probing the internal dynamics of the spinning flake. A 671 nm circularly polarized laser was used to provide a spinning torque to the levitated micron-sized flakes, while a linear 532 nm laser, oriented orthogonal to the first one, acted as a light source. We have studied the effects of 671 nm laser power on measured frequency spectra at pressures of $10^{-7}-10^{-9}$ Torr, where spinning frequencies of greater than 6 MHz have been achieved. Frequency decay data was collected by turning the laser on and off, which allowed us to estimate damping ratios from the flake deceleration. The spectra measured during the spinning acceleration showed multiple harmonics and other non-commensurate frequencies. We compare the observed frequencies to the behavior expected from a rigid body and from a membrane under the centrifugal tension. \\[0pt][1] P. Nagornykh, J. E. Coppock, B. E. Kane, Appl. Phys. Lett. \textbf{106}, 244102 (2015)   

Bosonic Dirac Materials in 2 dimensions

We examine the low energy effective theory of phase oscillations in a two dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Two different types of collective phase oscillations are obtained, which are analogous to the massive Leggett and massless Bogoliubov-Anderson-Gorkov modes for two-band superconductor. It is explicitly shown that the spectra of these collective Bosonic modes cross each other at {\$}K{\$} and {\$}K'{\$} points in the Brillouin zone and form a Dirac node. This Dirac node behavior in Bosonic excitations represent the case of Bosonic Dirac Materials (BDM). Dirac node is preserved in presence of an inter-grain interaction despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sub lattice symmetry by choosing different on-site potentials for the two sub lattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac material.   

Double Dirac cones in two-dimensional phononic crystals.

By utilizing the accidental degeneracy of two double-degenerate Bloch eigenstates, a double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can be accurately predicted by the method from first-principles. A slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated.   

Mechanical Flip-Chip for Ultra-High Electron Mobility Devices

We present a novel ``flip-chip'' microfabrication method that was used to make a quantum point contact (QPC) on a two-dimensional electron gas (2DEG) without any fabrication process on the 2DEG. Electrostatic gates are of paramount importance for the physics of devices based on 2DEG since they allow depletion of electrons in selected areas. This field-effect gating enables the fabrication of a wide range of devices such as, electron interferometers and quantum dots. To fabricate these gates, processing is usually performed on the 2DEG, which is in many cases detrimental to its electron mobility. Our approach does not require any processing of the 2DEG material leaving it pristine and reusable. It relies on processing a separate wafer that is then mechanically mounted on the 2DEG material in a flip-chip fashion. This technique proved successful to fabricate QPC on GaAs/AlGaAs materials with high electron mobility ranging from 1e6 to 1e7 cm$^{\mathrm{2}}$V/s. (Bennaceur, K.~ \textit{et al. }~Scientific Reports 5, 13494 (2015)). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Topological States in Multi-Orbital Honeycomb Lattices of HgTe Quantum Dots

Recent works demonstrate that 2D single-crystalline sheets of semiconductors forming a honeycomb lattice can be synthesized by oriented attachment of semiconductor nanocrystals. Inspired by these results, we have performed atomistic tight-binding calculations of the band structure of CdSe [1] and HgTe [2] sheets with honeycomb nano-geometry. In the case of CdSe [1], we predict that their conduction band exhibits Dirac cones at two distinct energies. The lowest one has s-orbital character. The bands higher in energy present a Dirac cone and nontrivial flat bands because of their p-orbital character. We show that lattices of HgTe [2] combine the effects of the honeycomb geometry and strong spin-orbit coupling. The conduction bands can be described by a tight-binding lattice model as in graphene, but including multi-orbital degrees of freedom and spin-orbit coupling. This results in very large topological gaps and a flattened band detached from the others. Honeycomb structures of HgTe constitute a promising platform for the observation of a fractional Chern insulator or a fractional quantum spin Hall phase. [1] E. Kalesaki et al., Phys. Rev. X 4, 011010 (2014). [2] W. Beugeling et al., Nat. Commun. doi: 10.1038/ncomms7316 (2015).   

Interaction of water molecules with hexagonal 2D systems. A DFT study

Over the years water sources have been contaminated with many chemical agents, becoming issues that affect health of the world population. The advances of the nanoscience and nanotechnology in the development new materials constitute an alternative for design molecular filters with great efficiencies and low cost for water treatment and purification. In the nanoscale, the process of filtration or separation of inorganic and organic pollutants from water requires to study interactions of these atoms or molecules with different nano-materials. Specifically, it is necessary to understand the role of these interactions in physical and chemical properties of the nano-materials. In this work, the main interest is to do a theoretical study of interaction between water molecules and 2D graphene-like systems, such as silicene (h-Si) or germanene (h-Ge). Using Density Functional Theory we calculate total energy curves as function of separation between of water molecules and 2D systems. Different spatial configurations of water molecules relative to 2D systems are considered. Structural relaxation effects and changes of electronic charge density also are reported.