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DOE OSTI2016

Quantum Hall edge states in topological insulator nanoribbons

We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically doped Bi 2 Se 3 -family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our theory is based on a simple continuum model of sidewall states whose parameters are extracted from detailed ribbon and film geometry tight-binding model calculations. In contrast to the familiar case of the quantum Hall effect in semiconductor quantum wells, the number of microscopic chiral channels depends simply and systematically on the ribbon thickness and on the position of the Fermi level within the surface state gap. Further, we use our theory to interpret recent transport experiments that exhibit nonzero longitudinal resistance in samples with accurately quantized Hall conductances.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Oxygen-modulated quantum conductance for ultrathin HfO 2 -based memristive switching devices

Memristive switching devices, candidates for resistive random access memory technology, have been shown to switch off through a progression of states with quantized conductance and subsequent noninteger conductance (in terms of conductance quantum G 0 ). We have performed calculations based on density functional theory to model the switching process for a Pt-HfO 2 -Pt structure, involving the movement of one or two oxygen atoms. Oxygen atoms moving within a conductive oxygen vacancy filament act as tunneling barriers, and partition the filament into weakly coupled quantum wells. We show that the low-bias conductance decreases exponentially when one oxygen atom moves away from interface. In conclusion, our results demonstrate the high sensitivity of the device conductance to the position of oxygen atoms.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Charge metastability and hysteresis in the quantum Hall regime

We report simultaneous quasi-dc magnetotransport and high-frequency surface acoustic wave measurements on bilayer two-dimensional electron systems in GaAs. Near strong integer quantized Hall states, a strong magnetic-field-sweep hysteresis in the velocity of the acoustic waves is observed at low temperatures. This hysteresis indicates the presence of a metastable state with anomalously high conductivity in the interior of the sample. This nonequilibrium state is not revealed by conventional low-frequency transport measurements which are dominated by dissipationless transport at the edge of the two-dimensional system. We find that a field-cooling technique allows the equilibrium charge configuration within the interior of the sample to be established. A simple model for this behavior is discussed.

2-dimensional systems↗

DOE OSTI2017

Quantitative relationship between polarization differences and the zone-averaged shift photocurrent

A relationship is derived between differences in electric polarization between bands and the “shift vector” that controls part of a material's bulk photocurrent, then demonstrated in several models. Electric polarization has a quantized gauge ambiguity and is normally observed at surfaces via the surface charge density, while shift current is a bulk property and is described by shift vector gauge invariant at each point in momentum space. They are connected because the same optical transitions that are described in shift currents pick out a relative gauge between valence and conduction bands. We also discuss subtleties arising when there are points at the Brillouin zone where optical transitions are absent. Finally, we conclude that two-dimensional materials with significant interband polarization differences should have high bulk photocurrent, meaning that the modern theory of polarization can be used as a straightforward way to search for bulk photovoltaic material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Optical nonlinearities of excitons in monolayer MoS 2

We calculate linear and nonlinear optical susceptibilities arising from the excitonic states of monolayer MoS 2 for in-plane light polarizations, using second-quantized bound and unbound exciton operators. Optical selection rules are critical for obtaining the susceptibilities. We derive the valley-chirality rule for the second-order harmonic generation in monolayer MoS 2 and find that the third-order harmonic process is efficient only for linearly polarized input light while the third-order two-photon process (optical Kerr effect) is efficient for circularly polarized light using a higher order exciton state. The absence of linear absorption due to the band gap and the unusually strong two-photon third-order nonlinearity make the monolayer MoS 2 excitonic structure a promising resource for coherent nonlinear photonics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Robustness of the biaxial charge density wave reconstructed electron pocket against short-range spatial antiferromagnetic fluctuations

Recent experiments on underdoped high-temperature superconductors have shown that a biaxial charge density wave coexisting with antiferromagnetism is able to account for the hole-doping dependences of the Hall coefficient and the charge density wave ordering vector. Owing to the loss of long-range order over the range of hole dopings where charge density waves are observed, however, antiferromagnetism poses a serious challenge to the viability of Landau quantization and quantum oscillations. In this work, we make the surprising finding that the states along the antiferromagnetic Brillouin zone boundary, which are usually the most heavily broadened by antiferromagnetic fluctuations, become gapped once the biaxial charge density wave forms. This gapping along with the location of the electron pocket produced by Fermi surface reconstruction at a momentum-space point of high symmetry causes the single nodal electron pocket to be largely protected against antiferromagnetic fluctuations in strong magnetic fields, enabling resolved Landau levels and quantum oscillations to remain robust against antiferromagnetic correlation lengths as short as ~10 Å .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. We argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d -wave superconducting pairing amplitude when antiferromagnetic interactions are included. Furthermore, our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Probing one-dimensional systems via noise magnetometry with single spin qubits

The study of exotic one-dimensional states, particularly those at the edges of topological materials, demand new experimental probes that can access the interplay between charge and spin degrees of freedom. One potential approach is to use a single spin probe, such as a nitrogen vacancy center in diamond, which has recently emerged as a versatile tool to probe nanoscale systems in a noninvasive fashion. Here, we present a theory describing how noise magnetometry with spin probes can directly address several questions that have emerged in experimental studies of 1D systems, including those in topological materials. We show that by controlling the spin degree of freedom of the probe, it is possible to measure locally and independently local charge and spin correlations of 1D systems. Visualization of 1D edge states, as well as sampling correlations with wave-vector resolution can be achieved by tuning the probe-to-sample distance. Furthermore, temperature-dependent measurements of magnetic noise can clearly delineate the dominant scattering mechanism (impurities versus interactions)—this is of particular relevance to quantum spin Hall measurements where conductance quantization is not perfect. Here, the possibility to probe both charge and spin excitations in a wide range of length scales opens new pathways to bridging the large gap between atomic scale resolution of scanning probes and global transport measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Half-filled Landau levels: A continuum and sign-free regularization for three-dimensional quantum critical points

In this paper, we explore a method for regulating 2+1D quantum critical points in which the ultraviolet cutoff is provided by the finite density of states of particles in a magnetic field rather than by a lattice. Such Landau-level quantization allows for numerical computations on arbitrary manifolds, like spheres, without introducing lattice defects. In particular, when half-filling a Landau level with $N = 4$ electron flavors, with appropriate interaction anisotropies in flavor space, we obtain a fully continuum regularization of the $\mathrm{O}(5)$ nonlinear sigma model with a topological term, which has been conjectured to flow to a deconfined quantum critical point. We demonstrate that this model can be solved by both infinite density-matrix renormalization group (DMRG) calculations and sign-free determinantal quantum Monte Carlo. DMRG calculations estimate the scaling dimension of the $\mathrm{O}(5)$ vector operator to be in the range $\mathrm{Δ_V}$ ~ $0.55-0.7$, depending on the stiffness of the nonlinear sigma model. Future Monte Carlo simulations will be required to determine whether this dependence is a finite-size effect or further evidence for a weak first-order transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Probing the Berry curvature and Fermi arcs of a Weyl circuit

The Weyl particle is the massless fermionic cousin of the photon. While no fundamental Weyl particles have been identified, they arise in condensed matter and metamaterial systems, where their spinor nature imposes topological constraints on low-energy dispersion and surface properties. Here we demonstrate a topological circuit with Weyl dispersion at low momentum, realizing a 3D lattice that behaves as a half-flux Hofstadter model in all principal planes. The circuit platform provides access to the complete complex-valued spin texture of all bulk and surface states, thereby revealing not only the presence of Weyl points and the Fermi arcs that connect their surface projections, but also the Berry curvature distribution through the Brillouin zone and the associated quantized chiral charge of the Weyl points. Furthermore, this work opens a path to exploration of interacting Weyl physics in superconducting circuits, as well as studies of how manifold topology impacts band topology in three dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Fractional Chern insulator edges and layer-resolved lattice contacts

Fractional Chern insulators (FCIs) realized in fractional quantum Hall systems subject to a periodic potential are topological phases of matter for which space group symmetries play an important role. In particular, lattice dislocations in an FCI can host non-Abelian topological defects, known as genons. Genons can increase the ground-state degeneracy of the system and are thus potentially useful for topological quantum computing. In this work, we study FCI edges and how they can be used to detect genons. We find that translation symmetry can impose a quantized momentum difference between the edge electrons of a partially filled Chern band. We propose layer-resolved lattice contacts, which utilize this momentum difference to selectively contact a particular FCI edge electron. The relative current between FCI edge electrons can then be used to detect the presence of genons in the bulk FCI. Recent experiments have demonstrated graphene is a viable platform to study FCI physics. Here, we describe how the lattice contacts proposed here could be implemented in graphene subject to an artificial lattice, thereby outlining a path forward for experimental dectection of non-Abelian topological defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Interacting invariants for Floquet phases of fermions in two dimensions

We construct a many-body quantized invariant that sharply distinguishes among two-dimensional nonequilibrium driven phases of interacting fermions. This is an interacting generalization of a band-structure Floquet quasienergy winding number and describes chiral pumping of quantum information along the edge. In particular, our invariant sharply distinguishes between a trivial and anomalous Floquet Anderson insulator in the interacting, many-body localized setting. It also applies more generally to models where only fermion parity is conserved, where it differentiates between trivial models and ones that pump Kitaev Majorana chains to the boundary, such as ones recently introduced in the context of emergent fermions arising from eigenstate $ \mathbb{Z}_2$ topological order. We evaluate our invariant for the edge of such a system with eigenstate $ \mathbb{Z}_2$ topological order, and show that it is necessarily nonzero when the Floquet unitary exchanges electric and magnetic excitations, proving a connection between bulk anyonic symmetry and edge chirality that was recently conjectured.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect

We study the Josephson effect in the multiterminal junction of topological superconductors. We use the symmetry-constrained scattering matrix approach to derive band dispersions of emergent subgap Andreev bound states in a multidimensional parameter space of superconducting phase differences. We find distinct topologically protected band crossings that serve as monopoles of finite Berry curvature. Particularly, in a four-terminal junction the admixture of 2π and 4π periodic levels leads to the appearance of finite-energy Majorana-Weyl nodes. This topological regime in the junction can be characterized by a quantized nonlocal conductance that measures the Chern number of the corresponding bands. In addition, we calculate current-phase relations, variance, and cross correlations of topological supercurrents in multiterminal contacts and discuss the universality of these transport characteristics. At the technical level these results are obtained by integrating over the group of a circular ensemble that describes the scattering matrix of the junction. Furthermore, we briefly discuss our results in the context of observed fluctuations of the gate dependence of the critical current in topological planar Josephson junctions and comment on the possibility of parity measurements from the switching current distributions in multiterminal Majorana junctions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Thermoelectric Hall conductivity and figure of merit in Dirac/Weyl materials

In this paper, we calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient α xy and the Seebeck coefficient S xx , which are well-defined even in the dissipationless limit. We contrast the behaviors of α xy and S xx with those of traditional Schrödinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials α xy acquires a constant, quantized value at sufficiently large magnetic field, which is independent of the magnetic field or the Fermi energy, and this leads to unprecedented growth in the thermopower and the thermoelectric figure of merit. We further show that even relatively small fields, such that ω c τ~1 (where ω c is the cyclotron frequency and τ is the scattering time), are sufficient to produce a more than 100% increase in the figure of merit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Gyrotropic Hall effect in Berry-curved materials

We study the ac Hall response induced by passage of dc transport current in two- and three-dimensional metals with gyrotropic point groups—the gyrotropic Hall effect—and consider the phenomenon of current-induced optical activity in noncentrosymmetric metals as a physical application of our theory. While the effect is expected to be present in single crystals of any noncentrosymmetric metal, we expect it to be strongest in enantiomorphic Weyl semimetals. Using the semiclassical kinetic equation approach, we present several mechanisms underlying the gyrotropic Hall effect. Amongst them, the intrinsic mechanism is determined by the Berry curvature dipole, while extrinsic impurity-induced processes are related to skew scattering and side-jump phenomena. In general, the intrinsic and extrinsic contributions can be of similar magnitude. We discuss the gyrotropic Hall effect for all frequencies of practical interest, from the dc transport limit, to optical frequencies. We show that for frequencies that are small compared to relevant band splittings, the trace of the gyrotropic Hall tensor in three-dimensional materials is proportional to a topological, quantized Berry charge, and therefore is robust in gyrotropic Weyl systems. This implies that polycrystals of strongly gyrotropic Weyl semimetals will demonstrate strong current-induced optical activity, whereas the response vanishes for polycrystalline ordinary metals. Furthermore the current-induced optical activity can be considered a valuable tool in identifying the topological nature of a material.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Multiple magnetic droplet soliton modes

Droplet solitons are large amplitude localized spin-wave excitations that can be created in magnetic thin films with uniaxial anisotropy by a spin-polarized current flowing through an electrical nanocontact. Here, we report a low-temperature (4 K) experimental study that shows there are multiple and, under certain conditions, combinations of droplet modes, each mode with a distinct high-frequency spin precession (tens of gigahertz). Low-frequency (≲1GHz) voltage noise is used to assess the stability of droplet modes. Furthermore, it is found that droplets are stable only in a limited range of applied field and current, typically near the current and field at which they nucleate, in agreement with recent predictions. Applied fields in the film plane favor multiple droplet modes, whereas fields perpendicular to the film plane tend to stabilize a single droplet mode. Furthermore, micromagnetic simulations are used to show that spatial variation in the energy landscape in the nanocontact region (e.g., spatial variation of magnetic anisotropy or magnetic field) can lead to quantized droplet modes and low-frequency mode modulation, characteristics observed in our experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

High Landau levels of two-dimensional electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts

In the presence of spin-orbit coupling two branches of the energy spectrum of two-dimensional electrons get shifted in the momentum space. Application of an in-plane magnetic field causes the splitting of the branches in energy. When both spin-orbit coupling and Zeeman splitting are present, the branches of the energy spectrum cross at a certain energy. Near this energy, the Landau quantization becomes peculiar since semiclassical trajectories, corresponding to individual branches, get coupled. We study this coupling as a function of the proximity to the topological transition. Remarkably, the dependence on the proximity is strongly asymmetric, reflecting the specifics of the behavior of the trajectories near the crossing. Equally remarkable, on one side of the transition, the magnitude of coupling is an oscillating function of this proximity. These oscillations can be interpreted in terms of the Stückelberg interference. Scaling of characteristic detuning with magnetic length is also unusual. Furthermore, this unusual behavior cannot be captured by simply linearizing the Fermi contours near the crossing point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗