arXiv subjects

Piet W. Brouwer

Publications and source records attributed to Piet W. Brouwer.

At least 73 records · Page 4Linked to original sources

arXiv2016

Weyl node with random vector potential

We study Weyl semimetals in the presence of generic disorder, consisting of a random vector potential as well as a random scalar potential. We derive renormalization group flow equations to second order in the disorder strength. These flow equations predict a disorder-induced phase transition between a pseudo-ballistic weak-disorder phase and a diffusive strong-disorder phase for sufficiently strong random scalar potential or for a pure three-component random vector potential. We verify these predictions using a numerical study of the density of states near the Weyl point and of quantum transport properties at the Weyl point. In contrast, for a pure single-component random vector potential the diffusive strong-disorder phase is absent.

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arXiv2016

Parity anomaly and spin transmutation in quantum spin Hall Josephson junctions

We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by $2π$. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reserval symmetry is preserved. We discuss the resulting $8π$-periodic (or $\mathbb{Z}_4$) fractional Josephson effect in the context of recent experiments.

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arXiv2016

Drude weight fluctuations in many-body localized systems

We numerically investigate the distribution of Drude weights $D$ of many-body states in disordered one-dimensional interacting electron systems across the transition to a many-body localized phase. Drude weights are proportional to the spectral curvatures induced by magnetic fluxes in mesoscopic rings. They offer a method to relate the transition to the many-body localized phase to transport properties. In the delocalized regime, we find that the Drude weight distribution at a fixed disorder configuration agrees well with the random-matrix-theory prediction $P(D) \propto (γ^2+D^2)^{-3/2}$, although the distribution width $γ$ strongly fluctuates between disorder realizations. A crossover is observed towards a distribution with different large-$D$ asymptotics deep in the many-body localized phase, which however differs from the commonly expected Cauchy distribution. We show that the average distribution width $\langle γ\rangle $, rescaled by $LΔ$, $Δ$ being the average level spacing in the middle of the spectrum and $L$ the systems size, is an efficient probe of the many-body localization transition, as it increases/vanishes exponentially in the delocalized/localized phase.

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arXiv2016

Graphene pn-junction in a quantizing magnetic field: Conductance at intermediate disorder strength

In a graphene {\em pn} junction at high magnetic field, unidirectional "snake states" are formed at the {\em pn} interface. In a clean {\em pn} junction, each snake state exists in one of the valleys of the graphene band structure, and the conductance of the junction as a whole is determined by microscopic details of the coupling between the snake states at the {\em pn} interface and quantum Hall edge states at the sample boundaries [Tworzydlo {\em et al.}, Phys. Rev. B {\bf 76}, 035411 (2007)]. Disorder mixes and couples the snake states. We here report a calculation of the full conductance distribution in the crossover between the clean limit and the strong disorder limit, in which the conductance distribution is given by random matrix theory [Abanin and Levitov, Science {\bf 317}, 641 (2007)]. Our calculation involves an exact solution of the relevant scaling equation for the scattering matrix, and the results are formulated in terms of parameters describing the microscopic disorder potential in bulk graphene.

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arXiv2016

Disordered double Weyl node

Double Weyl nodes are topologically protected band crossing points which carry chiral charge $\pm2$. They are stabilized by $C_4$ point group symmetry and are predicted to occur in $\mathrm{SrSi_2}$ or $\mathrm{HgCr_{2}Se_{4}}$. We study their fate in the presence of quenched disorder by numerical transport calculations and scaling arguments. We find that a double Weyl node is unstable in a disordered environment and splits into a pair of emergent simple Weyl nodes which carry equal chiral charge of $\pm1$. This pair of simple Weyl nodes is robust to disorder up to a certain critical disorder strength, in complete analogy to their `elementary' counterparts.

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arXiv2016

Gating a single-molecule transistor with individual atoms

Transistors, regardless of their size, rely on electrical gates to control the conductance between source and drain contacts. In atomic-scale transistors, this conductance is exquisitely sensitive to single electrons hopping via individual orbitals. Single-electron transport in molecular transistors has been previously studied using top-down approaches to gating, such as lithography and break junctions. But atomically precise control of the gate - which is crucial to transistor action at the smallest size scales - is not possible with these approaches. Here, we used individual charged atoms, manipulated by a scanning tunnelling microscope, to create the electrical gates for a single-molecule transistor. This degree of control allowed us to tune the molecule into the regime of sequential single-electron tunnelling, albeit with a conductance gap more than one order of magnitude larger than observed previously. This unexpected behaviour arises from the existence of two different orientational conformations of the molecule, depending on its charge state. Our results show that strong coupling between these charge and conformational degrees of freedom leads to new behaviour beyond the established picture of single-electron transport in atomic-scale transistors.

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arXiv2016

The weak side of strong topological insulators

Strong topological insulators may have nonzero weak indices. The nonzero weak indices allow for the existence of topologically protected helical states along line defects of the lattice. If the lattice admits line defects that connect opposite surfaces of a slab of such a "weak-and-strong" topological insulator, these states effectively connect the surface states at opposite surfaces. Depending on the phases accumulated along the dislocation lines, this connection results in a suppression of in-plane transport and the opening of a spectral gap or in an enhanced density of states and an increased conductivity.

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arXiv2015

Transport signatures of interacting fermions in quasi-one-dimensional topological superconductors

A topological superconducting wire with an effective time reversal symmetry is known to have a $\mathbb{Z}_8$ topological classification in the presence of interactions. The topological index $|n| \le 4$ counts the number of Majorana end states, negative $n$ corresponding to end states that are odd under time reversal. If such a wire is weakly coupled to a normal-metal lead, interactions induce a Kondo-like correlated state if $|n| = 4$. We show that the Kondo-like state manifests itself in an anomalous temperature dependence of the zero-bias conductance and by an anomalous Fano factor for the zero-temperature normally-reflected current at finite bias. We also consider the splitting of the effective Kondo resonance for weak symmetry-breaking perturbations.

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arXiv2015

Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $ν$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $ν=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $ν$ is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an $ε$-expansion scheme. We further obtain $z=1.49\pm0.02$ from the scaling of the conductivity with chemical potential.

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arXiv2015

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.

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arXiv2015

Electronic transport in graphene with particle-hole-asymmetric disorder

We study the conductivity of graphene with a smooth but particle-hole-asymmetric disorder potential. Using perturbation theory for the weak-disorder regime and numerical calculations we investigate how the particle-hole asymmetry shifts the position of the minimal conductivity away from the Dirac point $\varepsilon = 0$. We find that the conductivity minimum is shifted in opposite directions for weak and strong disorder. For large disorder strengths the conductivity minimum appears close to the doping level for which electron and hole doped regions ("puddles") are equal in size.

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arXiv2015

Quantum transport in Dirac materials: signatures of tilted and anisotropic Dirac and Weyl cones

We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance g, but leaves the Fano factor F (the ratio of shot noise power and current) unchanged, a tilt affects both g and F. Since F is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of strained graphene and a pyrochlore Weyl semi-metal.

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arXiv2014

Density of states at disorder-induced phase transitions in a multichannel Majorana wire

An $N$-channel spinless p-wave superconducting wire is known to go through a series of $N$ topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity $ν(\varepsilon) \propto \varepsilon^{-1}|\ln\varepsilon|^{-3} $, whereas $ν(\varepsilon) \propto \varepsilon^{|α|-1}$ has a power-law singularity for small energies $\varepsilon$ away from the critical points. Using the concept of "superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent $α$ to the wire's transport properties at zero energy and, hence, to the mean free path $l$ and the superconducting coherence length $ξ$.

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arXiv2014

Quantum transport of disordered Weyl semimetals at the nodal point

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.

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arXiv2014

Spin-wave-induced correction to the conductivity of ferromagnets

We calculate the correction to the conductivity of a disordered ferromagnetic metal due to spin-wave-mediated electron--electron interactions. This correction is the generalization of the Altshuler-Aronov correction to spin-wave-mediated interactions. We derive a general expression for the conductivity correction to lowest order in the spin-wave-mediated interaction and for the limit that the exchange splitting $Δ$ is much smaller than the Fermi energy. For a "clean" ferromagnet with $Δτ_{\rm el}/\hbar \gg 1$, with $τ_{\rm el}$ the mean time for impurity scattering, we find a correction $δσ\propto -T^{5/2}$ at temperatures $T$ above the spin wave gap. In the opposite, "dirty" limit, $Δτ_{\rm el}/\hbar \ll 1$, the correction is a non-monotonous function of temperature.

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arXiv2014

Quantum corrections to transport in graphene: a trajectory-based semiclassical analysis

We review a calculation of the quantum corrections to electrical transport in graphene using the trajectory-based semiclassical method. Compared to conventional metals, for graphene the semiclassical propagator contains an additional pseudospin structure, which influences the results for weak localization, and interaction-induced effects, such as the Altshuler-Aronov correction and dephasing. Our results apply to a sample of graphene that is doped away from the Dirac point and subject to a smooth disorder potential, such that electrons follow classical trajectories. In such system, the Ehrenfest time enters as an additional timescale.

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arXiv2014

Density of states as a probe of electrostatic confinement in graphene

We theoretically analyze the possibility to confine electrons in single-layer graphene with the help of metallic gates, via the evaluation of the density of states of such a gate-defined quantum dot in the presence of a ring-shaped metallic contact. The possibility to electrostatically confine electrons in a gate-defined ``quantum dot'' with finite-carrier density, surrounded by an undoped graphene sheet, strongly depends on the integrability of the electron dynamics in the quantum dot. With the present calculations we can quantitatively compare confinement in dots with integrable and chaotic dynamics, and verify the prediction that the Berry phase associated with the pseudospin leads to partial confinement in situations where no confinement is expected according to the arguments relying on the classical dynamics only.

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arXiv2014

Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach

The role of disorder in the field of three-dimensional time reversal invariant topological insulators has become an active field of research recently. However, the computation of Z2 invariants for large, disordered systems still poses a considerable challenge. In this paper we apply and extend a recently proposed method based on the scattering matrix approach, which allows the study of large systems at reasonable computational effort with few-channel leads. By computing the Z2 invariant directly for the disordered topological Anderson insulator, we unambiguously identify the topological nature of this phase without resorting to its connection with the clean case. We are able to efficiently compute the Z2 phase diagram in the mass-disorder plane. The topological phase boundaries are found to be well described by the self consistent Born approximation, both for vanishing and finite chemical potential.

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