91 research outputs found
Effective mass and tricritical point for lattice fermions localized by a random mass
This is a numerical study of quasiparticle localization in symmetry class
\textit{BD} (realized, for example, in chiral \textit{p}-wave superconductors),
by means of a staggered-fermion lattice model for two-dimensional Dirac
fermions with a random mass. For sufficiently weak disorder, the system size
dependence of the average (thermal) conductivity is well described by
an effective mass , dependent on the first two moments of the
random mass . The effective mass vanishes linearly when the average
mass , reproducing the known insulator-insulator phase boundary
with a scale invariant dimensionless conductivity and
critical exponent . For strong disorder a transition to a metallic phase
appears, with larger but the same . The intersection of the
metal-insulator and insulator-insulator phase boundaries is identified as a
\textit{repulsive} tricritical point.Comment: 6 pages, 9 figure
Scattering theory of the chiral magnetic effect in a Weyl semimetal: Interplay of bulk Weyl cones and surface Fermi arcs
We formulate a linear response theory of the chiral magnetic effect in a
finite Weyl semimetal, expressing the electrical current density induced by
a slowly oscillating magnetic field or chiral chemical potential in
terms of the scattering matrix of Weyl fermions at the Fermi level. Surface
conduction can be neglected in the infinite-system limit for , but not for : The chirally circulating surface Fermi
arcs give a comparable contribution to the bulk Weyl cones no matter how large
the system is, because their smaller number is compensated by an increased flux
sensitivity. The Fermi arc contribution to has the
universal value , protected by chirality against impurity scattering
--- unlike the bulk contribution of opposite sign.Comment: 8 pages, 8 figures; V2: added references with discussion; V3: To be
published in the Focus Issue on "Topological semimetals" of New Journal of
Physic
Weyl-Majorana solenoid
A Weyl semimetal wire with an axial magnetization has metallic surface states
(Fermi arcs) winding along its perimeter, connecting bulk Weyl cones of
opposite topological charge (Berry curvature). We investigate what happens to
this "Weyl solenoid" if the wire is covered with a superconductor, by
determining the dispersion relation of the surface modes propagating along the
wire. Coupling to the superconductor breaks up the Fermi arc into a pair of
Majorana modes, separated by an energy gap. Upon variation of the coupling
strength along the wire there is a gap inversion that traps the Majorana
fermions.Comment: 6 pages, 6 figures; V2: added discussion of charge operator, updated
figures; V3: added a section on analytical mode-matching calculations, an
appendix, and three new figures. To be published in the Focus Issue on
"Topological semimetals" of New Journal of Physic
Switching of electrical current by spin precession in the first Landau level of an inverted-gap semiconductor
We show how the quantum Hall effect in an inverted-gap semiconductor (with
electron- and hole-like states at the conduction- and valence-band edges
interchanged) can be used to inject, precess, and detect the electron spin
along a one-dimensional pathway. The restriction of the electron motion to a
single spatial dimension ensures that all electrons experience the same amount
of precession in a parallel magnetic field, so that the full electrical current
can be switched on and off. As an example, we calculate the magnetoconductance
of a p-n interface in a HgTe quantum well and show how it can be used to
measure the spin precession due to bulk inversion asymmetry.Comment: 5 pages, 4 figures, extended versio
Metallic phase of the quantum Hall effect in four-dimensional space
We study the phase diagram of the quantum Hall effect in four-dimensional
(4D) space. Unlike in 2D, in 4D there exists a metallic as well as an
insulating phase, depending on the disorder strength. The critical exponent
of the diverging localization length at the quantum Hall
insulator-to-metal transition differs from the semiclassical value of
4D Anderson transitions in the presence of time-reversal symmetry. Our
numerical analysis is based on a mapping of the 4D Hamiltonian onto a 1D
dynamical system, providing a route towards the experimental realization of the
4D quantum Hall effect.Comment: 4+epsilon pages, 3 figure
Majorana bound states without vortices in topological superconductors with electrostatic defects
Vortices in two-dimensional superconductors with broken time-reversal and
spin-rotation symmetry can bind states at zero excitation energy. These
socalled Majorana bound states transform a thermal insulator into a thermal
metal and may be used to encode topologically protected qubits. We identify an
alternative mechanism for the formation of Majorana bound states, akin to the
way in which Shockley states are formed on metal surfaces: An atomic-scale
electrostatic line defect can have a pair of Majorana bound states at the end
points. The Shockley mechanism explains the appearance of a thermal metal in
vortex-free lattice models of chiral p-wave superconductors and (unlike the
vortex mechanism) is also operative in the topologically trivial phase.Comment: 8 pages, 7 figures; the appendices are included as supplemental
material in the published versio
Theory of the topological Anderson insulator
We present an effective medium theory that explains the disorder-induced
transition into a phase of quantized conductance, discovered in computer
simulations of HgTe quantum wells. It is the combination of a random potential
and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian
that can drive an ordinary band insulator into a topological insulator (having
an inverted band gap). We calculate the location of the phase boundary at weak
disorder and show that it corresponds to the crossing of a band edge rather
than a mobility edge. Our mechanism for the formation of a topological Anderson
insulator is generic, and would apply as well to three-dimensional
semiconductors with strong spin-orbit coupling.Comment: 4 pages, 3 figures (updated figures, calculated DOS
Phase shift of cyclotron orbits at type-I and type-II multi-Weyl nodes
Quantum oscillations of response functions in high magnetic fields tend to reveal some of the most interesting properties of metals. In particular, the oscillation phase shift is sensitive to topological band features, thereby helping to identify the presence of Weyl fermions. In this work, we predict a characteristic parameter dependence of the phase shift for Weyl fermions with tilted and overtilted dispersion (type-I and type-II Weyl fermions) and an arbitrary topological charge (multi-Weyl fermions). For type-II Weyl fermions our calculations capture the case of magnetic breakthrough between the electron and the hole part of the dispersion. Here, the phase shift turns out to depend only on the quantized topological charge due to the cancellation of nonuniversal contributions from the electron and the hole part
Weak localization of the open kicked rotator
We present a numerical calculation of the weak localization peak in the
magnetoconductance for a stroboscopic model of a chaotic quantum dot. The
magnitude of the peak is close to the universal prediction of random-matrix
theory. The width depends on the classical dynamics, but this dependence can be
accounted for by a single parameter: the level curvature around zero magnetic
field of the closed system.Comment: 8 pages, 8 eps figure
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