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We propose a Corbino-disk geometry of a graphene membrane under out-of-plane strain deformations as a convenient path to detect pseudo-magnetic and electric fields via electronic transport. The three-fold symmetric pseudo-magnetic field changes sign six times as function of angle, leading to snake states connecting the inner and outer contacts and to nearly quantized transport. For dynamical strain obtained upon AC gating, the system supports an AC pseudo-electric field which, in the presence of the pseudo-magnetic field, produces a net electronic charge current in the absence of an external voltage, via a pseudo-Hall effect.
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We have measured the diffusion thermopower of a quantum Hall system in a Corbino setup. A concentric electron-temperature gradient is introduced by irradiating microwaves, via a coplanar waveguide, near the outer rim of a circular mesa of a two-dimensional electron gas. The resulting radial thermovoltages exhibit sawtooth-like oscillations with the magnetic field, taking large positive (negative) values just below (above) integer fillings with sign reversal at the center of the quantum Hall plateaus. The behavior is in agreement with a recent theory [Y. Barlas and K. Yang: Phys. Rev. B 85 (2012) 195107], which treats disorder within the self-consistent Born approximation.
Electrons in low-temperature solids are governed by the non-relativistic Schr$ddot{o}$dinger equation, since the electron velocities are much slower than the speed of light. Remarkably, the low-energy quasi-particles given by electrons in various materials can behave as relativistic Dirac/Weyl fermions that obey the relativistic Dirac/Weyl equation. We refer to these materials as Dirac/Weyl materials, which provide a tunable platform to test relativistic quantum phenomena in table-top experiments. More interestingly, different types of physical fields in these Weyl/Dirac materials, such as magnetic fluctuations, lattice vibration, strain, and material inhomogeneity, can couple to the relativistic quasi-particles in a similar way as the $U(1)$ gauge coupling. As these fields do not have gauge-invariant dynamics in general, we refer to them as pseudo-gauge fields. In this chapter, we overview the concept and physical consequences of pseudo-gauge fields in Weyl/Dirac materials. In particular, we will demonstrate that pseudo-gauge fields can provide a unified understanding of a variety of physical phenomena, including chiral zero modes inside a magnetic vortex core of magnetic Weyl semimetals, a giant current response at magnetic resonance in magnetic topological insulators, and piezo-electromagnetic response in time-reversal invariant systems. These phenomena are deeply related to various concepts in high-energy physics, such as chiral anomaly and axion electrodynamics.
Using the Onsager relation between electric and heat transport coefficients, and considering the very different roles played by the quantum Hall condensate and quasiparticles in transport, we argue that near the center of a quantum Hall plateau thermopower in a Corbino geometry measures {it entropy per quasiparticle per quasiparticle charge}. This relation indicates that thermopower measurement in a Corbino setup is a more direct measure of quasiparticle entropy than in a Hall bar. Treating disorder within the self-consistent Born approximation, we show through an explicit microscopic calculation that this relation holds on an integer quantum Hall plateau at low temperatures. Applying this to non-Abelian quantum Hall states, we argue that Corbino thermopower at sufficiently low temperature becomes temperature-independent, and measures the quantum dimension of non-Abelian quasiparticles that determines the topological entropy they carry.
A phase from an adiabatic exchange of Majorana bound states (MBS) reveals their exotic anyonic nature. For detecting this exchange phase, we propose an experimental setup consisting of a Corbino-geometry Josephson junction on the surface of a topological insulator, in which two MBS at zero energy can be created and rotated. We find that if a metallic tip is weakly coupled to a point on the junction, the time-averaged differential conductance of the tip-Majorana coupling shows peaks at the tip voltages $eV = pm (alpha - 2pi l) hbar/ T_J$, where $alpha = pi/2$ is the exchange phase of the two circulating MBS, $T_J$ is the half rotation time of MBS, and $l$ an integer. This result constitutes a clear experimental signature of Majorana fermion exchange.
The detailed analytical and numerical analysis of the electron spectrum, persistent currents, and their densities for an annulus placed in a constant magnetic field (Corbino disk geometry) is presented. We calculate the current density profiles and study their dependence on the inner and outer radii of the annular. We study evolution of the persistent currents and track their emergence and decay for different limiting cases of such a geometry, starting from a nanodot and ending by a macroscopic circle. Our analytical results for the currents are confirmed by the agreement between the integration of the corresponding current densities and the application of the Byers-Yang formula, when it is applicable. Among other results we find the general expression for the persistent current in a narrow annulus, which in the one channel approximation reproduces the well-known result for quasi-one dimensional mesoscopic metallic ring. Moreover it allows to analyze the multi-channel case of a relatively wide annulus. Our study can be used for more accurate treatment and interpretation of the experimental data with measurements of the persistent currents in different doubly-connected systems.
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