arXiv subjects

E. M. Hankiewicz

Publications and source records attributed to E. M. Hankiewicz.

At least 19 recordsLinked to original sources

arXiv2023

Dissipative Callan-Harvey mechanism in 2+1 D Dirac system: The fate of edge states along a domain wall

The Callan-Harvey mechanism in 2+1 D Jackiw-Rebbi model is revisited. We analyzed Callan-Harvey anomaly inflow in the massive Chern insulator (quantum anomalous Hall system) subject to external electric field. In addition to the conventional current flowing from the bulk to edge due to parity anomaly, we considered the dissipation of the edge charge due to interaction with external bosonic bath in 2+1 D and due to external bath of photons in 3+1 D. In the case of 2+1 D bosonic bath, we found the new stationary state, which is defined by the balance between Callan-Harvey current and the outgoing flow caused by the dissipation processes. In the case of 3+1 D photon bath, we found a critical electric field, below which this balance state can be achieved, but above which there is no such a balance. Furthermore, we estimated the photon-mediated transition rate between 2+1 D bulk and 1+1 D topological edge state of the order of one ns$^{-1}$ (nanosecond) at the room temperature.

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arXiv2020

Temperature and Chemical Potential Dependence of the Parity Anomaly in Quantum Anomalous Hall Insulators

The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a momentum-dependent mass term. Each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. In this work, we analyze the finite temperature Hall conductivity of a single Chern insulator in 2+1 space-time dimensions under the influence of a chemical potential and an out-of-plane magnetic field. At zero magnetic field, this non-dissipative transport coefficient originates from the parity anomaly of planar quantum electrodynamics. We show that the parity anomaly itself is not renormalized by finite temperature effects. However, it induces two terms of different physical origin in the effective action of a Chern insulator, which is proportional to the Hall conductivity. The first term is temperature and chemical potential independent, and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction and valence band states. In particular, we show that the relativistic mass of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic mass enhances these corrections. Moreover, we extend our analysis to finite magnetic fields and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in orbital fields.

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arXiv2020

Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly

Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates the Onsager relation, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with $σ_\mathrm{xy}= -\mathrm{e}^2/\mathrm{h}$ to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.

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arXiv2020

Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly

The Dirac mass of a two-dimensional QAH insulator is directly related to the parity anomaly of planar quantum electrodynamics, as shown initially in Phys. Rev. Lett. 52, 18 (1984). In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. By calculating the effective action, we reveal that the Newtonian mass term acts like a parity-breaking element of a high-energy regularization scheme. As such, it is directly related to the parity anomaly. In addition, the calculation of the effective action allows us to determine the finite frequency correction to the DC Hall conductivity of a QAH insulator. We derive that the leading order AC correction contains a term proportional to the torsional Hall viscosity. This paves the way to measure this non-dissipative transport coefficient via electrical or magneto-optical experiments. Moreover, we prove that the Newtonian mass significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene.

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arXiv2020

Topological Quantum Computing Using Nanowire Devices

The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing. In branched nanowire networks one can exchange Majorana states by time-dependently tuning topologically non-trivial parameter regions. In this work, we simulate the exchange of four Majorana modes in T-shaped junctions made out of p-wave superconducting Rashba wires. We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes. Contrary to the widespread opinion, we show for the first time that in the adiabatic limit the gating time needs to be smaller than the inverse of the squared superconducting order parameter and scales linearly with the gating potential. Further, we show how to circumvent the formation of additional Majorana modes in branched nanowire systems, arising at wire intersection points of narrow junctions. Finally, we propose a multi qubit setup, which allows for universal and in particular topologically protected quantum computing.

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arXiv2017

Josephson junction dynamics in the presence of $2π$- and $4π$-periodic supercurrents

We investigate theoretically the dynamics of a Josephson junction in the framework of the RSJ model. We consider a junction that hosts two supercurrrent contributions: a $2π$- and a $4π$-periodic in phase, with intensities $I_{2π}$ and $I_{4π}$ respectively. We study the size of the Shapiro steps as a function of the ratio of the intensity of the mentioned contributions, i.e. $I_{4π}/I_{2π}$. We provide detailed explanations where to expect clear signatures of the presence of the $4π$-periodic contribution as a function of the external parameters: the intensity AC-bias $I_\text{ac}$ and frequency $ω_\text{ac}$. On the one hand, in the low AC-intensity regime (where $I_\text{ac}$ is much smaller than the critical current, $I_\text{c}$), we find that the non-linear dynamics of the junction allows the observation of only even Shapiro steps even in the unfavorable situation where $I_{4π}/I_{2π}\ll 1$. On the other hand, in the opposite limit ($I_\text{ac}\gg I_\text{c}$), even and odd Shapiro steps are present. Nevertheless, even in this regime, we find signatures of the $4π$-supercurrent in the beating pattern of the even step sizes as a function of $I_\text{ac}$.

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arXiv2016

Observation of the universal magnetoelectric effect in a 3D topological insulator

The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of $e^2 / 2 h c $ per surface. Here, we report on the observation of this so-called topological magnetoelectric (TME) effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semi-transparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant $α= e^2 / \hbar c$ when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

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arXiv2016

Anomalous Spin Response and Virtual-Carrier-Mediated Magnetism in a Topological Insulator

We present a comprehensive theoretical study of the static spin response in HgTe quantum wells, revealing distinctive behavior for the topologically nontrivial inverted structure. Most strikingly, the q=0 (long-wave-length) spin susceptibility of the undoped topological-insulator system is constant and equal to the value found for the gapless Dirac-like structure, whereas the same quantity shows the typical decrease with increasing band gap in the normal-insulator regime. We discuss ramifications for the ordering of localized magnetic moments present in the quantum well, both in the insulating and electron-doped situations. The spin response of edge states is also considered, and we extract effective Lande g-factors for the bulk and edge electrons. The variety of counter-intuitive spin-response properties revealed in our study arises from the system's versatility in accessing situations where the charge-carrier dynamics can be governed by ordinary Schrodinger-type physics, mimics the behavior of chiral Dirac fermions, or reflects the material's symmetry-protected topological order.

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arXiv2015

Conductivity Corrections for Topological Insulators with Spin-Orbit Impurities: A New Hikami-Larkin-Nagaoka Formula

The Hikami-Larkin-Nagaoka (HLN) formula [Prog. Theor. Phys. 63, 707 (1980)] describes the quantum corrections to the magnetoconductivity of a quasi-2D electron gas (quasi-2DEG) with parabolic dispersion. It predicts a crossover from weak localization to antilocalization as a function of the strength of scattering off spin-orbit impurities. Here, we derive the conductivity correction for massless Dirac fermions in 3D topological insulators (TIs) in the presence of spin-orbit impurities. We show that this correction is always positive and therefore we predict weak antilocalization for every value of the spin-orbit disorder. Furthermore, the correction to the diffusion constant is surprisingly linear in the strength of the impurity spin-orbit. Our results call for a reinterpretation of experimental fits for the magnetoconductivity of 3D TIs which have so far used the standard HLN formula.

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arXiv2015

Magneto-optics of massive Dirac fermions in bulk Bi2Se3

We report on magneto-optical studies of Bi2Se3, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parameters: the fundamental bandgap and the band velocity. In a magnetic field, this model implies a unique property - spin splitting equal to twice the cyclotron energy: Es = 2Ec. This explains the extensive magneto-transport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The Es = 2Ec match differentiates the massive Dirac electrons in bulk Bi2Se3 from those in quantum electrodynamics, for which Es = Ec always holds.

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arXiv2015

Superconducting quantum spin-Hall systems with giant orbital g-factors

Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. We examine hybrid QSHS/superconductor structures in an external magnetic field and predict a gapless superconducting state with protected edge modes. It originates entirely from the orbital magnetic-field effect caused by the locking of the electron spin to the momentum of the superconducting condensate flow. We show that such spin-momentum locking can generate a giant orbital g-factor of order of several hundreds, allowing one to achieve significant spin polarization in the QSHS in the fields well below the critical field of the superconducting material. We propose a three-terminal setup in which the spin-polarized edge superconductivity can be probed by Andreev reflection, leading to unusual transport characteristics: a non-monotonic excess current and a zero-bias conductance splitting in the absence of the Zeeman interaction.

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arXiv2015

Quantum interference of edge supercurrents in a two-dimensional topological insulator

Josephson weak links made of two-dimensional topological insulators (TIs) exhibit magnetic oscillations of the supercurrent that are reminiscent of those in superconducting quantum interference devices (SQUIDs). We propose a microscopic theory of this effect that goes beyond the approaches based on the standard SQUID theory. For long junctions we find a temperature-driven crossover from Phi_0-periodic SQUID-like oscillations to a 2 Phi_0-quasiperiodic interference pattern with different peaks at even and odd values of the magnetic flux quantum Phi_0=ch/2e. This behavior is absent in short junctions where the main interference signal occurs at zero magnetic field. Both types of interference patterns reveal gapless (protected) Andreev bound states. We show, however, that the usual sawtooth current-flux relationship is profoundly modified by a Doppler-like effect of the shielding current which has been overlooked previously. Our findings may explain recently observed even-odd interference patterns in InAs/GaSb-based TI Josephson junctions and uncover unexplored operation regimes of nano-SQUIDs.

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arXiv2014

Voltage Induced Dynamical Quantum Phase Transitions in Exciton Condensates

We explore non-analytic quantum phase dynamics of dipolar exciton condensates formed in a system of 1D quantum layers subjected to voltage quenches. We map the exciton condensate physics on to the pseudospin ferromagnet model showing an additional oscillatory metastable and paramagnetic phase beyond the well-known ferromagnetic phase by utilizing a time-dependent, non-perturbative theoretical model. We explain the coherent phase of the exciton condensate in quantum Hall bilayers, observed for currents equal to and slightly larger than the critical current, as a stable time-dependent phase characterized by persistent charged meron flow in each of the individual layers with a characteristic AC Josephson frequency. As the magnitude of the voltage quench is further increased, we find that the time-dependent current oscillations associated with the charged meron flow decay, resulting in a transient pseudospin paramagnet phase characterized by partially coherent charge transfer between layers, before the state relaxes to incoherent charge transfer between the layers.

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arXiv2013

Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions

Currently, much effort is being put into detecting unconventional p-wave superconductivity in Josephson junctions based on topological insulators (TIs). For that purpose we propose to use superconducting Klein tunneling, i.e. the reflectionless passage of Cooper pairs through a potential barrier in a gated ballistic junction. This phenomenon occurs due to the fact that the supercurrent is carried by helical Andreev bound states (ABSs) characterized by spin-momentum locking similar to the normal-state carriers. We derive the spectrum of the helical ABSs and the corresponding Josephson current for a junction made on the surface of a three-dimensional TI. The superconducting Klein tunneling is predicted to yield a non-sinusoidal current-phase relation and an anomalous critical current $I_c$ that does not vanish with increasing barrier strength. We also analyze the dependence of the I_cR_n product (where R_n is the normal-state junction resistance) on the microscopic parameters of the superconductor/TI interface, which leads to lower I_cR_n values than expected from previous models of the proximity-effect Josephson junctions.

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arXiv2013

Anomalous spin precession and spin Hall effect in semiconductor quantum wells

Spin-orbit (SO) interactions give a spin-dependent correction r_so to the position operator, referred to as the anomalous position operator. We study the contributions of r_so to the spin-Hall effect (SHE) in quasi two-dimensional (2D) semiconductor quantum wells with strong band structure SO interactions that cause spin precession. The skew scattering and side-jump scattering terms in the SHE vanish, but we identify two additional terms in the SHE, due to r_so, which have not been considered in the literature so far. One term reflects the modification of the spin precession due to the action of the external electric field (the field drives the current in the quantum well), which produces, via r_so, an effective magnetic field perpendicular to the plane of the quantum well. The other term reflects a similar modification of the spin precession due to the action of the electric field created by random impurities, and appears in a careful formulation of the Born approximation. We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order. In electron systems with weak momentum scattering, the contribution of the anomalous spin precession due to the external electric field equals 1/2 the usual side-jump SHE, while the additional impurity-dependent contribution depends on the form of the band structure SO coupling. For band structure SO linear in wave vector the two additional contributions cancel. For band structure SO cubic in wave vector only the contribution due to external electric field is present, and can be detected through its density dependence. In 2D hole systems both anomalous spin precession contributions vanish identically.

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arXiv2013

One-dimensional weak antilocalization and band Berry phases in HgTe wires

We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells (QWs) with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL signal in wires with normal band ordering is an order of magnitude smaller than for inverted ones. These observations are attributed to a Dirac-like topology of the energy bands in HgTe QWs. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a non-universal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.

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arXiv2013

Proposal for an all-electrical measurement of crossed Andreev reflection in topological insulators

Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator (QSHI) - superconductor (SC) - QSHI junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a 5-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.

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arXiv2012

Spin-helical transport in normal and superconducting topological insulators

In a topological insulator (TI) the character of electron transport varies from insulating in the interior of the material to metallic near its surface. Unlike, however, ordinary metals, conducting surface states in TIs are topologically protected and characterized by spin helicity whereby the direction of the electron spin is locked to the momentum direction. In this paper we review selected topics regarding recent theoretical and experimental work on electron transport and related phenomena in two-dimensional (2D) and three-dimensional (3D) TIs. The review provides a focused introductory discussion of the quantum spin Hall effect in HgTe quantum wells as well as transport properties of 3DTIs such as surface weak antilocalization, the half-integer quantum Hall effect, s + p-wave induced superconductivity, superconducting Klein tunneling, topological Andreev bound states and related Majorana midgap states. These properties of TIs are of practical interest, guiding the search for the routes towards topological spin electronics.

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