arXiv subjects

Anders Mathias Lunde

Publications and source records attributed to Anders Mathias Lunde.

13 recordsLinked to original sources

arXiv2018

Strain-enhanced optical absorbance of topological insulator films

Topological insulator films are promising materials for optoelectronics due to a strong optical absorption and a thickness dependent band gap of the topological surface states. They are superior candidates for photodetector applications in the THz-infrared spectrum, with a potential performance higher than graphene. Using a first-principles $k\cdot p$ Hamiltonian, incorporating all symmetry-allowed terms to second order in the wave vector $k$, first order in the strain $ε$ and of order $εk$, we demonstrate significantly improved optoelectronic performance due to strain. For Bi$_2$Se$_3$ films of variable thickness, the surface state band gap, and thereby the optical absorption, can be effectively tuned by application of uniaxial strain, $ε_{zz}$, leading to a divergent band edge absorbance for $ε_{zz}\gtrsim 6\%$. Shear strain breaks the crystal symmetry and leads to an absorbance varying significantly with polarization direction. Remarkably, the directional average of the absorbance always increases with strain, independent of material parameters.

cond-mat.mes-hall↗

arXiv2018

Symmetry analysis of strain, electric and magnetic fields in the $\text{Bi}_2\text{Se}_3$-class of topological insulators

Based on group theoretical arguments we derive the most general Hamiltonian for the $\text{Bi}_2\text{Se}_3$-class of materials including terms to third order in the wave vector, first order in electric and magnetic fields, first order in strain and first order in both strain and wave vector. We determine analytically the effects of strain on the electronic structure of $\text{Bi}_2\text{Se}_3$. For the most experimentally relevant surface termination we analytically derive the surface state spectrum, revealing an anisotropic Dirac cone with elliptical constant energy counturs giving rise to different velocities in different in-plane directions. The spin-momentum locking of strained $\text{Bi}_2\text{Se}_3$ is shown to be modified and for some strain configurations we see a non-zero spin component perpendicular to the surface. Hence, strain control can be used to manipulate the spin degree of freedom via the spin-orbit coupling. We show that for a thin film of $\text{Bi}_2\text{Se}_3$ the surface state band gap induced by coupling between the opposite surfaces changes opposite to the bulk band gap under strain. Tuning the surface state band gap by strain, gives new possibilities for the experimental investigation of the thickness dependent gap and optimization of optical properties relevant for, e.g., photodetector and energy harvesting applications. We finally derive analytical expressions for the effective mass tensor of the Bi$_2$Se$_3$ class of materials as a function of strain and electric field.

cond-mat.mtrl-sci↗

arXiv2016

Decoherence of high-energy electrons in weakly disordered quantum Hall edge states

We investigate theoretically the phase coherence of electron transport in edge states of the integer quantum Hall effect at filling factor $ν=2$, in the presence of disorder and inter-edge state Coulomb interaction. Within a Fokker-Planck approach, we calculate analytically the visibility of the Aharonov-Bohm oscillations of the current through an electronic Mach-Zehnder interferometer. In agreement with recent experiments, we find that the visibility is independent of the energy of the current-carrying electrons injected high above the Fermi sea. Instead, it is the amount of disorder at the edge that sets the phase space available for inter-edge state energy exchange and thereby controls the visibility suppression.

cond-mat.mes-hall↗

arXiv2016

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

cond-mat.mes-hall↗

arXiv2016

Statistical theory of relaxation of high energy electrons in quantum Hall edge states

We investigate theoretically the energy exchange between electrons of two co-propagating, out-of-equilibrium edge states with opposite spin polarization in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the edge states locally injects electrons at high energy. Thereby a narrow peak in the energy distribution is created at high energy above the Fermi level. A second downstream quantum dot performs an energy resolved measurement of the electronic distribution function. By varying the distance between the two dots, we are able to follow every step of the energy exchange and relaxation between the edge states - even analytically under certain conditions. In the absence of translational invariance along the edge, e.g. due to the presence of disorder, energy can be exchanged by non-momentum conserving two-particle collisions. For weakly broken translational invariance, we show that the relaxation is described by coupled Fokker-Planck equations. From these we find that relaxation of the injected electrons can be understood statistically as a generalized drift-diffusion process in energy space for which we determine the drift-velocity and the dynamical diffusion parameter. Finally, we provide a physically appealing picture in terms of individual edge state heating as a result of the relaxation of the injected electrons.

cond-mat.mes-hall↗

arXiv2013

Hyperfine interactions in two-dimensional HgTe topological insulators

We study the hyperfine interaction between the nuclear spins and the electrons in a HgTe quantum well, which is the prime experimentally realized example of a two-dimensional topological insulator. The hyperfine interaction is a naturally present, internal source of broken time-reversal symmetry from the point of view of the electrons. The HgTe quantum well is described by the so-called Bernevig-Hughes-Zhang (BHZ) model. The basis states of the BHZ model are combinations of both S- and P-like symmetry states, which means that three kinds of hyperfine interactions play a role: (i) The Fermi contact interaction, (ii) the dipole-dipole like coupling and (iii) the electron orbital to nuclear-spin coupling. We provide benchmark results for the forms and magnitudes of these hyperfine interactions within the BHZ model, which give a good starting point for evaluating hyperfine interactions in any HgTe nanostructure. We apply our results to the helical edge states of a HgTe two-dimensional topological insulator and show how their total hyperfine interaction becomes anisotropic and dependent on the orientation of the sample edge within the plane. Moreover, for the helical edge states the hyperfine interactions due to the P-like states can dominate over the S-like contribution in certain circumstances.

cond-mat.mes-hall↗

arXiv2013

Temperature-dependent dynamical nuclear polarization bistabilities in double quantum dots in the spin-blockade regime

The interplay of dynamical nuclear polarization (DNP) and leakage current through a double quantum dot in the spin-blockade regime is analyzed. A finite DNP is built up due to a competition between hyperfine (HF) spin-flip transitions and another inelastic escape mechanism from the triplets, which block transport. We focus on the temperature dependence of the DNP for zero energy-detuning (i.e. equal electrostatic energy of one electron in each dot and a singlet in the right dot). Our main result is the existence of a transition temperature, below which the DNP is bistable, so a hysteretic leakage current versus external magnetic field B appears. This is studied in two cases: (i) Close to the crossing of the three triplet energy levels near B=0, where spin-blockade is lifted due to the inhomogeneity of the effective magnetic field from the nuclei. (ii) At higher B-fields, where the two spin-polarized triplets simultaneously cross two different singlet energy levels. We develop simplified models leading to different transition temperatures T_TT and T_ST for the crossing of the triplet levels and the singlet-triplet level crossings, respectively. We find T_TT analytically to be given solely by the HF couplings, whereas T_ST depends on various parameters and T_ST>T_TT. The key idea behind the existence of the transition temperatures at zero energy-detuning is the suppression of energy absorption compared to emission in the inelastic HF transitions. Finally, by comparing the rate equation results with Monte Carlo simulations, we discuss the importance of having both HF interaction and another escape mechanism from the triplets to induce a finite DNP.

cond-mat.mes-hall↗

arXiv2012

Helical edge states coupled to a spin bath: Current-induced magnetization

We study current carrying helical edge states in a two-dimensional topological insulator coupled to an environment of localized spins, i.e. a spin bath. The localized spins mediate elastic spin-flip scattering between the helical edge states, and we show how this induces a spin-bath magnetization for a finite current through the edge states. The magnetization appears near the boundaries of the topological insulator, while the bulk remains unmagnetized, and it reaches its maximal value in the high bias regime. Furthermore, the helical edge states remain ballistic in steady state, if no additional spin-flip mechanisms for the localized spins are present. However, we demonstrate that if such mechanisms are allowed, then these will induce a finite current decrease from the ballistic value.

cond-mat.mes-hall↗

arXiv2009

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..

cond-mat.mes-hall↗

arXiv2007

Electron-electron interaction effects in quantum point contacts

We consider interaction effects in quantum point contacts on the first quantization plateau, taking into account all non momentum-conserving processes. We compute low-temperature linear and non-linear conductance, shot noise, and thermopower by perturbation theory, and show that they are consistent with experimental observations on the so-called "0.7 anomaly". The full temperature-dependent conductance is obtained from self-consistent second-order perturbation theory and approaches ~ e^2/h at higher temperatures, but still smaller than the Fermi temperature.

cond-mat.mes-hall↗

arXiv2007

Three-particle collisions in quantum wires: Corrections to thermopower and conductance

We consider the effect of electron-electron interaction on the electron transport through a finite length single-mode quantum wire with reflectionless contacts. The two-particle scattering events cannot alter the electric current and therefore we study the effect of three-particle collisions. Within the Boltzmann equation framework, we calculate corrections to the thermopower and conductance to the leading order in the interaction and in the length of wire $L$. We check explicitly that the three-particle collision rate is identically zero in the case of several integrable interaction potentials. In the general (non-integrable) case, we find a positive contribution to the thermopower to leading order in $L$. The processes giving rise to the correction involve electron states deep in the Fermi sea. Therefore the correction follows an activation law with the characteristic energy of the order of the Fermi energy for the electrons in the wire.

cond-mat.mes-hall↗

arXiv2006

Interaction-Induced Resonance in Conductance and Thermopower of Quantum Wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multi-channel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away; the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, four-fold splitting of the resonance in a magnetic field provides a unique signature of the effect.

cond-mat.mes-hall↗

arXiv2005

On the Mott formula for thermopower of non-interactions electrons in quantum point contacts

We calculate the linear response thermopower S of a quantum point contact using the Landauer formula and therefore assume non-interacting electrons. The purpose of the paper, is to compare analytically and numerically the linear thermopower S of non-interacting electrons to the low temperature approximation, S^1=(pi^2/3e)k^2 T d(ln G(mu,T=0))/dmu, and the so-called Mott expression, S^M=(pi^2/3e)k^2 T d(ln G(mu,T))/dmu, where G(mu,T) is the (temperature dependent) conductance. This comparison is important, since the Mott formula is often used to detect deviations from single-particle behavior in the thermopower of a point contact.

cond-mat.mes-hall↗