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.Comment: To be published in Journal of Physics: Condensed Matter (7 pages, 2 figures.

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.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm

Symmetry analysis of strain, electric and magnetic fields in the Bi2Se3\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

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..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio

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.Comment: 21 pages (main text 11 pages), 11 figure

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.Comment: 26 pages, 17 figure

Intershell resistance in multiwall carbon nanotubes: A Coulomb drag study

We calculate the intershell resistance R_{21} in a multiwall carbon nanotube as a function of temperature T and Fermi level (e.g. a gate voltage), varying the chirality of the inner and outer tubes. This is done in a so-called Coulomb drag setup, where a current I_1 in one shell induces a voltage drop V_2 in another shell by the screened Coulomb interaction between the shells neglecting the intershell tunnelling. We provide benchmark results for R_{21}=V_2/I_1 within the Fermi liquid theory using Boltzmann equations. The band structure gives rise to strongly chirality dependent suppression effects for the Coulomb drag between different tubes due to selection rules combined with mismatching of wave vector and crystal angular momentum conservation near the Fermi level. This gives rise to orders of magnitude changes in R_{21} and even the sign of R_{21} can change depending on the chirality of the inner and outer tube and misalignment of inner and outer tube Fermi levels. However for any tube combination, we predict a dip (or peak) in R_{21} as a function of gate voltage, since R_{21} vanishes at the electron-hole symmetry point. As a byproduct, we classified all metallic tubes into either zigzag-like or armchair-like, which have two different non-zero crystal angular momenta m_a, m_b and only zero angular momentum, respectively.Comment: 17 pages, 10 figure

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.Comment: 13 pages, 4 figure

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570