ICTS

The Kohn-Sham density functional theory is an essential tool for treating complex systems of interacting electrons spanning the disciplines of physics, chemistry, materials science and biology. Surprisingly little work has been done, however, in applying this approach to one of the most remarkable manifestations of interelectron interactions, namely the fractional quantum Hall effect, wherein the Coulomb interaction produces, through a non-perturbative reorganization, fractional quantization of the Hall resistance and fractionally charged particles that are neither fermions obeying fractional statistics. I will present a Kohn-Sham formulation for the fractional quantum Hall effect [1] by mapping the original electron problem into a reference problem of non-interacting composite fermions, which are emergent particles formed from the binding of electrons and quantum vortices, and which experience a density dependent magnetic field. Self-consistent solutions demonstrate that this formulation not only captures fractional quantum Hall states with non-uniform densities, but also topological properties such as fractional charge and fractional statistics. This should enable an accurate and realistic modeling of edge states as well as of mesoscopic geometries designed to measure fractional charge and fractional statistics [1] Yayun Hu and J. K. Jain, unpublished

Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on details of the measured system. Among them the electrical Hall conductance, which is expressed in units of e2/h, is easiest to probe. In the fractional quantum Hall effect regime, fractional quantized values of the electrical Hall conductance attest to topologically ordered states, which are states that carry quasi-particles with fractional charge and (expected) anyonic statistics. Another topological invariant, which is much harder to measure, is the thermal Hall conductance, KT, expressed in units of κ0T=(π2kB2/3h)T. In 1D transport it does not depend on the particles charge, particles exchange statistics, and is even insensitive to the interaction strength among the particles. A fractional value of the quantized thermal Hall conductance shows that the probed state of matter is non-abelian. Quasiparticles in nonabelian states may be useful for topological quantum computation. In this talk, I will report our measurements of the thermal Hall conductance of the v=5/2 state to be fractional, implying non-abelian nature of the state.

Thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized non-integer value kappa=5/2, which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict kappa=3/2 or 7/2. I will briefly review the contradictory experimental and theoretical findings and discuss how they may be reconciled. Specifically, I will describe a possible resolution based on disorder-induced formation of mesoscopic puddles. Interactions between these puddles can generate a coherent macroscopic state that exhibits a plateau with quantized kappa=5/2 and non-Abelian quasiparticles that are distinct from those of the microscopic puddles.

We experimentally investigate electron-electron interaction effects in quantum Hall edge states using a combination of an energy selective electron injector and an energy selective electron detector. The quantum Hall edge is realized in the two-dimensional electron gas of a Ga[Al]As heterostructure by patterned surface gates, which deplete the electron gas below them and thereby form the edge of the two-dimensional system. Both, electron injector and detector, are quantum dots in the Coulomb blockade regime, for which only a single addition energy level is relevant. While the injector quantum dot allows us to inject single non-equilibrium electrons at a well-known energy into the quantum Hall edge, the detector quantum dot allows us to independently probe the edge channel occupation function at a distance of two micrometers from the injector with high energy resolution. Interaction effects are observed in this setting in various ways. For example, tunneling of an electron from a dot into the edge channel leads to a Fermi-edge singularity. Beyond that, the traveling non-equilibrium electron creates electron-hole pairs on its way to the detector leading to a shake-up of the equilibrium population of states. The resulting non-equilibrium distribution observed with the detector contains single-electron and single-hole excitations. Our detection scheme also allows us, thanks to the long-range nature of the Coulomb interaction, to observe interaction processes between electrons separated by large distances. The experimental data will be complemented by a theoretical model that captures many of the experimental observations.

A novel electron spectrometer, devised in the Ensslin/Ihn research groups at the ETH Zürich, allows to analyze charge transfer processes caused solely by energetic relaxation of the device’s electronic system. The spectrometer, in which two quantum dots couple to a two-dimensional electron gas, reveals several transfer processes with distinct energetic signatures. Surprisingly, transfer is measured at energies exceeding the energy of originally injected electrons. Taking into account both tunneling as well as interactions within and between the setup’s individual components, a non-equilibrium diagrammatic approach allows us to assign a series of diagrams to these transfer processes, and to thereby pinpoint their physical origin. Our results indicate that interactions between well-separated edge channels play a more significant role for energy relaxation than commonly expected.

We develop a theory for the thermal Hall effect in a spin-1/2 system on a strip of Kagome lattice, where a chiral spin-interaction term is present. To this end, we model the Kagome strip as a three-leg XXZ spin-ladder, and use Bosonization to derive a low-energy theory for the spinons in this system. Introducing further a Dzyaloshinskii-Moriya interaction (D) and a tunable magnetic field (B), we identify three distinct B-dependent quantum phases: a valence-bond crystal (VBC), a "metallic" spin liquid (MSL) and a chiral spin liquid (CSL). In the presence of a temperature difference between the top and the bottom edges of the strip, we evaluate the net heat current generated along the strip, and consequently the thermal Hall conductivity. We find that the VBC-MSL-CSL transitions are accompanied by a pronounced change in the behavior of thermal Hall coefficient as a function of B. In particular, analogously to the quantum Hall effect, in the CSL phase the thermal Hall conductivity exhibits a quantized plateau centered around a commensurate value of the spinon 'filling factor' B/D.

2D topological insulators have attracted much attention lately, due to their gapless helical edge modes, which should display maximal charge-spin entanglement and be protected from time-reversal-invariant backscattering at low temperatures. However, significant low-energy backscattering was measured in recent experiments, an observation that has hitherto remained elusive. In this work we study the possible role that may be played by magnetic impurities with spin larger than 1/2, such as the ubiquitous S=5/2 Mn in HgTe. For the first time we treat the case of arbitrary isotropy in the impurity-edge exchange, as well as the self-exchange (local anisotropy) of the impurity. We find the latter may strongly enhance backscattering, not only at low temperatures and voltages (where it can exponentially suppress Kondo screening), but also at relatively high energies. The resulting rich behavior of the current-voltage characteristics and noise may allow experiments to reveal the complex internal structure of the magnetic impurities. In particular, we find that the noise Fano factor may become arbitrarily large, reflecting bunching of large batches of electrons.

Backscattering at a point contact in a quantum Hall setup plays a crucial role in determining transport properties. Here we address hole-conjugate bulk filling factors, focussing on the $\nu=2/3$ case in the presence of edge reconstruction. We identify two symmetries, a continuous $SU(3)$ and a discrete $Z_3$, whose presence or absence (different symmetry scenarios) dictate the behavior of conductance and shot noise in a qualitative way. While recent measurements are consistent with one of these symmetry scenarios, others can be realized in future experiments.

Tunnelling density of states (TDOS) in geometries comprising of junctions of chiral Luttinger liquid formed between different filling fraction of quantum Hall effect is discussed. It is well-known that the TDOS of electron in Luttinger liquid is suppressed in general. In this talk, I will discuss various possibilities of obtaining enhancement in TDOS in superconducting and normal junction of such edge states.

Abstract

Known quantum adiabatic pumps can be split into two classes: those that pump a fixed integer number of quanta each cycle (and are, therefore, noiseless) and those that produce noise. The former ones are robust against small changes in the system parameters, while for the latter the current and its noise are sensitive to the precise shape of the pumping cycle. I will discuss an exotic pump that produces a universal noise. That is, the pumped current, noise (and, in fact, the whole counting statistics) become largely independent of the system parameters in the adiabatic limit. The pump is based on a system of parafermionic zero modes that can be created at fractional quantum Hall edges. I will give an introduction to adiabatic pumps, an introduction to parafermions, and then describe in detail our exotic pump.

We study the effect of introducing a vortex in a second order topological superconductor and show that the flux periodicity changes from φ0 = hc/e to φ0/2 = hc/2e as the corner Majorana states, which are the signatures of the topological superconducting state, mix with the bulk states leading to a crossover to an ordinary superconductor. The measurement of this change in periodicity would be a direct confirmation of the topology change and indirectly of the corner Majorana modes. We also show that the change in periodicity can be tuned by shining light on the superconductor.

An infinite edge of a quantum Hall system prohibits indirect exchange coupling between two spins whereas a quantum spin-Hall edge prohibits out-of-plane coupling. In this study we analyze an unexpected breakdown of this behaviors in a finite system, where the two spins can interact also via a longer path that traverses the whole perimeter of the system. We explain this using an analytical model as well as using tight binding models in real space. Based on this finding, we propose how using a lead far away from the spins can switch the coupling on and off among them non-locally. Based on Phys. Rev. B (R) 99, 121409 (2019).

Our understanding of topological phases and nontrivial boundary physics is heavily influenced by ideas in band theory and hence clean systems. In this talk, I will describe our investigations on how nontrivial topological phases can be realised in amorphous systems. In particular I will illustrate how such systems may be better suited to realise "pristine" boundaries since the bulk inadvertently comprises of localized/gapped states. In this context, I will describe topologically insulating phase and its signatures in Witten effect in electronic glass. I will further point out how Higher-Order Topological Phases with stable corner modes can also be realised in such systems, albeit by retaining the crystalline symmetry at the boundary.