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Monday, 10 June 2019
Time Speaker Title Resources
09:15 to 10:30 Ganpathy Murthy Introduction to integer quantum Hall effect
10:30 to 11:30 Jainendra Jain Kohn Sham theory of the fractional quantum Hall effect

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of mesoscopic geometries designed to measure fractional charge and fractional statistics [1] Yayun Hu and J. K. Jain, unpublished

11:30 to 12:00 Tea/coffee Break
12:00 to 13:00 Mitali Banerjee Quantization of heat flow in the fractional quantum Hall regime

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.

13:00 to 14:15 Break Lunch
15:00 to 16:00 David Mross Theory of disorder-induced half-integer thermal Hall conductance

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.

16:00 to 16:15 Break Tea/coffee
16:15 to 17:15 Ganpathy Murthy A Tale of Two Reconstructions

Reconstructions at integer quantum Hall edges as the edge potential is made smoother have been known since the 90's. Earlier work concentrated on reconstructions preserving the translation symmetry along the edge, and found either the generation of new pairs of modes (Chamon-Wen) or the separation of previously coincident modes (Dempsey-Gelfand-Halperin). Later it was realized that the energy could be lowered by spontaneously breaking the translation symmetry along the edge, sometimes in conjunction with the breaking of spin-rotation invariance as well. I will illustrate these ideas with two examples. The first is the nu=2 edge, which spontaneously breaks translation invariance along the edge for very shallow edge potentials. The second is an edge between a singlet nu=4 and a fully polarized nu=3, which spontaneously breaks spin-rotations.

Tuesday, 11 June 2019
Time Speaker Title Resources
09:00 to 10:15 Yuval Gefen Introduction to Edge Physics of the Quantum Hall Effect: A subjective point of view.
10:15 to 10:45 Break Tea/coffee
10:45 to 12:00 Jainendra Jain Introduction to fractional quantum Hall effect
12:00 to 14:15 Break Lunch
14:30 to 15:30 Mandar Deshmukh Tunable symmetries and Berry’s phase in trilayer graphene probed using quantum Hall transport

There is an increasing interest in the electronic properties of few-layer graphene as it offers an incredibly rich and tunable system -- the dispersion of bands can be tuned with number and stacking of layers in combination with an electric field. Bernal (ABA) stacked trilayer graphene (TLG) is the simplest system that hosts both Dirac-like massless linear bands and massive quadratic bands. Interplay between multiple bands and different competing symmetries give rise to a variety of quantum phenomena. Here, we will talk about our recent studies on very high mobility (~500,000 cm2V-1s-1) ABA-trilayer graphene samples in quantum Hall regime.

First, we study the effect of the trigonal warping which despite being small in magnitude, has important effects on the low energy physics of few-layer graphene. In presence of a magnetic field, it leads to a selection rule for the coupling between different Landau levels. In particular, we observe anti-crossings between some LLs, which result from the breaking of the continuous rotational symmetry to C3 symmetry by the trigonal warping. Our experiment provides smoking-gun evidence for the trigonal warping of the low energy bands. [1]

Second, we study the consequence of the non-uniform charge distribution in the ABA-stacked TLG. It is theoretically predicted that the charge distribution on the three layers of the ABA-stacked TLG can be non-uniform and this has an important effect on the substructure of the lowest Landau level. In particular, the sequence of the zeroth Landau levels between filling factors -6 to 6 in ABA-stacked trilayer graphene depends sensitively on this non-uniform charge distribution. Using the sensitivity of quantum Hall data on the electric field and magnetic field, we quantitatively estimate the non-uniformity of the electric field and determine the sequence of the zeroth LLs. [1]

Third, we will discuss about the existence of a new quantum oscillation phase shift in multiband systems. In particular, we observe that Shubnikov-de Haas (SdH) oscillation of the quadratic band in ABA-trilayer graphene is shifted by a phase that sharply departs from the expected 2π Berry's phase and is inherited from the non-trivial Berry's phase of the linear band. Our analysis reveals that this happens due to the simultaneous filling of both the bands -- required by the uniform Fermi energy. Moreover, we measure a continuous gate tuning of the extracted phase from π to – π across the weakly gapped linear Dirac band. Given that many topological materials contain multiple bands, our work indicates how additional bands, which are thought to obscure the analysis, can actually be exploited to tease out the effect of often subtle quantum mechanical geometric phases. [2]

[1] Biswajit Datta, et al. Physical Review Letters  121, 056801 (2018)

[2] Biswajit Datta et al. arXiv:1902.04264   (2019).

15:30 to 15:45 Break Tea/coffee
15:45 to 16:45 Arindam Ghosh Electrical properties of quantum states at the boundary of graphene

The zigzag (ZZ) edge of both single and bilayer graphene is a perfect one dimensional (1D) conductor due to a set of zero energy gapless states that are topologically protected against backscattering. Competing effects of edge topology and electron-electron interaction in these channels have been probed with scanning probe microscopy, which reveals unique local thermodynamic and magnetic properties. Direct evidence of edge-bound electrical conduction, however, has remained largely elusive, primarily due to the lack of graphitic nanostructures with low structural and/or chemical edge disorder, as well as a clear understanding of the impact of edge disorder and confinement on electrical transport. In this talk I shall present experimental protocols to access pure edge transport in single and bilayer graphene, and unique electrical characteristics of such states. Using a new method to observe ballistic edge-mode transport in suspended atomic-scale constrictions of single and multilayer graphene, created during nanomechanical exfoliation of graphite, we observe quantization of conductance close to multiples of e2/h even at room temperature [1]. On the other hand, electrical transport in gapped bilayer graphene was found to occur through a set of purely one-dimensional states at the edge that are strongly localized in nature [2]. I shall highlight several unconventional features of these localized states. [1] A. Kinikar, T. P. Sai, S. Bhattacharyya, A. Agarwala, T. Biswas, S. Sarker, H. R. Krishnamurthy, M. Jain, V. Shenoy, A. Ghosh, Nature Nanotechnology (2017) doi:10.1038/nnano.2017.24. [2] M. A. Aamir, P. Karnatak, A. Jayaraman, T. P. Sai, T. V. Ramakrishnan, R. Sensarma, and A. Ghosh Phys. Rev. Lett. 121, 136806 (2018).

18:00 to 23:00 Poster session Poster session + Conference dinner
Wednesday, 12 June 2019
Time Speaker Title Resources
09:15 to 10:15 Anindya Das Universal quantized thermal conductance in graphene

In the last one decade, graphene, a single carbon atomic layer, has emerged as an ideal platform to experimentally verify many theoretical predictions in condensed matter physics. Among these predictions, two of the most remarkable ones are the quantization of electrical and thermal conductance. Although the quantization of electrical Hall conductance (in units of the quantum limit e2/h) has been observed in graphene, the demonstration of quantization of thermal conductance in terms of its quantum limit [endif]-->) remains challenging due to the requirement of accurate measurement of verysmall temperature (few millikelvin) change. The quantum limit of thermal conductance has been demonstrated recently in GaAs-AlGaAs heterostructures but its measurement in graphene-based QH will open a new path to study the spontaneously symmetry-broken phases predicted to exist near the Dirac point, which can be directly identified by the thermal conductance measurements. Motivated by this we have carried out the thermal conductance measurement in the integer as well as fractional QH regime of hexagonal boron nitride (hBN) encapsulated monolayer graphene devices by sensitive noise thermometry setup with an accuracy of ~2 mK temperature change. We have measured the thermal conductance for integer n = 1, 2 and 6 plateaus and its values agree with the quantum limit within 5% error. We further show that the measured thermal conductance values for fractional plateau n = 4/3 and integer plateau n = 2 are same, emphasizing the universality of flow of information irrespective of the nature of quasi-particle. These thermal transport measurements in graphene QH will pave the way to get new insight into exotic systems like even denominator QH fractions in bilayer graphene as well as symmetry protected quantum spin Hall state in graphene.

10:15 to 11:15 Thomas Ihn Energy-selective detection of edge channel shake-up caused by single-electron tunneling

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.

11:15 to 11:45 Break Tea/coffee
11:45 to 12:45 Stefan Fischer Interaction-induced charge transfer in a mesoscopic electron spectrometer

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.

12:45 to 14:15 Break Lunch
15:00 to 16:00 Efrat Shimshoni Quantum Thermal Hall Effect of Chiral Spinons in a Kagome Strip

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.

16:00 to 16:15 Break Tea/coffee
16:15 to 17:15 Moshe Goldstein Large-Spin Magnetic Impurity near a 2D Topological Edge

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.

Thursday, 13 June 2019
Time Speaker Title Resources
09:15 to 10:15 Herbert A. Fertig RKKY Interactions on Dirac Surfaces

Conduction electrons mediate indirect spin-exchange interactions between dilute magnetic degrees of freedom hosted by impurities or lattice defects. This mechanism, first identified by Ruderman, Kittel, Kasuya, and Yosida (RKKY), can endow otherwise non-magnetic metals with ferromagnetism or other magnetic ground states. More recently, the possibility of controlling magnetic interactions using two-dimensional materials in which electrons are governed by a Dirac equation ("Dirac surfaces") has been explored. We review how this plays out in a basic such system, graphene, and discuss how they can be further controlled by the introduction of an effective magnetic field when the lattice is subject to strain. We then consider related Dirac surfaces hosted by topological insulators. A particularly interesting example, topological crystalline insulators, hosts a variety of ferromagnetic ground states, which in principle can be controlled by a gate potential. Finally, we show that the form of RKKY interactions on Dirac surfaces leads to an "emergent" long-range interaction among spin-gradients, and discuss the implications of this for domain wall excitations of the system.

10:15 to 11:15 Bernd Rosenow Conductance quantization and noise on the plateau: the role of a continuous and a discrete symmetry

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.

11:15 to 11:45 Break Tea/coffee
11:45 to 12:45 Sourin Das Tunnelling density of states in chiral Luttinger liquids

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.

12:45 to 14:15 Break Lunch
15:00 to 16:00 Marc Röösli Time-resolved tunneling between Landau levels in a weakly coupled quantum dot in the integer and fractional quantum Hall regimes
16:00 to 16:15 Break Tea/coffee
16:15 to 17:15 Kyrylo Snizhko Universal quantum noise in adiabatic pumping

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.

Friday, 14 June 2019
Time Speaker Title Resources
09:15 to 10:15 Diptiman Sen Generating a second-order topological insulator with multiple corner states by periodic driving

We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and non-topological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a non-topological phase which has modes localized on only two of the four edges of a finite-sized square. When an appropriate term is added, the edge modes get gapped and gapless states appear at the four corners of a square. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss how the system can be characterized by topological invariants such as the Chern number and a winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at both the time-reversal invariant momenta and other momenta which have no special symmetries.

10:15 to 11:15 Sumathi Rao Flux periodicity crossover in higher order topological superconductors

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.

11:15 to 11:45 Break Tea/coffee
11:45 to 12:45 Arijit Kundu Spin-spin cooupling in finite geometry helical edge

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).

12:45 to 14:15 Break Lunch
14:30 to 15:30 Adhip Agarwala Topological phases in electronic glasses

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.

15:30 to 15:45 Break Tea/coffee