Financial Support
Junior participants can avail of financial support for travel and accommodation. If you wish to make use of this, please say so in the comments section of the registration form.
Finding us
The Institute is located at
10 Burlington Road
Number 10 Burlington Road, Dublin 4 ( GPS +53° 19′ 53.08″, 6° 14′ 45.08″ )( Loc8:NN515W23 )
Accommodation details
There are several hotels and guesthouses in close proximity to DIAS.
http://www.waterloolodge.com/
http://www.baggotcourt.com/
http://www.waterloohouse.ie/
http://www.pembroketownhouse.ie/
http://www.mespilhotel.com/
Prices in Dublin 4 tend to be slightly above average however. You may also like to try the following websites:
http://www.booking.com/city/ie/dublin.html
http://www.irelandhotels.com/hotels/ireland/dublin
Please contact us if you need any help.
Hans Benjamin Braun: Topological effects in nanoscale magnetism
Recent years have seen increased interest in topologically stable configurations in nanoscale magnetic systems which can potentially be used as bits for information storage. Racetrack memory devices based on domain walls or skyrmions are prominent examples. The ever increasing demand for higher data storage density forces us to understand topological defects at ever decreasing length scales where thermal and quantum effects play an increasingly important role. In this talk I will focus on two examples which illustrate the transition from classical to quantum regime and the emergence of new phenomena: Firstly, in anisotropic spin chains, quantum fluctuations induce dynamics of domain walls or spinons, and this gives rise to a spontaneous chirality and spin currents which are measured via neutron scattering. Secondly, systems of classically coupled dipoles such as spin ice have recently shown to exhibit remarkable phenomena such as emergent magnetic monopoles as elementary excitations. The quantum nature of the dipolar interaction for example becomes manifest for vortex phases in certain rare earth trihalides. It is shown how an applied field triggers a series of quantum phase transition in which the Berry phase plays a pivotal role. Such behaviour is observed in neutron scattering experiments and it is shown that the rare earth trihalide are described by a quantum spin version of the Bose Hubbard model.
Piet Brouwer: Interacting end states in onedimensional superconductors
In the presence of an effective timereversal symmetry, multiple Majorana end states may coexist at the ends of a onedimensional superconducting wire. Fidkowski and Kitaev have shown that such systems have a ℤ8 topological classification once local interactions are taken into account. I’ll consider the fate of these eight topological classes once the superconductor is coupled to a normalmetal lead. Interestingly, the coupling to a normal metal creates an additional topological structure, which is well described by the trace of the Andreev reflection matrix r_he.
Jonathan Coleman: Kitchen Physics: Using the methods of physics to produce state of the art nanomaterials using household implements
Graphene is one of the most important of all nanomaterials. For many applications, high quality, defect free graphene is required. However by and large it is possible to make either small quantities of highquality graphene or a large quantities of low quality graphene. In this talk, I will describe a method produce large quantities of highquality, few layer graphene nanosheets. In order to make this process scalable, simplicity is a significant virtue. We have used one of the simplest chemical processing technologies, high shear mixing, to exfoliate graphite to give large quantities of graphene dispersed in liquids. Although the graphene sheets produced in this way are rather small they are virtually defect free. We have developed a basic understanding of the exfoliation process, supported by a simple mathematical model. This model predicts that even our humble kitchen blender can be used to produce exfoliated graphene. We have tested this prediction by exfoliating not only graphite, but born nitride, molybdenum disulphide and tungsten disulphide in kitchen blenders. Furthermore, we showed that the graphene produced in this way can be easily inserted into storebought elastic bands to create strain sensors with stateoftheart properties. We believe that this is an important demonstration of the power of nano materials.
Clotilde Cucinotta : Electronic Properties and Chemical Reactivity of TiS2 nanoflakes from first principles
Transition metal dichalcogenides have a laminar structure, weakly bound through van der Waals interactions. They are of special interest also because of the unique properties stemming from their exfoliation in nanoflakes. By means of ab initio simulations we study the oxidation process of a TiS2 nanoflake, in terms of electronic structure, reaction energies and pathways. We find that the oxidation process is thermodynamically and kinetically viable when initiated by the generation of a surface vacancy, with an energy barrier of about 1 eV. A finetuning control of the gap of this material is enabled by Oinsertion. Important technological applications for surface catalysis and photovoltaics are enabled by this possibility.
Klaus Ensslin: Imaging of integer and fractional quantum Hall edge states
The integer and fractional quantum Hall effect are two different macroscopic quantum phenomena, which lead to similar observations in electron transport experiments on twodimensional electron gases at high magnetic fields. The phenomenology of both effects is a result of onedimensional channels at the sample edge, which transmit electrical signals without losses between contacts separated by macroscopic distances. We explore the internal structure of integer and fractional quantum Hall edge channels by modifying the edge potential locally with the voltagebiased tip of a scanning force microscope, and find unprecedented rich structure on local scales. We measure the conductance of a quantum point contact (QPC) while the scanning tip induces a depleted region in the electron gas underneath. We find a sequence of lensshaped regions in the maps of conductance as a function of tip position, which resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The stripes are rugged on the micron scale, i.e. on a scale much smaller than the zerofield elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are abundant even in highquality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions. Nevertheless the macroscopic quantization of the Hall resistance, which is experimentally measured in a nonlocal contact configuration, survives, and the relevant local energy scales turn out to be independent of tip position.
Karsten Flensberg: Tunneling spectroscopy of Majorana bound states
Mikael Fremling: Hall viscosity of hierarchical quantum Hall states
Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. For the filling factor ν = 2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function andthe numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.
Jørgen Fulsebakke: Quantum Hall pair correlations
The pair correlation is useful in studying quantum Hall trial wave functions, revealing physical quantities such as the energy gap through the single mode approximation and exhibiting signatures of second Landau level electron pairing. Using an efficient Monte Carlo algorithm, we can calculate the pair correlation for trial wave functions such as the negative flux composite fermion states and the BondersonSlingerland states, which may describe conductance plateaus observed in the second Landau level that could harbour nonAbelian anyons. Until recently, these systems could only be studied for very small numbers of electrons.
Mark Goerbig: Twodimensional semiconductors: massive Dirac fermions or nothing new?
Beyond graphene, several other 2D crystals have now been isolated and might provide novel materials for nextgeneration electronics. Apart from boron nitride, transitionmetal dichalcogenides are at present heavily investigated, both on an experimental and a theoretical level.
One of the most remarkable aspects of graphene is certainly its electronic properties that are described in terms of ultrarelativistic (massless) Dirac fermions. One may thus raise the question to what extent the abovementioned new class of 2D (semiconducting) crystals calls for a description in terms of (now massive) Dirac fermions or whether they are correctly described in terms of usual Schroedingertype fermions. Naturally this question is only pertinent if there are physical phenomena that allow one to distinguish between the two types of fermions.
In this talk, I will first discuss the differences between Schroedinger and Dirac fermions in 2D directgap semiconductors with triangular symmetry. These differences are most prominently revealed in a magnetic field. Namely the position of the “zeroenergy” Landau levels sensitively depends on the fermions’ character. Furthermore, we expect particular selection rules in magnetooptical measurements, e.g. in transitionmetal dichalcogenides if the latter are correctly described in terms of Dirac fermions [1]. Finally, I will try to discuss the nature of the lowenergy electrons in 2D semiconductors from a more general viewpoint and show that it is principally possible to interpolated between Schroedinger and Dirac fermions [2]. This interpolation may be characterised via a parameter (“Diracness”) that could be identified experimentally in magnetotransport measurements or numerically via a calculation of the Berry curvature at the gap.
[1] F. Rose, MOG, F. Piéchon, Phys. Rev. B 88, 125438 (2013).
[2] MOG, G. Montambaux, F. Piéchon, EPL 105, 57005 (2014).
Kareljan Schoutens: Strange Metals in One Spatial Dimension
We consider a 1+1 dimensional Strange Metal, which arises from SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The high density limit is characterized by a deconfined Fermi surface, with low energy fluctuations described by a coset conformal field theory with central charge c=(N^21)/3 and an emergent N=(2,2) supersymmetry. We determine the exact scaling dimensions of the operators associated with Friedel oscillations and pairing correlations and explore the N→∞ limit.
Steve Simon: Update on Sr2RuO4
Cristiane Morais Smith: Topological states in higher orbitals
The recent realization of “synthetic graphene” by the selfassembling of semiconducting nanocrystals into a honeycomb lattice has opened new perspectives into the realization of topological materials in condensed matter [1]. By choosing the chemical elements in the nanocrystal, the spinorbit coupling can be tuned to a great extent, thus allowing us to engineer new materials that could be useful for technological applications. A honeycomb lattice made of CdSe nanocrystals was shown to exhibit Dirac cones in the s and p conduction bands, as well as a topological phase in the valence band [1].
Topological states of matter are being studied not only in condensed matter, but also in quantum optics. By loading ultracold fermions or bosons into optical lattices, it is possible to simulate condmat systems, thus custom tailoring model Hamiltonians which are supposed to describe complex quantum systems. The recent experimental realization of a p_x + i p_y BoseEinstein condensate of Rb in a 2D optical lattice, for which timereversal symmetry is spontaneously broken, is a fascinating example of the numerous possibilities to be explored with those systems [2].
[1] E. Kalesaki, C. Delerue, C. Morais Smith, W. Beugeling, G. Allen, and D. Vanmaekelbergh, PRX 4, 011010 (2014).
[2] M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith and A Hemmerich, New Journal Phys.15, 083041 (2013).
Kyrylo Snizhko: Tunnelling current noise in fractional quantum Hall effect and the information it can give
Tunnelling current noise measurements are not new in studies of the quantum Hall effect (QHE). Perhaps, the most famous use of these was the confirmation of fractional charges of the fractional QHE (FQHE) quasiparticles [1, 2]. Experiments that are more recent confirmed the existence of counterpropagating neutral transport channels in several FQHE states with the help of such measurements [3]. I will briefly introduce a theoretical framework [4] that allows one to analyse such measurements quantitatively. I will show that one can extract a lot of information from such measurements, including the scaling dimension of the tunnelling quasiparticle [5] and the behaviour of tunnelling amplitudes [4].
[1] R. DePicciotto et al., Direct observation of a fractional charge, Nature, 389(6647):162, 1997.
[2] L. Saminadayar et al., Observation of the e/3 fractionally charged Laughlin quasiparticle, Physical Review Letters 79(13):2526, 1997.
[3] A. Bid et al., Observation of neutral modes in the fractional quantum Hall regime, Nature, 466(7306):585, 2010.
[4] O. Shtanko, K. Snizhko, V. Cheianov, Nonequilibrium noise in transport across a tunneling contact between ν = 2/3 fractional quantum Hall edges, Phys. Rev. B 89(12):125104, 2014.
[5] K. Snizhko, V. Cheianov, Scaling dimension of quantum Hall quasiparticles from tunneling current noise measurements, arXiv:1410.2400.
Awadhesh Narayan : Topological tuning in threedimensional Dirac semimetals.
Graphene is, by now, a wellknown twodimensional Dirac semimetal. Recently, threedimensional Dirac semimetals have been theoretically proposed and experimentally realized. In this work, we study with firstprinciples methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological phase transition in Na_{3}Bi_{1−x}Sb_{x }and Cd_{3}[As_{1−x}P_{x}]_{2 }alloys, where the material goes from a Dirac semimetal to a trivial insulator upon changing Sb or P con centrations. Tuning the composition allows us to engineer the position of the bulk Dirac points in reciprocal space. Interestingly, the phase transition coincides with the reversal of the band or dering between the conduction and valence bands. The ab initio results are corroborated using a lowenergy Diraclike model.
Reference: A. Narayan, D. Di Sante, S. Picozzi, and S. Sanvito, arXiv:1408.3509.
Frank Verstraete: Shadows of Anyons
We will discuss topological quantum order from the point of view of quantum tensor networks. In particular, we will show how boundary theories and edge modes arise naturally on the virtual space, and show how topological phase transitions are related to symmetry breaking phase transitions in that picture
Susanne Viefers: Rotational properties of twocomponent gases in the lowest Landau level
In recent years there has been substantial interest in the study of strongly correlated states of cold atoms, analogous to exotic states known from lowdimensional electron systems – one ’holy grail’ being experimental realisation of quantum Halllike states in atomic Bose condensates. In particular there have been many studies on the rotational properties of cold atom systems, as rotation is the conceptually simplest way of simulating a magnetic field for electrically neutral bosonic or fermionic atoms. Even richer physics is expected in the case of twospecies gases, such as mixtures of two types of bosonic atoms, since (for species independent interactions), the system then possesses an additional pseudospin symmetry.
In this talk I will give an introduction to the field, followed by some recent results[1] on the rotational properties of twospecies Bose gases in the lowangular momentum regime of the lowest Landau level. Interestingly, an experimental realisation of this regime for single species Bose gases was reported recently[2]. In particular we show that, contrary to expectations, trial wave functions of the composite fermion (CF) type, known from quantum Hall physics, give a very accurate description of the low energy states of this system. It is also shown how working only with a certain subset of possible CF candidate wave functions constitutes a major computational simplification without much loss of accuracy for the lowlying states. Finally I will briefly discuss some striking mathematical identities between seemingly different CF candidate states, of interest for a better understanding of the CF method in general[3].
1. M. L. Meyer, G. J. Sreejith, and S. Viefers, Phys. Rev. A 89, 043625 (2014). 2. N. Gemelke, E. Sarajlic, and S. Chu, arXiv:1007.2677.
3. A. C. Balram, A. Wojs, and J. K. Jain, Phys. Rev. B 88, 205312 (2013).
Felix Von Oppen: Magnetic adatoms on superconductors – a new venue for Majorana bound states?
Jan Zaanen: Holography and the strange metals of condensed matter physics.
The holographic duality (or “AdS/CFT” correspondence) of string theory has delivered very recently a series of predictions for novel states of compressible quantum matter. This method addresses physics that is not accessible by conventional field theoretical methods: strongly interacting fermionic matter at finite density, residing behind the “fermion sign problem brick wall”. The fermion signs appear to give rise to long range quantum entanglements of a new kind, translating into the emergence of strongly interacting quantum critical phases with very unusual scaling properties. In turn, these “holographic strange metals” are naturally unstable towards superconducting and other ordered phases, invoking a generalized form of the Cooper instability. I will review this development, with a special emphasis on the prediction that the transport is governed by a ‘minimal viscosity’ hydrodynamics. This appears to yield a natural explanation for the linear resistivity of the cuparte strange metal, while a number of (falsifiable) predictions follow invoking unconventional experiments.
Martin Zirnbauer: Bott periodicity and the “Periodic Table” of topological insulators and superconductors
Bott periodicity is said to be one the most surprising phenomena in topology. Perhaps even more surprising is its recent appearance in condensed matter physics. Building on work of Schnyder et al, Kitaev argued that symmetryprotected ground states of gapped freefermion systems, also known as topological insulators and superconductors, organize into a kind of periodic table governed by a variant of the Bott periodicity theorem. In this talk, I will sketch the mathematical background, the physical context, and some new results of this ongoing story of mathematical physics.

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Last Updated: 22nd March 2016 by Administrator
Introduction
at the
School of Theoretical Physics
Dublin Institute for Advanced Studies
Dates: November 10th, 11th, and 12th, 2014
The goal of this workshop is to bring together researchers in nanoscience, condensed matter and quantum information with a view to fostering interdisciplinary communication and collaboration. Although there will be a strong emphasis on topological and surface state aspects of condensed matter, the workshop will also include related areas such as material design, quantum information, and statistical and quantum field theories.
You can register for the event using the form below .
Official registration for this event will close on the 31st of October.
For late registration please email the organisers.
Invited Speakers
HansBenjamin Braun
Piet Brouwer
Jonathan Coleman
Cristiane Morais Smith
Klaus Ensslin
Karsten Flensberg
Mark Goerbig
Kareljan Schoutens
Steve Simon
Frank Verstraete
Susanne Viefers
Felix von Oppen
Jan Zaanen
Martin Zirnbauer
Local organisers
Graham Kells
Marianne Leitner
Werner Nahm
Joost Slingerland
Jiri Vala
Tentative timetable
Monday, November 10
Tuesday, November 11
17101730 Mikael Fremling 17301750 Jorgen Fulsebakke
Wednesday, November 12
Financial Support
Junior participants can avail of financial support for travel and accommodation. If you wish to make use of this, please say so in the comments section of the registration form.
Finding us
The Institute is located at
10 Burlington Road
Number 10 Burlington Road, Dublin 4 ( GPS +53° 19′ 53.08″, 6° 14′ 45.08″ )( Loc8:NN515W23 )
Accommodation details
There are several hotels and guesthouses in close proximity to DIAS.
http://www.waterloolodge.com/
http://www.baggotcourt.com/
http://www.waterloohouse.ie/
http://www.pembroketownhouse.ie/
http://www.mespilhotel.com/
Prices in Dublin 4 tend to be slightly above average however. You may also like to try the following websites:
http://www.booking.com/city/ie/dublin.html
http://www.irelandhotels.com/hotels/ireland/dublin
Please contact us if you need any help.
Hans Benjamin Braun: Topological effects in nanoscale magnetism
Recent years have seen increased interest in topologically stable configurations in nanoscale magnetic systems which can potentially be used as bits for information storage. Racetrack memory devices based on domain walls or skyrmions are prominent examples. The ever increasing demand for higher data storage density forces us to understand topological defects at ever decreasing length scales where thermal and quantum effects play an increasingly important role. In this talk I will focus on two examples which illustrate the transition from classical to quantum regime and the emergence of new phenomena: Firstly, in anisotropic spin chains, quantum fluctuations induce dynamics of domain walls or spinons, and this gives rise to a spontaneous chirality and spin currents which are measured via neutron scattering. Secondly, systems of classically coupled dipoles such as spin ice have recently shown to exhibit remarkable phenomena such as emergent magnetic monopoles as elementary excitations. The quantum nature of the dipolar interaction for example becomes manifest for vortex phases in certain rare earth trihalides. It is shown how an applied field triggers a series of quantum phase transition in which the Berry phase plays a pivotal role. Such behaviour is observed in neutron scattering experiments and it is shown that the rare earth trihalide are described by a quantum spin version of the Bose Hubbard model.
Piet Brouwer: Interacting end states in onedimensional superconductors
In the presence of an effective timereversal symmetry, multiple Majorana end states may coexist at the ends of a onedimensional superconducting wire. Fidkowski and Kitaev have shown that such systems have a ℤ8 topological classification once local interactions are taken into account. I’ll consider the fate of these eight topological classes once the superconductor is coupled to a normalmetal lead. Interestingly, the coupling to a normal metal creates an additional topological structure, which is well described by the trace of the Andreev reflection matrix r_he.
Jonathan Coleman: Kitchen Physics: Using the methods of physics to produce state of the art nanomaterials using household implements
Graphene is one of the most important of all nanomaterials. For many applications, high quality, defect free graphene is required. However by and large it is possible to make either small quantities of highquality graphene or a large quantities of low quality graphene. In this talk, I will describe a method produce large quantities of highquality, few layer graphene nanosheets. In order to make this process scalable, simplicity is a significant virtue. We have used one of the simplest chemical processing technologies, high shear mixing, to exfoliate graphite to give large quantities of graphene dispersed in liquids. Although the graphene sheets produced in this way are rather small they are virtually defect free. We have developed a basic understanding of the exfoliation process, supported by a simple mathematical model. This model predicts that even our humble kitchen blender can be used to produce exfoliated graphene. We have tested this prediction by exfoliating not only graphite, but born nitride, molybdenum disulphide and tungsten disulphide in kitchen blenders. Furthermore, we showed that the graphene produced in this way can be easily inserted into storebought elastic bands to create strain sensors with stateoftheart properties. We believe that this is an important demonstration of the power of nano materials.
Clotilde Cucinotta : Electronic Properties and Chemical Reactivity of TiS2 nanoflakes from first principles
Transition metal dichalcogenides have a laminar structure, weakly bound through van der Waals interactions. They are of special interest also because of the unique properties stemming from their exfoliation in nanoflakes. By means of ab initio simulations we study the oxidation process of a TiS2 nanoflake, in terms of electronic structure, reaction energies and pathways. We find that the oxidation process is thermodynamically and kinetically viable when initiated by the generation of a surface vacancy, with an energy barrier of about 1 eV. A finetuning control of the gap of this material is enabled by Oinsertion. Important technological applications for surface catalysis and photovoltaics are enabled by this possibility.
Klaus Ensslin: Imaging of integer and fractional quantum Hall edge states
The integer and fractional quantum Hall effect are two different macroscopic quantum phenomena, which lead to similar observations in electron transport experiments on twodimensional electron gases at high magnetic fields. The phenomenology of both effects is a result of onedimensional channels at the sample edge, which transmit electrical signals without losses between contacts separated by macroscopic distances. We explore the internal structure of integer and fractional quantum Hall edge channels by modifying the edge potential locally with the voltagebiased tip of a scanning force microscope, and find unprecedented rich structure on local scales. We measure the conductance of a quantum point contact (QPC) while the scanning tip induces a depleted region in the electron gas underneath. We find a sequence of lensshaped regions in the maps of conductance as a function of tip position, which resemble theoretically predicted compressible and incompressible stripes of quantum Hall edge states. The stripes are rugged on the micron scale, i.e. on a scale much smaller than the zerofield elastic mean free path of the electrons. Our experiments demonstrate that microscopic inhomogeneities are abundant even in highquality samples and lead to locally strongly fluctuating widths of incompressible regions even down to their complete suppression for certain tip positions. Nevertheless the macroscopic quantization of the Hall resistance, which is experimentally measured in a nonlocal contact configuration, survives, and the relevant local energy scales turn out to be independent of tip position.
Karsten Flensberg: Tunneling spectroscopy of Majorana bound states
Mikael Fremling: Hall viscosity of hierarchical quantum Hall states
Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. For the filling factor ν = 2/5 Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex τ plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function andthe numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.
Jørgen Fulsebakke: Quantum Hall pair correlations
The pair correlation is useful in studying quantum Hall trial wave functions, revealing physical quantities such as the energy gap through the single mode approximation and exhibiting signatures of second Landau level electron pairing. Using an efficient Monte Carlo algorithm, we can calculate the pair correlation for trial wave functions such as the negative flux composite fermion states and the BondersonSlingerland states, which may describe conductance plateaus observed in the second Landau level that could harbour nonAbelian anyons. Until recently, these systems could only be studied for very small numbers of electrons.
Mark Goerbig: Twodimensional semiconductors: massive Dirac fermions or nothing new?
Beyond graphene, several other 2D crystals have now been isolated and might provide novel materials for nextgeneration electronics. Apart from boron nitride, transitionmetal dichalcogenides are at present heavily investigated, both on an experimental and a theoretical level.
One of the most remarkable aspects of graphene is certainly its electronic properties that are described in terms of ultrarelativistic (massless) Dirac fermions. One may thus raise the question to what extent the abovementioned new class of 2D (semiconducting) crystals calls for a description in terms of (now massive) Dirac fermions or whether they are correctly described in terms of usual Schroedingertype fermions. Naturally this question is only pertinent if there are physical phenomena that allow one to distinguish between the two types of fermions.
In this talk, I will first discuss the differences between Schroedinger and Dirac fermions in 2D directgap semiconductors with triangular symmetry. These differences are most prominently revealed in a magnetic field. Namely the position of the “zeroenergy” Landau levels sensitively depends on the fermions’ character. Furthermore, we expect particular selection rules in magnetooptical measurements, e.g. in transitionmetal dichalcogenides if the latter are correctly described in terms of Dirac fermions [1]. Finally, I will try to discuss the nature of the lowenergy electrons in 2D semiconductors from a more general viewpoint and show that it is principally possible to interpolated between Schroedinger and Dirac fermions [2]. This interpolation may be characterised via a parameter (“Diracness”) that could be identified experimentally in magnetotransport measurements or numerically via a calculation of the Berry curvature at the gap.
[1] F. Rose, MOG, F. Piéchon, Phys. Rev. B 88, 125438 (2013).
[2] MOG, G. Montambaux, F. Piéchon, EPL 105, 57005 (2014).
Kareljan Schoutens: Strange Metals in One Spatial Dimension
We consider a 1+1 dimensional Strange Metal, which arises from SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The high density limit is characterized by a deconfined Fermi surface, with low energy fluctuations described by a coset conformal field theory with central charge c=(N^21)/3 and an emergent N=(2,2) supersymmetry. We determine the exact scaling dimensions of the operators associated with Friedel oscillations and pairing correlations and explore the N→∞ limit.
Steve Simon: Update on Sr2RuO4
Cristiane Morais Smith: Topological states in higher orbitals
The recent realization of “synthetic graphene” by the selfassembling of semiconducting nanocrystals into a honeycomb lattice has opened new perspectives into the realization of topological materials in condensed matter [1]. By choosing the chemical elements in the nanocrystal, the spinorbit coupling can be tuned to a great extent, thus allowing us to engineer new materials that could be useful for technological applications. A honeycomb lattice made of CdSe nanocrystals was shown to exhibit Dirac cones in the s and p conduction bands, as well as a topological phase in the valence band [1].
Topological states of matter are being studied not only in condensed matter, but also in quantum optics. By loading ultracold fermions or bosons into optical lattices, it is possible to simulate condmat systems, thus custom tailoring model Hamiltonians which are supposed to describe complex quantum systems. The recent experimental realization of a p_x + i p_y BoseEinstein condensate of Rb in a 2D optical lattice, for which timereversal symmetry is spontaneously broken, is a fascinating example of the numerous possibilities to be explored with those systems [2].
[1] E. Kalesaki, C. Delerue, C. Morais Smith, W. Beugeling, G. Allen, and D. Vanmaekelbergh, PRX 4, 011010 (2014).
[2] M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith and A Hemmerich, New Journal Phys.15, 083041 (2013).
Kyrylo Snizhko: Tunnelling current noise in fractional quantum Hall effect and the information it can give
Tunnelling current noise measurements are not new in studies of the quantum Hall effect (QHE). Perhaps, the most famous use of these was the confirmation of fractional charges of the fractional QHE (FQHE) quasiparticles [1, 2]. Experiments that are more recent confirmed the existence of counterpropagating neutral transport channels in several FQHE states with the help of such measurements [3]. I will briefly introduce a theoretical framework [4] that allows one to analyse such measurements quantitatively. I will show that one can extract a lot of information from such measurements, including the scaling dimension of the tunnelling quasiparticle [5] and the behaviour of tunnelling amplitudes [4].
[1] R. DePicciotto et al., Direct observation of a fractional charge, Nature, 389(6647):162, 1997.
[2] L. Saminadayar et al., Observation of the e/3 fractionally charged Laughlin quasiparticle, Physical Review Letters 79(13):2526, 1997.
[3] A. Bid et al., Observation of neutral modes in the fractional quantum Hall regime, Nature, 466(7306):585, 2010.
[4] O. Shtanko, K. Snizhko, V. Cheianov, Nonequilibrium noise in transport across a tunneling contact between ν = 2/3 fractional quantum Hall edges,
Phys. Rev. B 89(12):125104, 2014.
[5] K. Snizhko, V. Cheianov, Scaling dimension of quantum Hall quasiparticles from tunneling current noise measurements, arXiv:1410.2400.
Awadhesh Narayan : Topological tuning in threedimensional Dirac semimetals.
Graphene is, by now, a wellknown twodimensional Dirac semimetal. Recently, threedimensional Dirac semimetals have been theoretically proposed and experimentally realized. In this work, we study with firstprinciples methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological phase transition in Na_{3}Bi_{1−x}Sb_{x }and Cd_{3}[As_{1−x}P_{x}]_{2 }alloys, where the material goes from a Dirac semimetal to a trivial insulator upon changing Sb or P con centrations. Tuning the composition allows us to engineer the position of the bulk Dirac points in reciprocal space. Interestingly, the phase transition coincides with the reversal of the band or dering between the conduction and valence bands. The ab initio results are corroborated using a lowenergy Diraclike model.
Reference: A. Narayan, D. Di Sante, S. Picozzi, and S. Sanvito, arXiv:1408.3509.
Frank Verstraete: Shadows of Anyons
We will discuss topological quantum order from the point of view of quantum tensor networks. In particular, we will show how boundary theories and edge modes arise naturally on the virtual space, and show how topological phase transitions are related to symmetry breaking phase transitions in that picture
Susanne Viefers: Rotational properties of twocomponent gases in the lowest Landau level
In recent years there has been substantial interest in the study of strongly correlated states of cold atoms, analogous to exotic states known from lowdimensional electron systems – one ’holy grail’ being experimental realisation of quantum Halllike states in atomic Bose condensates. In particular there have been many studies on the rotational properties of cold atom systems, as rotation is the conceptually simplest way of simulating a magnetic field for electrically neutral bosonic or fermionic atoms. Even richer physics is expected in the case of twospecies gases, such as mixtures of two types of bosonic atoms, since (for species independent interactions), the system then possesses an additional pseudospin symmetry.
In this talk I will give an introduction to the field, followed by some recent results[1] on the rotational properties of twospecies Bose gases in the lowangular momentum regime of the lowest Landau level. Interestingly, an experimental realisation of this regime for single species Bose gases was reported recently[2]. In particular we show that, contrary to expectations, trial wave functions of the composite fermion (CF) type, known from quantum Hall physics, give a very accurate description of the low energy states of this system. It is also shown how working only with a certain subset of possible CF candidate wave functions constitutes a major computational simplification without much loss of accuracy for the lowlying states. Finally I will briefly discuss some striking mathematical identities between seemingly different CF candidate states, of interest for a better understanding of the CF method in general[3].
1. M. L. Meyer, G. J. Sreejith, and S. Viefers, Phys. Rev. A 89, 043625 (2014). 2. N. Gemelke, E. Sarajlic, and S. Chu, arXiv:1007.2677.
3. A. C. Balram, A. Wojs, and J. K. Jain, Phys. Rev. B 88, 205312 (2013).
Felix Von Oppen: Magnetic adatoms on superconductors – a new venue for Majorana bound states?
Jan Zaanen: Holography and the strange metals of condensed matter physics.
The holographic duality (or “AdS/CFT” correspondence) of string theory has delivered very recently a series of predictions for novel states of compressible quantum matter. This method addresses physics that is not accessible by conventional field theoretical methods: strongly interacting fermionic matter at finite density, residing behind the “fermion sign problem brick wall”. The fermion signs appear to give rise to long range quantum entanglements of a new kind, translating into the emergence of strongly interacting quantum critical phases with very unusual scaling properties. In turn, these “holographic strange metals” are naturally unstable towards superconducting and other ordered phases, invoking a generalized form of the Cooper instability. I will review this development, with a special emphasis on the prediction that the transport is governed by a ‘minimal viscosity’ hydrodynamics. This appears to yield a natural explanation for the linear resistivity of the cuparte strange metal, while a number of (falsifiable) predictions follow invoking unconventional experiments.
Martin Zirnbauer: Bott periodicity and the “Periodic Table” of topological insulators and superconductors
Bott periodicity is said to be one the most surprising phenomena in topology. Perhaps even more surprising is its recent appearance in condensed matter physics. Building on work of Schnyder et al, Kitaev argued that symmetryprotected ground states of gapped freefermion systems, also known as topological insulators and superconductors, organize into a kind of periodic table governed by a variant of the Bott periodicity theorem. In this talk, I will sketch the mathematical background, the physical context, and some new results of this ongoing story of mathematical physics.
Category: Dublin Area Workshop on Nanoscience and Low Dimensional Quantum Matter
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