Condensed Matter Theory Seminar (2015–2016)

27 May 2015

Dirk Manske

Superconductors in Non-Equilibrium

MPI Stuttgart

Time-resolved pump-probe experiments recently attracted great interest, since they allow to detecting hidden states and they provide new information on the underlying dynamics in solids in real time. Recently, we have established a theory for superconductors in non-equilibrium, for example in a pump-probe experiment [1,2]. Using the Density-Matrix-Theory (DMT) we have developed an approach to calculate the response of conventional and unconventional superconductors in a time-resolved experiment. In particular, DMT method is not restricted to small timescales; in particular it provides a microscopic description of the quench, and also allows also the incorporation of phonons [2]. Furthermore, we employ DMT to time-resolved Raman scattering experiments [3] and make predictions for 2-band superconductors [4]. Very recently, we have focused on the theory for order parameter amplitude (‘Higgs’) oscillations which are the realization of the Higgs mode in superconductors [5,2]. Our prediction has been recently confirmed experimentally [6,7].

References
1. J. Unterhinninghofen, D. Manske, and A. Knorr, Phys. Rev. B 77, 180509(R) (2008).
2. A. Schnyder, D. Manske, and A. Avella, Phys. Rev. B 84, 214513 (2011).
3. R.P. Saichu et al., Phys. Rev. Lett. 102, 177004 (2009).
4. A. Akbari, A. Schnyder, I. Eremin, and D. Manske, Europhys. Lett. 101, 17002 (2013).
5. H. Krull, D. Manske, A. Schnyder, G. Uhrig, Phys. Rev. B 90, 014514 (2014).
6. R. Matsunaga et al., PRL 111, 057002 (2013).
7. A. Rusydi, D. Manske et al., submitted to Science

3 June 2015

Arun Paramekanti

Topology meets correlations - From solids to cold atoms

University of Toronto

The interplay between band topology and correlation effects is an active field of research. The talk will give an introduction to this field and discuss some of our theoretical work in solids, including oxide heterostructures as a platform to realize quantum anomalous Hall phases, Kitaev magnetism in a class of frustrated fcc lattice materials, the emergence of nematic phases at topological quantum critical points, and unusual magnetic orders in the correlated Haldane-Hubbard model.

17 June 2015

Samuel Bieri

Chiral Quantum Spin Liquids in a Kagome Heisenberg model

LPTMC, UPMC/Sorbonne - Paris 6

Recently, new quantum magnets have been synthesized and characterized which are described by spin S=1/2 Heisenberg models on the kagome lattice with farther-neighbor exchange interactions. One of them - the kapellasite material - does not show ordering, a fluctuating behavior down to very low temperature, and gapless spin excitations. Motivated by these facts, we use the projective symmetry group classification to list all quantum spin liquids with fermionic spinons on the kagome lattice. Comparing a wide range of microscopic wave functions, we find a variational phase diagram for this model. We propose that, at low temperature, kapellasite exhibits a novel chiral (time-reversal breaking) spin liquid phase with a spinon Fermi surface.

23 June 2015

Jan Budich

Dynamical topological order parameters far from equilibrium

Universität Innsbruck

Topological states of quantum matter such as topological insulators and superconductors have been an active field of research in physics for many years. While their ground state properties  are rather well understood by now, much less is known about dynamical phenomena occurring when such quantum many-body systems are driven far away from thermal equilibrium, e.g., by quantum quenches. Here, we discuss a novel topological quantum number that serves as a dynamical order parameter in the context of dynamical quantum phase transitions (DQPTs). DQPTs have been introduced as a non-equilibrium analog in quantum real-time evolution of conventional phase transitions, where increasing time replaces the notion of conventional control parameters such as temperature. However, establishing a non-equilibrium analog of order parameters in this framework has so far remained elusive. Studying quantum quenches in two-banded Bogoliubov de Gennes models, we identify a dynamical order parameter which changes its discrete value at DQPTs and which is represented by a momentum space winding number of the Pancharatnam geometric phase. By contrast, straightforward non-equilibrium generalizations of conventional topological invariants are well known to be constants of motion under coherent time evolution.

29 June 2015

Emanuele Dalla Torre

Temperature as an Emergent Property of Non-Equilibrium Systems

Bar Ilan University

Depicted by P. W. Anderson as "more is different", an emergent phenomenon occurs when a large number of identical objects behaves differently than its original constituents. This situation lays at the core of our understanding of strongly correlated materials, such as insulators and superconductors. However, present theories are often limited to equilibrium systems that can be described by a thermal ensemble at a fixed temperature. How can we extend these ideas to non-equilibrium environments? I will describe a recent approach to the problem, where the temperature is represented as an emergent phenomenon. Although the microscopic degrees of freedom are externally driven and do not equilibrate, the macroscopic properties of the system often display a thermal behavior. Starting from specific case studies, I will present successes and failures of this approach.

9 July 2015

Maciej Koch-Janusz

Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice from t_2g Orbitals

Weizmann Institute of Science

The two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) model on a honeycomb lattice has been shown to be a universal resource for quantum computation. In this valence bond solid, however, the spin interactions involve higher powers of the Heisenberg coupling (S_i*S_j)^n, making these states seemingly unrealistic on bipartite lattices, where one expects a simple antiferromagnetic order. We show that those interactions can be generated by orbital physics in multi-orbital Mott insulators. We focus on t_2g electrons on the honeycomb lattice and propose a physical realization of the spin-3/2 AKLT state. We find a phase transition from the AKLT to the Néel state on increasing Hund’s rule coupling, which is confirmed by density matrix renormalization group simulations. An experimental signature of the AKLT state consists of protected, free S=1/2 spins on lattice vacancies, which may be detected in the spin susceptibility.

16 July 2015

Hideo Aoki

Higgs and Leggett modes in superconductors

University of Tokyo

24 July 2015

Florian Marquardt

Topological Phases of Sound and Light

University of Erlangen-Nürnberg

Optomechanical systems, coupling light to nanomechanical motion, are now being investigated for many possible applications like sensitive measurements, quantum state manipulation, and quantum communication, as well as fundamental tests of quantum mechanics. These systems have now reached the stage where one can envisage making them into larger-scale arrays, coupling many vibrational and optical modes. In this talk I will first give a brief introduction to optomechanics. I will then recount our theoretical ideas on how to produce synthetic magnetic fields for photons via the optomechanical interaction. Finally, I will describe our proposal for achieving topologically protected transport of sound waves, which is an outstanding challenge in any solid-state platform.

21 August 2015

Alexei Koshelev

Anomalies of magneto transport in multiple-band antiferromagnetic metals due to the 'hot-spot' scattering and Fermi-surface reconstruction

Argonne National Laboratory (USA)

Multiple-band electronic structure and proximity to antiferromagnetic (AF) instability are the key properties of iron-based superconductors. Parent materials of most compounds are AF metals. Several compounds demonstrate anomalous magnetotransport properties both in paramagnetic and AF states such as linear magnetoresistance and strong field dependence of the Hall resistivity. We explore the influence of Fermi-surface reconstruction and scattering on AF fluctuations of transport of multiple-band metals both above and below the magnetic transition. A salient feature of scattering on AF fluctuations is that it is strongly enhanced at the Fermi surface locations where the nesting is perfect ('hot spots' or 'hot lines'). In the paramagnetic state, such enhanced scattering rate near the 'hot lines' leads to anomalous behavior of transport in the magnetic field. The magnetic field dependences are characterized by the two field scales, the lower scale is set by the width of the 'hot spots' and the higher scale is set by the total scattering amplitude. In the range in between these two scales the longitudinal conductivity has linear dependence on the magnetic field and the Hall conductivity has quadratic dependence. The linear dependence of the diagonal component reflects growth of the Fermi-surface area affected by 'hot spots' proportional to the magnetic field. In the AF state the Fermi surface is reconstructed near the nesting lines leading to appearance of sharp tips. Behavior of magnetotransport is thus determined by interplay in between this reconstruction and scattering by AF fluctuations. We discuss applicability of this theoretical framework to different iron pnictides and selenides.

31 August 2015

Hidetoshi Fukuyama

Dirac Electrons in Solids

Tokyo University of Science, Japan

Motions of electrons in solids are governed by the energy bands, which sometimes have features similar to Dirac electrons in vacuum in a region of momentum of physical interest. Well-known examples are bismuth and graphite; 4x4 original Dirac matrix in three-dimension with strong spin-orbit interaction in the former and massless Dirac (Weyl electrons) in two-dimensional layer stacks in the latter. Recent examples include one-layer graphene, layered bulk molecular solid, (BEDT-TTF)2I3, Iron-pnictide superconductors, inverse perovskite Ca3PbO and surface states of topological insulators.
In these systems there are many interesting physical responses, e.g. orbital susceptibility, Hall effect and spin-Hall effect, which will be explained in detail by focusing on bismuth and molecular solids.

Reference
1. “Transport Properties and Diamagnetism of Dirac Electrons in Bismuth”. Y.Fuseya, M. Ogata and H. Fukuyama, J. Phys. Soc. Jpn 84(2015) 012001-1-22. [Invited Review Paper]
2. “Achievements and Challenges in Molecular Conductors”, H. Fukuyama, open access “Crystals” 2012, 2, 875-892

31 August 2015

Laimei Nie

Fluctuating orders, quenched randomness, and vestigial nematicity in the cuprates

Stanford University, USA

Recent developments from NMR, X-ray, and STM studies indicate a tendency towards short-range incommensurate charge-density wave (CDW) order in the pseudogap regime of cuprates, intertwined with superconductivity (SC) order. Additionally, transport, STM and neutron scattering experiments have provided evidence for a relatively long-range point-group symmetry breaking with an electron-nematic character. In this talk, we will show that dimensionality and quenched randomness play key roles in these phenomena, by studying a quasi-2D Ginzburg-Landau effective field theory of CDW and SC order parameters in the presence of quenched disorder [1,2]. We will show that weak disorder inevitably eliminates the existence of long-range CDW correlations, yet leave behind an associated “vestigial” nematic phase. Analytic calculations which are controlled in a formal large-N limit are shown to give qualitatively similar results as are obtained by direct simulation using classical Monte Carlo methods.
[1] L. Nie, G. Tarjus, S. A. Kivelson, PNAS 111, 7980 (2014)
[2] L. Nie, L. E. H. Sierens, R. G. Melko., S. Sachdev, S. A. Kivelson, arXiv: 1505.06206

15 September 2015

David Möckli

Temperature dependence of the multi-gaps in Fe-based superconductors

Universidade Federal Fluminense, Rio de Janeiro, Brazil

We generalize the Chebyshev-Bogoliubov-deGennes method to treat multi-band systems to address the temperature dependence of the superconducting gaps of iron based superconductors. Four superconducting gaps associated with different electron and hole pockets of optimally Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ were clearly identified by angle resolved photo-emission spectroscopy. The few approaches that reproduce with success this gap structure are based on strong-coupling theories and required many adjustable parameters. We show that a weak-coupling approach with a redistribution of electron population between the hole and electron pockets with evolving temperature reproduces the high coupling ratios $2\Delta(0)/k_B T_c$ in these materials. We define the parameters to fit the four zero temperature gaps $\Delta(0)$ and after that all $\Delta(T)$ is obtained without any additional parameter.

11 April 2016

Philipp Strack

Universality in strange metals

Universität zu Köln, Cologne, Germany

The universality hypothesis in physics states that seemingly disparate materials, with different lattice structure, different chemical composition, and at different overall temperatures can obey, when undergoing a phase transition, the same universal laws effective at long distances. For metals, that is, billions of moving and mutually interacting electrons, undergoing phase transitions at zero temperature, the quest for universality and scale invariance has so far fallen short despite 40 years of research [1].
Here I will introduce a novel quantum field theory technique and soft frequency regulators capable of renormalizing the compact Fermi surfaces of metals at quantum phase transitions despite strangely short lifetimes of the electronic excitations and the absence of quasiparticles [2]. The power of the technique is demonstrated by the first computation of critical exponents and the associated universal shape of the Fermi surface at the spin-density wave quantum-critical point in a two-dimensional metal. Moreover, we resolve explicitly multiple scaling regimes across the entire range of energies and determine the (non-universal) crossover scales at which universality sets in.
Our technique [2] can pave the way for systematic investigations of strange metals and their emergent quantum phases relevant for many strongly correlated materials ranging from high-temperature superconductors, frustrated magnets, to the half-filled Landau level of electron gases in magnetic field.

References:
[1] John A. Hertz,
Quantum critical phenomena, Phys. Rev. B 14, 1165 (1976).
external pagehttp://journals.aps.org/prb/abstract/10.1103/PhysRevB.14.1165call_made

[2] Stefan Maier and Philipp Strack,
Universality in antiferromagnetic strange metals, arXiv:1510.01331 (2015).
external pagehttp://arxiv.org/abs/1510.01331call_made

8 July 2016

Vittorio Peano

Topological Quantum Fluctuations and Travelling Wave Amplifiers

University of Erlangen-Nürnberg, Germany

It is now well-established that photonic systems can exhibit topological energy bands; similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against back-scattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a non-zero topological invariant guarantees the presence of a parametrically-unstable chiral edge mode in a system with boundaries, even though there are no bulk-mode instabilities. We show that one can exploit this to realize a topologically protected, quantum-limited travelling-wave parametric amplifier. The device is naturally protected both against internal losses and back-scattering; the latter feature is in stark contrast to standard travelling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.

31 August 2016

Aris Alexandradinata

The first nonsymmorphic topological insulator: prediction and discovery

Yale University, USA

Spatial symmetries in crystals are distinguished by whether they preserve the spatial origin. I will show how this basic geometric property gives rise to a new topology in band insulators, which we propose (and subsequently discover) to lie in the large-gap insulators: KHgX (X=As,Sb,Bi). These insulators are described by generalized symmetries that combine space-time transformations with quasimomentum translations in the Brillouin torus. This provides a natural generalization of space groups, such that real and quasimomentum spaces are placed on equal footing. A broader consequence of our theory is a connection between band topology and group cohomology.

References:
Nature 532, 189-194,
Phys. Rev. X 6, 021008

2 September 2016

Erez Berg

Topological phenomena in periodically driven systems: the role of disorder and interactions

Weizmann Institute of Science, Israel

Periodically driven quantum systems, such as semiconductors subject to light and cold atoms in optical lattices, provide a novel and versatile platform for realizing topological phenomena. Some of these are analogs of topological insulators and superconductors, attainable also in static systems; others are unique to the periodically driven case. I will describe how periodic driving, disorder, and interactions can conspire to give rise to new robust steady states, with no analogues in static systems. In disordered two-dimensional driven systems, a phase with chiral edge states and fully localized bulk states is possible; this phase can realize a non-adiabatic quantized charge pump. In interacting one dimensional driven systems, current carrying states with excessively long lifetimes can arise.

27 September 2016

Hiroyuki Inoue

Detecting surface-bulk connectivity in Weyl semimetal TaAs via scanning tunneling microscopy

Princeton University, USA

Weyl semimetals host topologically protected surface states, known as Fermi arcs, which are expected to penetrate into the bulk upon approaching the surface projections of the bulk’s Weyl nodes. Following a theoretical prediction of TaAs being a candidate Weyl semimetal, angle-resolved photoemission spectroscopy studies showed the presence of Weyl cones and corresponding Fermi arcs. In this talk I will describe our scanning tunneling microscope experiment where we performed a spectroscopic mapping to visualize quasiparticle interference on the [001] surface of TaAs. Thanks to the stoichiometric nature of the sample, measuring atomically flat and pristine terraces revealed a rich variety of scattering wave vectors, which can be reproduced with a DFT calculation that takes into account the shape, spin texture, and sub-surface distribution of the Fermi arc surface states. Our observation demonstrates the momentum-dependent penetration of the Fermi arcs into the bulk, namely, surface-bulk connectivity in the Weyl semimetal.

Reference:
H. Inoue, A. Gyneis, Z. Wang, J. Li, S. W. Oh, S. Jiang, N. Ni, B. A. Bernevig and A. Yazdani, “Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of Weyl semimetals,” Science 351, 1184 (2016)

29 September 2016

David R. Nelson

Thermalized sheets and shells: curvature matters

Lyman Laboratory of Physics, Harvard University, Cambridge, USA

Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, characterized by a dimensionless coupling constant (the ”Foeppl- von Karman number”) that can easily reach vK = 107 in an ordinary sheet of writing paper. However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics, as exemplified by exper- iments from the McEuen group at Cornell that twist and bend individual atomically-thin free-standing graphene sheets (with vK = 1013). We review here the remarkable properties of thermalized sheets, where enhancements of the bending rigidity at T = 300 K by factors of ∼ 5000 have now been observed. We then move on to discuss thin amorphous spherical shells with a uniform nonzero curvature, accessible for example with soft matter experi- ments on diblock copolymers. This curvature couples the in-plane stretching modes with the out-of-plane undulation modes, giving rise to qualitative differences in the fluctuations of thermal spherical shells compared to flat membranes. Interesting effects arise because a shell can support a pressure difference between its interior and exterior. Thermal corrections to the pre- dictions of classical shell theory for microscale shells diverge as the shell radius tends to infinity.

28 October 2016

Wilhelm Zwerger

Exact results on the many-body problem from short-distance expansions

Technical University of Munich

It is shown that for the quantum many-body problem with zero range interactions, which appears naturally in the context of ultracold atoms, there are a number of exact relations which connect the short-distance behavior of the one- and two-body density matrix with thermodynamic properties and also the high-frequency or large momentum behavior of correlation functions. These relations follow from a Wilson operator product expansion and thus apply to arbitrary states of the many-body system. Three examples for their concrete application are given: the clock-shift in strongly interacting Fermi gases, the violation of scale invariance in two-dimensional gases and deep inelastic Bragg scattering on strongly interacting Bose gases at large momentum.