Final Report Summary - TEMSSOC (TOPOLOGICAL EFFECTS IN MATTER WITH STRONG SPIN-ORBIT COUPLING)
Executive Summary:
FINAL REPORT FOR THE PROJECT TEMSSOC (01/08/2010 to 31/07/2013)
During the first two years of the project, I had mainly worked with my hosts in UC Berkeley Profs Ashvin Vishwanath and Joel Moore (Physics Department UC Berkeley). Our dominant focus of research has been to find new ways to create, manipulate and probe topological phases of condensed matter systems (see parts I and II of this report). During the third year of the project (reintegration part), I have worked with Roderich Moessner and various theorists and experimentalists in Dresden on the idea of using light to drive ordinary insulators into a topological state (see part III of this report).
I) FIRST YEAR OF THE PROJECT, held at UC Berkeley (01/08/2010 to 31/07/2011):
During the first year of the project, we have initiated various works (3 accepted publications and one submitted preprint) on the properties of topological phases in two –dimensional systems.
1) Optical probe for helical edge states of 2D topological insulators
B. Dora, J. Cayssol, F. Simon, R. Moessner, Optically engineering the topological properties of a spin Hall insulator, Phys. Rev. Lett. 108, 056602 (2012).
Detail of the work: in this theoretical work, we propose to use photons (THz) in order to probe the helical structure and the robustness of the edge states of a two-dimensional topological insulator. When circularly polarized electromagnetic waves are shinned onto the topological insulator, a finite photocurrent is induced along the edge of the sample. The sign of this photocurrent is directly related to the handedness of the wave circular polarization. We have computed this photocurrent and shown that it could be measured in future experiments. As a function of the wave frequency, we have demonstrated the existence of two qualitatively distinct regimes. At low frequency, one electron is adiabatically pumped during each cycle/period of the wave. At higher frequency, the topological protection is lost and the current becomes dissipative. The experiments are more likely to be performed in this latter regime.
Collaboration: this work is a collaboration between Roderich Moessner (scientific in charge of the TEMSSOC project and director of the Max Planck Institute for the Physics of Complex Systems MPIPKS in Dresden), J. Cayssol (fellow of the TEMSSOC project) and B. Dora and F. Simon from Budapest University.
Presentations: this work has been presented by J. Cayssol at the APS March Meeting 2012 in Boston (see the presentation joined as a complement to this report) and will be also presented in Colloquium of the Physics department of Northridge University (May 2012), and in the seminar of Urbana Champain University (16th April 2012).
2) Spin Hall effect in materials with spin-orbit coupling
Yamakage, K-I Imura, J. Cayssol, and Y. Kuramoto, Interfacial charge and spin transport in Z2 topological insulators, Phys. Rev. B 83, 125401 (2011).
Details:
We have shown the existence of spin transport along a pn interface in graphene with intrinsic spin-orbit coupling. We have used the Kane-Mele model for graphene which has been a very important conceptual tool for the studies of topological phases in presence of time-reversal invariance. Nevertheless the spin-orbital coupling being small in graphene, the HgTe/CdTe quantum wells are better 2 dimensional electron gas to observe such an interfacial spin Hall effect which has motivated the next work 4).
Presentations: I have given an invited talk on this work during the international Workshop Superconducting hybrids: from conventional to exotic, held in Villard de Lans, 7-10 September 2011.
3) Spin Hall effect in materials with spin-orbit coupling
M. Guigou, P. Recher, J. Cayssol, and B. Trauzettel, Spin Hall effect at interfaces between HgTe/CdTe quantum wells and metals, Phys. Rev. B 84, 094534 (2011).
Details:
We have demonstrated that a new kind of spin Hall effect occurs along a potential step (or a junction between a normal and a superconducting regions) in the HgTe/CdTe quantum wells. In presence of an electric current (and field) perpendicular to the interface, a spin current is generated along this interface and thereby perpendicular to the electric field.
Collaborators: This work is a collaboration with colleagues of Wurzburg University (Bjoern Trauzettel) and Braunsweig University (Patrik Recher) that I plan to develop further especially during the return phase of the project in Germany (MPIPKS Dresden).
Presentations: I have given an invited talk on this work during the international Workshop Superconducting hybrids: from conventional to exotic, held in Villard de Lans, 7-10 September 2011.
II) SECOND YEAR OF THE PROJECT, held at UC Berkeley (01/08/2011 to 31/07/2012):
During the second year of the project, we have completed the work initiated in the first year (with 2 accepted publications in Physical Review Letters during first half of 2012), and we have also initiated completely new investigations (1 long paper accepted in New Journal of Physics, and one short paper under reviewing in Physical Review Letters).
Those new works introduce models that go beyond the simple idealized models commonly used to describe topological insulators. First we have predicted the new topological phases in graphene under strong mechanical strain (Ref 1 below) in a Letter that has already been cited by 16 preprints in few months. We think this publication might open a new subfield in the study of topological and Dirac matter. Second, we have derived the unusual transport properties of the surface states of topological insulators in presence of a strong hexagonal warping deformation of the Fermi surface (Ref 2 below). Finally we have shown that gate-induced Rashba coupling can also be used as a probe of the helical (or spin-locking) property of the one-dimensional edge modes of the QSH insulators (Ref 3 below).
4) Topological phases and superconductivity in strained graphene
P. Ghaemi, J. Cayssol, D. N. Sheng, A. Vishwanath, Fractional topological phases and broken time reversal symmetry in strained graphene, Physical Review Letters 108, 266801 (June 2012).
Details:
In this theoretical work, we propose a new platform for the study of fractional topological phases. Applying a proper strain on a monoatomic graphene sheet slightly changes the lengths of the carbon-carbon bonds, thereby modifying the electronic structure of graphene. For specific forms of the strain field, the spectrum consists in a succession of flat bands similar to Landau levels. In each valley of graphene, the electrons are submitted to a finite magnetic field. Since time-reversal symmetry is not broken, this nearly uniform pseudo-magnetic fields in one valley is opposite to the pseudofield in the other valley.
First, we have shown the existence of valley ferromagnetism which breaks this time- reversal symmetry spontaneously. This valley ferromagnet has been established by Hartree-Fock calculations (analytical and numerical) at neutral filling. At fractional filling 2/3 (from the bottom of the n=0 pseudo Landau level), we have performed exact diagonalization studies on small systems, and found that a 2/3 Laughlin state develops in one valley leaving the other valley unoccupied.
Second, we have studied other interaction models where the long range Coulomb interaction is modified at short distance (next nearest neighbors). We have found that a slightly attractive next
nearest neighbors attraction can destabilize the 2/3 valley ferromagnet towards a phase where a 1/3 state is realized in each valley. We called this latter state a valley fractional topological insulator by analogy with the spin fractional insulators.
Collaborators: This is a collaboration with Prof. Ashvin Vishwanath (Berkeley, host for the TEMSSOC project), Pouyan Ghaemi (postdoc, Berkeley), Donna Sheng (Prof. Northridge University, Los Angeles). This work has been submitted to Physical Review Letters.
Experimental: We are in contact with a group (Urbana Champain) which is planning transport measurements on strained graphene. We hope that the effect of the strained induced pseudomagnetic fields could induce some signature on the transport (like oscillations).
Our predictions can also be tested in other systems like in cold atoms lattices or in artificial graphenes obtained by patterning a 2 dimensional electron gas or a metallic surface state (H. Manoharan, Stanford).
Presentations: I have presented this work in several invited talks at Urbana Champain (April 2012), les Houches (May 2012), Nordita Stockholm (August 2012) and MPIPKS Dresden (August 2012).
Citations: This work is already cited by 16 preprints from other groups in the field. 5) Hexagonal warping in 3D topological insulators
5) Transport at the surface of 3D topological insulators
Pierre Adroguer, David Carpentier, J. Cayssol,Edmond Orignac, Diffusion at the surface of topological insulators, ArXiv:1205.5209 (Accepted for publication in New Journal of Physics in August 2012).
Detail of the work: We have considered the transport properties of topological insulators surface states in the presence of uncorrelated point-like disorder, both in the classical and quantum regimes. The transport properties of those two-dimensional surface states turned out to depend strongly on the amplitude of the hexagonal warping of their Fermi surface. We demonstrated that a perturbative analysis of the warping fails to describe the transport in experimentally available topological insulators, such as Bi2Se3 and Bi2Te3. Hence we develop a fully non-perturbative description of these effects going beyond existing models and relevant for current experiments. In particular, we find that the dependence of the warping amplitude on the Fermi energy manifests itself in a strong variation of the diffusion constant on this Fermi energy, leading to several important experimental consequences. Moreover, the combination of a strong warping with an in plane Zeeman effect leads to an attenuation of conductance fluctuations in contrast to the situation of unwarped Dirac surface states.
Collaboration: this work is a collaboration with a team in Europe: David Carpentier and Edmond Orignac (ENS-Lyon).
Presentations: preliminary results (before online submission of this work) have been presented by P. Adroguer at the APS March Meeting 2012 in Boston and will also be presented by Jerome Cayssol in a seminar at LPS Orsay in October 2012.
III) THIRD YEAR OF THE PROJECT, held at MPIPKS, Dresden (01/08/2012 to 31/07/2013):
6) Backscattering induced by Rashba coupling in the helical edge state of a QSH insulator
Roni Ilan, J. Cayssol, Jens Bardarson, Joel Moore, Nonequilibrium Transport Through a Gate-Controlled Barrier on the Quantum Spin Hall Edge, Phys. Rev. Lett. 109, 216602 (November 2012).
Detail of the work: The Quantum Spin Hall insulator is characterized by the presence of gapless helical edge states where the spin of the charge carriers is locked to their direction of motion. In order to probe the properties of the edge modes, we have proposed a design of a tunable quantum impurity realized by a local gate under an external magnetic field. This work is a proposal for a new experiment on the QSH insulators which can be readily implemented in current samples of HgTe/CdTe quantum wells. Using the integrability of the impurity model, we have evaluated the conductance for arbitrary interactions, temperatures and voltages, including the effect of Fermi liquid leads. The result can be used to infer the strength of interactions from transport experiments.
Collaboration: this work is a collaboration between Joel Moore (partner of the TEMSSOC project and Professor at UC Berkeley), J. Cayssol (fellow of the TEMSSOC project) and two postdocs at UC Berkeley (R. Ilan and J. Bardarson)
Experimental: Our proposal can be achieved in experimental groups like the one led by Laurens Molenkamp in Wurzburg or Amir Yacoby in Harvard.
Presentations: This work will be presented in the Workshop in Aussois (17 October 2012) and in a Seminar in Orsay, LPS, France (23 October 2012).
7) Floquet topological insulators
J. Cayssol, Balázs Dóra, Ferenc Simon, Roderich Moessner, Optically engineering the topological properties of a spin Hall insulator, PHYSICA STATUS SOLIDI-RAPID RESEARCH LETTERS 7, 101 (February 2013).
Detail of the work: In this short pedagogical review, we explain and discuss the concept of Floquet topological insulator. The light can be used to drive an ordinary insulator or semiconductor (or even semimetallic graphene) into a topological phase. Such a light-induced topological insulator can be of the Chern insulator type (also called Quantum Anomalous Hall Insulator) or of the Quantum Spin Hall insulator (QSH) type.
We also review the use of photons as probes of the 2D QSH insulators. Indeed Teraherz photons can probe the helical structure and the robustness of the edge states of a two-dimensional topological insulator. When circularly polarized electromagnetic waves are shinned onto the topological insulator, a finite photocurrent is induced along the edge of the sample. The sign of this photocurrent is directly related to the handedness of the wave circular polarization. We have computed this photocurrent and shown that it could be measured in future experiments. This idea is also valid for the 2D surface state of 3D topological insulators.
Collaboration: this work is a collaboration between Roderich Moessner (scientific in charge of the TEMSSOC project and director of the Max Planck Institute for the Physics of Complex Systems MPIPKS in Dresden), J. Cayssol (fellow of the TEMSSOC project) and B. Dora and F. Simon from Budapest University.
8) Aharonov-Bohm effect in topological insulator nanowires
J. Dufouleur, L. Veyrat, A. Teichgraber, S. Neuhaus, C. Nowka, S. Hampel, J. Cayssol, J. Schumann, B. Eichler, O. Schmidt, B. Buchner and R. Giraud Phys. Rev. Lett. 110, 186806 (2013)
Detail of the work: We have studied the quantum coherent transport of Dirac fermions in a mesoscopic nanowire of the 3D topological insulator Bi2Se3 in the weak-disorder limit. At very low temperatures, many harmonics are evidenced in the Fourier transform of Aharonov-Bohm oscillations, revealing the long phase- coherence length of surface states. Remarkably, from their exponential temperature dependence, we infer an unusual 1/T power law for the phase coherence length L!(T). This decoherence is typical for quasi- ballistic fermions weakly coupled to the dynamics of their environment.
Collaborators: This is a collaboration with experimentalists in Dresden: Romain Giraud and Joseph Dufouleur (Leibnitz Institute Dresden).
Presentations: This work will be presented in various conferences during the next year.
9) Persistent currents in Dirac fermion rings
D. Sticlet, B. Dora, and J. Cayssol, Persistent currents in Dirac-fermion rings, arXiv: 1307.6964
Descrition of the work: The persistent current in strictly one-dimensional Dirac systems is investigated within two differ- ent models, defined in the continuum and on a lattice, respectively. The object of the study is the effect of a single magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac model, an analytical expression for the persistent current flowing along a ring with a single delta-like magnetic impurity is obtained after regularization of the unbounded negative energy states. The predicted decay of the persistent agrees with the lattice simulations. The results are generalized to finite temperatures. To realize a single Dirac massless fermion, the lattice model breaks the time- reversal symmetry, and, in contrast with the continuum model, a pointlike nonmagnetic impurity can lead to a decay in the persistent current.
10) Chern insulators and Dirac materials
J. Cayssol, Dirac materials and Chern insulators, CRAS (to be published 2013), ArXiv 1301:5902
Details of the work: This review will be a synthesis of my work with different collaborators during the last three years (coinciding with the present project TEMSSOC). I will first explain how Dirac fermions emerge in condensed matter systems. At the most famous example, graphene, the atomic-thin layer of carbon atoms, was first isolated on an insulating substrate in 2004 by two groups in Manchester University and Columbia. Those milestone experiments established the Dirac nature of the charge carriers in graphene. The same year, C.L. Kane and E.G. Mele predicted that intrinsic spin-orbit coupling in graphene, if strong enough, would lead to a novel state of electronic matter called the Quantum Spin Hall (QSH) state. The QSH state is characterized by conducting gapless edge states circulating around an insulating bulk. Those edge states are protected from moderate disorder and interactions by a new topological invariant of the Z_2 nature. While the strength of spin-orbit coupling is too weak in graphene, it was soon predicted and verified by transport experiments that the QSH state is realized in HgTe/CdTe quantum wells. In this manuscript, I will summarize some selected aspects of this huge field of research focused on Dirac matter including graphene and topological insulators. By Dirac matter, we have in mind various systems whose excitations obey a relativistic Dirac-like equation instead of the non relativistic Schrodinger equation. This report is mainly focused on the 2D topological insulators using graphene as a guideline. In part I, the semimetallic character of graphene is derived and the symmetry protection of the Dirac points is discussed while parts II and III are devoted to Chern insulators and QSH insulators respectively.
Presentations: I have given an invited talk on this work in various laboratories in France and Germany. I will also give a pedagogical talk to introduce Topological insulators at the Workshop “Seminaire Dautreppe”, held in Grenoble, 24-25 October 2013.
USE OF RESOURCES: The research overheads have been used during the second year of the project (See financial report C)