Interactions in graphene

The electrons in graphene are particularly nimble and their interactions are usually ignored together with the effects of some defects. However, recently more and more attention have been paid to them, e.g., about superconductivity and other new orders. Here is a brief summary by P. Guinea [http://www.condmatjournalclub.org/wp-content/uploads/2011/09/JCCM_SEPTEMBER_2011_01.pdf].

1. Broken symmetry states and divergent resistance in suspended
bilayer graphene
Benjamin E. Feldman, Jens Martin, Amir Yacoby,
arXiv:0909.2883, Nature Physics 5, 889 (2009)
2. Local Compressibility Measurements of Correlated States in
Suspended Bilayer Graphene
Jens Martin, Benjamin E. Feldman, R. Thomas Weitz, Monica T. Allen,
Amir Yacoby,
arXiv:1009.2069, Phys. Rev. Lett. 105, 256806 (2010)
3. Interaction-Driven Spectrum Reconstruction in Bilayer Graphene
A. S. Mayorov, D. C. Elias, M. Mucha-Kruczynski, R. V. Gorbachev, T. Tu-
dorovskiy, A. Zhukov, S. V. Morozov, M. I. Katsnelson, V. I. Fal'ko, A. K.
Geim, K. S. Novoselov,
arXiv:1108.1742, Science 333, 860 (2011)
4. Transport Spectroscopy of Symmetry-Broken Insulating States
in Bilayer Graphene
J. Velasco Jr., L. Jing, W. Bao, Y. Lee, P. Kratz, V. Aji, M. Bockrath, C.N.
Lau, C. Varma, R. Stillwell, D. Smirnov, Fan Zhang, J. Jung,
A.H. MacDonald
arXiv:1108.1609

BEC on an optical hexagonal lattice

The technology with lasers has incredibly enriched our understanding of a huge width of systems. The ability to prepare honeycomb lattice offers chances to study graphene-type physics and beyond. In this PRL paper, the authors addressed the issues of what would befall a Bose-Einstein condensate moving on a honeycomb lattice. They employed Gross-Pitaviskii equation, which is a mean-field theory for describing superfluids, to compute the band structure and found that, arbitrary interaction would drastically alter the structure around the Dirac points. Is it possible to observe similar stuff using graphene instead of an artificial lattice ? One needs to have superfluid to flow on graphene. The candidate is cooper pairs condensate, which may be created by placing a superconductor in contact with a layer of graphene.

The ability to prepare ultracold atoms in graphenelike hexagonal optical lattices is expanding the types of systems in which Dirac dynamics can be observed. In such cold-atom systems, one could, in principle, study the interplay between superfluidity and Dirac physics. In a paper appearing in Physical Review Letters, Zhu Chen at the Chinese Academy of Sciences and Biao Wu of Peking University use mean-field theory to calculate the Bloch bands of a Bose-Einstein condensate confined to a hexagonal optical lattice.

The Dirac point is a point in the Brillouin zone around which the energy-momentum relation is linear. Its existence in graphene is at the heart of this material’s unusual properties, in which electrons behave as massless particles. Chen and Wu’s study predicts, surprisingly, that in the analog cold-atom system, the topological structure of the Dirac point is drastically modified: intersecting tubelike bands appear around the original Dirac point, giving rise to a set of new Dirac points that form a closed curve. More importantly, this transformation should occur even with an arbitrarily small interaction between the atoms, upending the idea that such topological effects can only occur in the presence of a finite interaction between atoms.

The modified band structure prevents an adiabatic evolution of a state across the Dirac point, violating the usual quantum rule that a system remains in its instantaneous eigenstate if an external perturbation is sufficiently slow. This effect could be tested experimentally in a so-called triple-well structure, which is a combination of rectangular and triangular optical lattices. – Hari Dahal [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.065301]

Electron induced rippling in graphene

Physicists are really blessed by nature in the sense that, they have all the time been offered some new objects that admit very rich phenomena to be explored. Latest examples include Graphene and Topological Insulators. Since its discovery, graphene never stops yielding surprising things for physicists. This time comes something that (again, considering Dirac physics) parallels particle physics: the strain field associated with the flexural phonon condenses in the same way as the Higgs field in the Standard Model [1]. Don't miss reading it !

[1]PRL, 106:045502(2011)

Graphene is really quantum

Some 'non-locality' is claimed with the electrons in graphene [Science 15 April 2011: 328-330]. The experimenters measure the voltages between two electrodes that are far away from the region where the currents are suppsed to flow. And the voltage does not vanish at even room temperature, which is not possible for classical electrons. They associate this with the strongly coherent motion of the graphene electrons. They are so quantum !

In their experiments, an electrical current is passed between two electrodes in close proximity to each other (see the figure, upper inset), and they detect a voltage far away from those electrodes. In an ordinary material under the same conditions (at room temperature and small magnetic fields), this would not happen because the electrons are incoherent and behave classically. After a few collisions with impurities in the system, the electrons would lose their phase information and undergo random walk. To reach nonlocal contacts, this would be a walk too far, and no voltage would be generated. This indicates that graphene is behaving in a quantum mechanical way and creating a nonlocal voltage under unexpected conditions. How is this possible? [http://www.sciencemag.org/content/332/6027/315.full]

Twist impacts graphene greatly

It is reported that, inter-layer rotation of a stack of graphene drastically changes the electronic properties. For large rotation, the inter-layer effects disappear.

" Stacks of graphene are expected to possess drastically different electronic properties compared to their single-layer components, as a result of interlayer coupling. Theory dictates that graphene’s massless low-energy excitations should disappear, even for the simple bilayer structure. However, experiments have shown that, paradoxically, the electronic properties of single layers somehow survive in layered structures. Theorists have suggested that a relative rotation of one layer with respect to the one below it—a “twist” in the stacking—might be the resolution of the paradox.

Now, in a paper appearing in Physical Review Letters, Adina Luican and collaborators from Rutgers University and the Massachusetts Institute of Technology, both in the US, and the University of Manchester, UK, provide experimental proof of the influence of twisting on the band structure of bilayer graphene. Using scanning tunneling microscopy and spectroscopy, the researchers find that for twist angles above 20°, the electronic properties of the twisted layers are practically indistinguishable from those of single-layer graphene. Based on their measurements, Luican et al. conclude that at small angles, the massless Dirac fermion picture of graphene breaks down and the electronic spectrum is dominated by a saddle point feature, while at large rotation angles, the intersection point in the spectrum shifts to irrelevant high energies and the familiar Dirac energy dispersion is recovered. – Alexios Klironomos " [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.106.126802]

Curved space generating mass ?

Since Newtonian times, physicists have to talk of mass, a quantity having its origin a deep myth. In Newtonian mechanics, mass is impedes the change of velocity. In relativity, mass (in the conventional sense) is no more than the static energy. In non-relativistic quantum mechanics, mass plays to make the entity more of a particle. In relativistic quantum mechanics, mass is the energy required to generate a pair of electron and positron. In condensed matter physics, mass is the minimum energy to excite a system. Besides, mass also measures some correlation length.

Although we know many things about mass, we don't have a clear clue where mass comes from. In the standard model, all masses are produced by Higss mechanism: every mass-less particle moves in some kind of ether that is the Higgs clouds and acquires mass. Another idea is, mass can be generated by curved space, or more accurately, compactified dimension. Compactifying a dimension yields finite motion, one that is confined. According to quantum mechanics, finite motion implies discrete levels and finite gaps, so comes the mass. Yet, a clear regime is missing.

Graphene provides a playground for studying this regime. These authors roll the graphene and obtain a massive 1D system from a 2D massless Dirac system [http://arxiv.org/ftp/arxiv/papers/1010/1010.3437.pdf]. This is no surprising and actually was known before. But this is an example showing how mass might be generated this way. However, back to elementary particle physics, where is the hidden dimension in addition to the 4D space-time we are all used to ? Another question is, how the as-obtained masses interact in a gravitational way ? Anyway, mass should be gravitationally active !!!!

Topological insulators and one of its creators

This is a talk by Mr. Zhang, on the pogress and history of topological insulators and its relation to other subjects in condensed matter physics.

Below is the link of this talk:

http://www.youtube.com/watch?v=Qg8Yu-Ju3Vw&NR=1

And Below is the link of an conversation with the talker:

http://www.youtube.com/watch?v=d5s6nZtPAHE&feature=related

New surge in topological insulators

[1]PRL 105, 076801 (2010)
[2]PHYSICAL REVIEW B 82, 081305 R 2010
[3]Physics 3, 66 (2010)

The prediction [1] and experimental discovery [2, 3] of a class of materials known as topological insulators is a major recent event in the condensed matter physics community. Why do two- and three-dimensional topological insulators (such as HgTe/CdTe [2] and Bi2Se3 [3], respectively) attract so much interest? Thinking practically, these materials open a rich vista of possible applications and devices based on the unique interplay between spin and charge. More fundamentally,
there is much to enjoy from a physics point of view, including the aesthetic spin-resolved Fermi surface topology [3], the possibility of hosting Majorana fermions (a fermion that is its own antiparticle) in a solid-state system [4], and the intrinsic quantum spin Hall effect, which can be thought of as two copies of the quantum Hall effect for spin-up and spin-down electrons [5]. Now, an exciting new addition to the above list comes from two teams that are reporting the first experimental observation of quantized topological surface states forming Landau levels in the presence of a magnetic field. The two papers - one appearing in Physical Review Letters by Peng Cheng and colleagues at Tsinghua University in China, and collaborators in the US, the other, appearing as a Rapid Communication in Physical Review B, by Tetsuo Hanaguri at Japan’s RIKEN Advanced Science Institute in Wako and scientists at the Tokyo Institute of Technology - pave the way for seeing a quantum Hall effect in topological insulators.

JPCM: 2009 highlights, now free for reading until the end of this year

JPCM has produced its 2009 highlights. The good news is that they are available for free till the end of this year. I would like to suggest the following pieces:

[1]The transport properties of graphen,

N M R Peres 2009 J. Phys.: Condens. Matter 21 323201,

We review the transport properties of graphene, considering both the case of bulk graphene and that of nanoribbons of this material at zero magnetic field. We discuss: Klein tunneling, transport by evanescent waves when the chemical potential crosses the Dirac point, the conductance of narrow graphene ribbons, the optical conductivity of pristine graphene, and the effect of disorder on the DC conductivity of graphene.

[2] Magnetic field induced confinement–deconfinement transition in graphene quantum dot,

G Giavaras et al 2009 J. Phys.: Condens. Matter 21 102201

Massless Dirac particles cannot be confined by an electrostatic potential. This is a problem for making graphene quantum dots but confinement can be achieved with a magnetic field and here general conditions for confined and deconfined states are derived. There is a class of potentials for which the character of the state can be controlled at will. Then a confinement–deconfinement transition occurs which allows the Klein paradox to be probed experimentally in graphene dots. A dot design suitable for this experiment is presented.

[3]Exact mapping of the d_x²−y² Cooper-pair wavefunction onto the spin fluctuations in cuprates: the Fermi surface as a driver for 'high T_c' superconductivity

Ross D McDonald et al 2009 J. Phys.: Condens. Matter 21 012201

We propose that the extraordinarily high superconducting transition temperatures in the cuprates are driven by an exact mapping of the d_x²−y² Cooper-pair wavefunction onto the incommensurate spin fluctuations observed in neutron-scattering experiments. This is manifested in the direct correspondence between the inverse of the incommensurability factor δ seen in inelastic neutron-scattering experiments and the measured superconducting coherence length ξ₀. Strikingly, the relationship between ξ₀ and δ is valid for both La_2−xSr_xCuO₄ and YBa₂Cu₃O_7−x, suggesting a common mechanism for superconductivity across the entire hole-doped cuprate family. Using data from recent quantum-oscillation experiments in the cuprates, we propose that the fluctuations responsible for superconductivity are driven by a Fermi-surface instability. On the basis of these findings, one can specify the optimal characteristics of a solid that will exhibit 'high T_c' superconductivity.

Simulation of Dirac equation

This is an experimental work [1] on mimicking the motion of a particle that is subject to Dirac-type model. It managed to detect a quivering motion, the so-called Zitterbewegung, which is understood to arise from the interference between positive energy components and negative energy components. Such quivering occurs at very high frequency (ten powered to 21 Hz) and with very tiny amplitude (of the order of Compton wavelength) for electrons in vacuum, and very difficult to observe. In this work, the authors considered the Dirac equation in 1+1 dimensions, which was realized with a single trapped ion. For such a 'relativistic' ion, the oscillation period is couple of microseconds.

Experimental recipes:
(1)trap a single 40Ca1 ion in a linear Paul trap22 with axial trapping frequency vax52p31.36MHz and radial trapping frequency vrad52p33 MHz;
(2)prepare the ion in the axial motional ground
state and in the internal state jS1/2,mJ51/2æ (mJ, magnetic quantum
number).
(3)identify spinor states.

How to measure the average position of the trapped ion without a full reconstruction of the state:
To measure the position for a motional state rm, we have to
(1) prepare the ion’s internal state in an eigenstate of sy,
(2) apply a unitary transformation, U(t), that maps information about rm onto the internal states;
(3) record the changing excitation as a function of the probe time t, by measuring
fluorescence22.

Results are displayed on the figures.


[1]Vol 463|7 January 2010| doi:10.1038/nature08688