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Condensed Matter Physics:

Past, present and future

Reza Asgari

SBU Tehran 4th February ( 2015)

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is a branch of physics that deals with the physical properties

of condensed phases of matter.

Condensed matter physicists seek to understand the behavior of

these phases by using physical laws. In particular, these include the

laws of quantum mechanics, electromagnetism and statistical mechanics.

From Wikipedia

Condensed Matter Physics

More descriptions? Applications? Future perspectives?

We will discuss

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Condensed matter physics is one of the largest and most vibrant areas of physics.

1. In the past 30 years the Nobel Prize in Physics has been awarded 14 times for work on condensed matter.

2. Since 1998 seven condensed matter physicists [Kohn, Heeger, Ertl, Shechtmann, Betzig, Hell, Moerner]

have received the Nobel Prize in Chemistry!

3. Of the 144 physicists who were most highly cited in 2014 for papers in the period 2002-2012

(ISI highlycited.com), more than one half are condensed matter physicists.

4. The largest physics conference in the world is the annual March meeting of the American

Physical Society. It attracts almost 10,000 attendees and is focused on condensed matter.

Many of the materials first studied by condensed matter physicists are now the basis of modern technology.

How important CM is

Adopted from Ross McKenzie’s webpage

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• Immediate aftermath of quantum mechanics: electricity;

diffraction, transport properties,…

• Many body physics in the cold war: degenerate electron gas;

Fermi liquid,….

• Modern era of correlated matter physics: Luttinger liquid;

FQHE,….

Different eras

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Fermions

With a heavy heart, I have decided that Fermi Dirac, not Einstein

is the correct statistics, and I have decided to write a short note

on paramagnetism.

Wolfgang Pauli, letter to Schrodinger, Nov 1925

Adopted from P Coleman, Ann. Herni Poincare, 4, 559 (2003)

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• First Nobel prize 1901 to W. C. Roentgen for the discovery of penetrating

x-rays. M. von Laue (1912) EM waves of very short wavelengths,

could be diffracted by the atoms of crystals

( cystography, metallurgy, elasticity, etc)

• In the 1940s these and other fields consolidated into the newly named

discipline of “ Solid State Physics”

• Two decades later, was enlarged to include the study of liquids and given

the name “ Condensed Matter Physics”.

Early 20th centaury

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• Many body community made a sequence of astonishing advances in the

1950s.

David Bohm and David Pines (1953) : could separate the strongly

interacting gas via a unitary transformation into two well-separated sets of

excitations, plasmons, and low-energy electrons.

• The idea that high energy modes of the system can be successively

eliminated to give rise to a renormalized picture of the residual low-

energy excitations.

( The idea of the renormalization group theory)

MB physics without Feynman diagrams

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• Brueckner (1955), Gell-Mann and Brueckner (1957), Galitski and Migdal

(1958), Matsubara (1955)

• Landau Fermi liquid theory (1957)

• Broken Symmetry: phase transitions take place via the process of

symmetry reduction. ( Landau) Onsager and Penrose (1962)

• Localizations ( Anderson 1958)

MB physics Feynman diagrams

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It is likely, then, considering the superconducting analog, that the way is now open for a degenerate-vacuum theory of the Nambu type without any difficulties involving either zero-mass Yang-Mills gauge bosons or zero-mass Goldstone bosons. These two types of bosons seem capable of “canceling each other out” and leaving finite mass bosons only.

Anderson Higgs mechanism

P W Anderson, Physical Review 1963

when you have both gauge symmetry and spontaneous symmetry breaking, the Nambu-

Goldstone massless mode can combine with the massless gauge field modes to produce a

physical massive vector field .

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Many body physics: complexity and diversity

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Scales

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Complexity

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Quantum matter

1) Systems containing a macroscopic number

obeying quantum statistics

1) Systems has macroscopic quantum properties

2) Metals, superfluids, ultra cold atomic gases, …

3) Topological insulators, FQHE,…

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Quantum states

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Theory for everything

Laughlin and Pines, PNAS 97, 28 (1999)

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How to solve it?

1) Structural reducibility

2) Universality

3) Concept of statistics

4) Symmetries

Altland and Simons, Condensed Matter Field Theory (2010)

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Examples

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Examples

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Examples

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• The whole is greater than the sum of the parts.

• A system consist of many interactions can have emergent properties

that are

a) qualitatively different from,

b) are not reducible to

c) are not predicted from

the properties of the constituent parts.

Emergence

Adopted from Ross McKenzie’s webpage

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Emergence leads to a stratification of physics

Properties at each level are

determined by interactions between

constituents at the lower level.

However, an effective Hamiltonian

can be defined at each level.

P. W. Anderson, More is Different

Science 177, 393 (1972)

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-In classical world we have solid, liquid and gas phases

-In quantum world we have metals, insulators, magnetisms

, superconductors, etc : spontenious symmetry breaking

Broken rotational symmetry Broken gauge symmetry

Phases of matter

Qi and Zhang PRB 2008

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New phases of matter in 2D quantum

electron systems

-Quantum Hall effect

-Super fluidity and superconductors

-Localization, disorder and quantum magnetism

Nobel prize ’85,’98

Nobel prize ’72,’73,’87,’96’03

Nobel prize ’70,’77,’94,’07

- Quantum phase transition, condensationNobel prize ’82,’01

Hasan and kane RMP, 2011

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Summary I: Condensed Matter Physics

-Study materials in which many particles interact to each others

-Deal with all materials and tools around us

-Asks many questions about materials that you can feel,

manipulate, change, perturb, built…. them

-Many of the materials first studied by condensed matter

physicists are now the basis of modern technology. Common examples include crystalline silicon in computer chips, superconductors

in hospital magnetic imaging machines, magnetic multilayers in computer memories,

and liquid crystals in digital displays.

-There are significant interactions with other fields

such as chemistry, materials science, biophysics, engineering environment, energy,

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We have been working on:

1. Phosphorene (2014-)

2. Oxide interfaces (2004-2007), (2011-)

3. Transition metal dichalcogenides (2004!, 2010-)

4. Silicene (2010-)

5. Artificial honeycomb structures (2011-)

6. Boron nitride (2012-)

7. Graphene (2004)

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Why 2D Systems?

1) New and exciting physics:

dimensionality, size-effect

correlated charge, spin and heat

2) Technologically useful properties

optical and electronic properties

mechanical and chemical response

• 3D materials with melting temperature over 1000

• 3D parents must be chemically inert and exhibit

no decomposed surface layer in air

• Insulating and semiconducting 2D crystals are more likely to

be stable than metallic ones

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A. K. Geim and I . V. Grigoieva, Nature, 499, 419 (2013)

2D candidate’s conditions

2D layered materials: Library

A. K. Geim and I . V. Grigoieva, Nature, 499, 419 (2013)

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Classification

How many 2D systems can we classified?

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Classification

• Layered van der Waals solids

• Layered ionic solids

• Surface growth of nanolayer materials

• 2D artificial systems

• 2D topological insulator solids

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Layered van der Waals solids

These crystal structures feature neutral, single-atom-thick or

polyhedral-thick layers of atoms that are covalently or ionically

connected with their neighbors within each layer, whereas the

layers are held together via van der Waals bonding along the

third axis.

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Layered van der Waals solids

• Mechanical exfoliation of large crystals using “Scotch tape”

• Chemical exfoliation

Novoselov, et al Nature 438,197 (2005)

Epitaxy, requires ultrahigh vacuum conditions: Expensive Science 312, 1192 (2006)

Various chemical methods. Nano Lett. 8, 2442 (2008) , Nature Nanotech. 3, 270 (2008); ibid

4,217(2009)

Chemical Vapour Deposition : Nature 457, 706 (2009), Nano Lett. 9, 30 (2009)

Atomic structure of graphene

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Band structure and saddle points

37A. Geim Science 324, 1530(2009)

dispersion relations & chirality

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Example: 2D system

Phosphorene( January 2014)

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white phosphorus, often abbreviated as WP. It consists of

tetrahedral P4 molecules, in which each atom is bound to the other

three atoms by a single bond. This P4 tetrahedron is also present in

liquid and gaseous phosphorus up to the temperature of 800 °C

when it starts decomposing to P2 molecules. Solid white exists in

two forms. At low-temperatures, the β form is stable. At high-

temperatures the α form is predominant. These forms differ in terms

of the relative orientations of the constituent P4 tetrahedra.

Wikipedia

Phosphorus

Red P Black PWhite P

40Liu, et al, ACS Nano, 8, 4033 (2014);

Li, et al, arXiv 1401.4117

Phosphorene

Black Phosphorus

41Liu, et al, ACS Nano, 8, 4033 (2014);

Band structure

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Electronic and Phonons

43M. Elahi, K. Khalij, S.M. Tabatabaei, M. Pourfath and R. Asgari to appear in Phys. Rev. B (2015)

Strain

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Rodin, et al, arXiv 1401.1801

Rudenko, Katsnelson, arXiv 1404.0618

Ezawa, arXiv 1404.5788

Effective low-energy Hamiltonian

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Another example

Oxide interfaces

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• Herbert Kroemer ( NP 2000):

“ The interface is the device”

• Fundamental questions:

What new physics (not occurring in bulk

in either component) occurs at interface?

Can we predict the changes in many-body phenomena (SC, MIT)

occurring near interfaces?

LaAlO3/SrTiO3

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48Hwang , et al Nature Materials, 11,103 (2012)

LaAlO3/SrTiO3

49Nakagawa , et al Nature 5,204 (2006)

50Nakagawa , et al Nature 5,204 (2006)

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Reyren, et al Science 317,1196 (2007)

Brinkman, et al, Nature Mater, 6, 493 (2007)

Li, et al, Nature Physics, 7, 762 (2011)

Bert et al, Nature Physics, 7, 767 (2011)

Dikin, et al, Phys. Rev. Lett. 107, 056802 (2011)

Michaeli, et al, Phys. Rev. Lett. 108, 117003 (2012)

Coexistence of magnetic order and superconductivity LaAlO3/SrTiO3

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LaAlO3/SrTiO3

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Another example

MoS2

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TMDCs: MoS2 crystal

Wilson and Yaffe, Adv. Phys. 18, 193 (1969)

Romley, Murray,Yoffe, J. Phys. C 5 (1972)

Mattheis, Phys. Rev. B 8, 3719 (1973)

Helveg, et al Phys. Rev. Lett. 84, 951 (2000)

kobayashi, Yamauchi, Phys. Rev. B 51, 17085 (1995)

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Bulk, quadri-, bi- and monolayer

Nature communication (2010)

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Valley polarization

Zeng, et al, Nature Nano 7, 490 (2012)

H Rostami, R. Asgari, Phys. Rev. B 89, 115413(2014)

T. Cao, et al Nature Commuin. DoI: 10.1038/ncomms1882 (2012)

)(||)()( kuippkukP yxc

c

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2222

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ktakPvc

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||||

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PP

PPP

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low-energy Hamiltonian

Di Xiao, et al , Phys. Rev. Lett. 108,196802 (2012)

Rostami, Moghaddam, Reza Asgari Phys. Rev. B 88, 085440 (2013)

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MoS2 crystal: Strain effects

Johari, Shenoy, ACS Nano 6, 5449 (2012),

A. Castellanos-Gomez, et al Nano lett. 13, 5361 (2013)

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MoS2 crystal: Strain effects

Yun, Han, Hong, Kim, Lee, Phys. Rev. B 85, 033305 (2012)

Thanks for your attention

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