Condensed Matter Theory Group Research

1. Introduction: Flora and Fauna, Individual flavors and colors

Plan

The Flora

AtomicClusters

StrongCorrelations

Graphene

Bose-Einstein Condensates

SuperconductivityHigh-Tc and Conventional

Density Functional Theory

Nonlinear Dynamics Turbulence

Transport, Traffic

Quantum AnnealingQuantum Transitions

Non-Equilibrium Stat Mech

Quantum Spin Dynamics

Molecular MotorsNano Pistons

Photonic Band-GapMeta materials

Nano-Particle Physics

Chaos

Metal-Insulator TransitionsAnti/Ferromagnetism

Quantum Information/ Computation

DecoherenceOpen Systems

The Fauna

the indiavidual flavors and colors...

Debashish Chowdhury

Professor (Ph.D., IIT Kanpur, 1984)

debch@iitk.ac.in Ph: 7039 (O – FB385)

Areas of Interest: Statistical and Biological Physics

http://www.proweb.org/kinesin/CrystalStruc/Dimer-down-rotaxis.jpg

Animated cartoon: MCRI, U.K.

Theoretical models of Nano-motors in living cells

MotorInput Output

Chemical energy

Mechanical energy

Challenges: Effects of design and mechano-chemical cycles on efficiency & power output of these cyclic machines operating far from thermodynamic equilibrium.

http://www.mpasmb-hamburg.mpg.de/

Helicase unzips double-stranded DNA and moves along one of the strands.

Chowdhury & collaborators, Phys. Rev. E (2008)

Ribosome moves along mRNA track, decodes the genetic message in the sequence on mRNA and synthesizes a protein

Debashish Chowdhury (with students & collaborators)

Kinesin protein is like a porter

(II) Theoretical models of Nano-pistons in living cells

K+

K-

α

Initiation

E P A E P A E P A

βModel of ribosome traffic during protein synthesis: A.Basu, A. Garai, D. Chowdhury, D. Chowdhury, T.V. Ramakrishnan , Phys. Rev. E (2007) (2009a) (2009b).

(III) Theoretical models of Collective movements: Traffic and pattern formation

KIF1A (Red)

10 pM

100 pM

1000pM

2 µmKinesin traffic on MT: D. Chowdhury & collaborators, Phys. Rev. Lett. (2005), (2007)

MT (Green)

Polymerizing stiff microtubule pushing an obstacle

Debashish Chowdhury (with students & collaborators)

List of major Publications in the last 3 years

1. Aakash Basu and Debashish Chowdhury, Phys. Rev. E (APS, USA) 75, 021902 (2007).

2. P. Greulich, Ashok Garai, K. Nishinari, A. Schadschneider and Debashish Chowdhury, Phys. Rev. E (APS, USA) 75, 041905 (2007).

3. Aakash Basu and Debashish Chowdhury, Amer. J. Phys. (AAPT/AIP, USA) 75, 931 (2007).

4. Tripti Tripathi and Debashish Chowdhury, Phys. Rev. E (APS, USA) 77, 011921 (2008).

5. Debashish Chowdhury, Aakash Basu, Ashok Garai, P. Greulich, K. Nishinari, A. Schadschneider and Tripti Tripathi, European Physical Journal B (Springer/ EDP Sciences/ IPS) 64, 593 (2008).

6. Debashish Chowdhury, Comp. Science and Engg. (AIP/IEEE) March issue, 80 (2008).

7. Debashish Chowdhury, Ashok Garai and J.S. Wang, Phys. Rev. E (APS, USA) 77, 050902 (Rapid Commun.)(2008).

8. Ashok Garai, Debashish Chowdhury and M. D. Betterton, Phys. Rev. E (APS, USA) 77, 061910 (2008).

9. B. Govindan, M. Gopalakrishnan and Debashish Chowdhury, Europhys. Lett. 83, 40006 (2008).

10. T. Tripathi and Debashish Chowdhury, Europhys. Lett. 84, 68004 (2008).

11. T. Tripathi, G.M. Schutz and Debashish Chowdhury, JSTAT (IOP,UK), P08018 (2009).

12. A. John, A. Schadschneider, Debashish Chowdhury and K. Nishinari, Phys. Rev. Lett. (APS, USA) 102, 108001 (2009).

13. A. Garai, Debashish Chowdhury and T.V. Ramakrishnan, Phys. Rev. E (APS, USA) 79 , 011916 (2009).

14. A. Garai, D. Chowdhury, Debashish Chowdhury and T.V. Ramakrishnan, Phys. Rev. E(APS, USA) 80, 011908 (2009).

Amit Dutta

Associate Professor (Ph.D., SINP, 2000)

dutta@iitk.ac.in Ph: 7471 (O – FB484)

Areas of Interest: Quantum phase transitions

Quantum Statistical Mechanics: Statics and Quantum Statistical Mechanics: Statics and DynamicsDynamicsAmit DuttaAmit Dutta

QuantumSystemsat T=0

Tune the quantum fluctuations Quantum Phase

Transitions

Classical Critical Point: Usually Driven by Temperature

Order parameter vanishes continuously at the critical pointOrder parameter vanishes continuously at the critical point

A characteristic length Scale diverges at the critical pointA characteristic length Scale diverges at the critical point

Quantum critical point (QCP):Quantum critical point (QCP):

• Driven by quantum mechanical uncertainity relation at T=0Driven by quantum mechanical uncertainity relation at T=0• Statics and Dynamics are entangledStatics and Dynamics are entangled• Diverging length scale & Diverging relaxation timeDiverging length scale & Diverging relaxation time• Although a T=0 phenomena, it shows its signature at finite temperatureAlthough a T=0 phenomena, it shows its signature at finite temperature

By changing a parameter

Experimental Systems: Experimental Systems: Quantum Spin GlassesQuantum Spin Glasses

Quantum Dynamics through a QCP: Quenching

Slow change ofa parameter

OptimizationAnneling

Defect Production

?What happens if a quantum system is driven through a Quantum Critical Point ?What happens if a quantum system is driven through a Quantum Critical Point

Sudden Change of aparameter

At the quantum critical pointquantum critical point the relaxation time is infinity: The system fails to respond to any external perturbation. Final state contains defects

Systems evolvesto the final stateQuantum Mechanicallyfrom a disordered initialcondition Defect Generation Defect Generation

: Quantum Annealing Optimization : Quantum Annealing Optimization

Classical Frustrated

System

Add a Non-commuting

Termh

h large;Ground state

known

Reduce h slowly to zero;

System evolves quantum

mechanically

Ground stateOf

Classical System

Optimization: Using Quantum Mechanical Adiabatic Theorem Faster than Thermal Annealing

Kibble-Zurek ScalingKibble-Zurek Scaling

The density of defect in the final state following a slow quench where a parameter is changed at a rate scales as

tτ

1ατ

αα depends on dimension and the critical exponents depends on dimension and the critical exponents of the quantum critical pointof the quantum critical point

:Questions We ask :Questions We ask How robust is the Universality in Kibble-Zurek Scaling?How robust is the Universality in Kibble-Zurek Scaling?Is there a similar Universality for a sudden Quench?Is there a similar Universality for a sudden Quench? How efficient is Quantum Annealing if system crosses a Critical Point?How efficient is Quantum Annealing if system crosses a Critical Point? How is the scaling form of defect density for generalized quenching schemes?How is the scaling form of defect density for generalized quenching schemes? What happens if the system is coupled to heat bath?What happens if the system is coupled to heat bath? Behavior of Fidelity, Entanglement and Entanglement Entropy Behavior of Fidelity, Entanglement and Entanglement Entropy

in passage through quantum Critical point??in passage through quantum Critical point??

Recent Publications:Victor Mukherjee and A. Dutta, J. Stat. Mech. (2009) P05005 Debanjan Chowdhury, Uma Divakaran, Amit Dutta ,Phys. Rev. E, 81, 012101 (2010) Uma Divakaran, Amit Dutta, Diptiman Sen, Phys. Rev. B 81, 054306 (2010) Amit Dutta, R. R. P. Singh and Uma Divakaran, to appear in Euro. Phys. Lett. (2010)

Tarun Kanti Ghosh

Assistant Professor (Ph.D., IMSc, 2003)

tkghosh@iitk.ac.in Ph: 7276 (O – FB352)

Areas of Interest: Utra-cold atomic gases, Nanoscopic physics

H=v F σ⋅p

E k ≈ℏ vF∣k∣

Quantum Condensed Matter Systems: Carbon-based Materials

Tarun Kanti Ghosh

Research Activities

1. Graphene magnetic waveguide

2. Effect of Coulomb interaction on transport properties of graphene nanoribbon

3. Electrical transport properties of graphene irradiated by microwave radiation

Reference: A. H. Castro Neto et al., Reviews of Modern Physics 81, 109 (2009)

Spintronics Electron: object with charge –e with spin-1/2: + =

So far, electronics has completely neglected the SPIN

Spintronics is a multidisciplinary field whose central theme is the active manipulation of spin degree of freedom in solid state systems

Examples:

1. GMR: Giant Magnetoresistive Effect

2. Spin polarized transport in semiconductor: Spin-Field Effect Transistor, Spind Diode

3. Spin based quantum computing

Research Activities

1. Effect of magnetic field due to electron’s spin magnetic moment on spin relaxation length

2. Effect of Hyperfine interaction on Spin Field Effect Transistor

3. Quantum Spin Hall effect

Reference: Introduction to Spintronics by S. Bandyopadhyay and M. Cahay

CollaboratorsProf. Reinhold Egger (Duesseldorf University, Germany)Dr. Bahniman Ghosh (EE, IIT-K)

Group Members:

Sk. Firoz Islam (Ph. D.) Akashdeep Kamra (B. Tech-M. Tech in EE) Tutul Biswas ( M. Sc.-Ph. D.) Debjit Kar (2 year M. Sc.)

Publications

• T. K. Ghosh, Journal of Physics: Condensed Matter 21, 045505 (2009)

• W. Hausler, A. De Martino, T. K. Ghosh and R. Egger, Phys. Rev. B 78, 165402 (2008)

Sutapa Mukherjee

Assistant Professor (Ph.D., IOP, Bhubaneswar, 1996)

sutapam@iitk.ac.in Ph: 7119 (O – FB386)

Areas of Interest: Non-Equilibrium Statistical Mechanics

Understanding phase transitions in non equilibrium systems through phase-plane analysis

Non-Equilibrium Statistical Mechanics: Sutapa Mukherji

Asymmetric simple exclusion processes: a class of non-equilibrium systems that show variety of boundary-induced phase transitions

Areas of recent interest are :

motion of molecular motors dynamics of biopolymers

transport on networks,

phase transitions in driven systems

α β

Sites occupied by particles Empty sites

Particles can hop to the forward site if it is empty asymmetry

Two particles cannot occupy the same site at the same time exclusion

Particle current

SIMPLEST MODEL: System out of equilibrium

Particle injection rate

β Particle withdrawal rate

At the end of the lattice:

Reason for being out of equilibrium

Depending on the boundary rates, there can be different phases with distinct particle distributionsacross the lattice

Boundary-induced phase transitions

¿

α

Phase diagram in the steady state

α

β

1 / 2

1 / 2

Maximal current phase

x x

High density phase

Low density phase

: Density profile at position

ρ b= 1 / 2

α

1 − β

1 − β

α

ρb1 / 2

ρb1 /2

ρ

ρ

x

Phase diagrams change significantly depending on the particle dynamics:

Repulsive/ attractive Interaction between the particles in addition to mutual exclusion

Two species of particles moving in opposite directions

More than one channel along which particles hop.

Numerical simulations

Numerical solution of the underlying differential equation describing the particle dynamics

Exact analysis in very special cases

Other approximation methods

Typically the methods that are followed

Phase diagrams:

The number of phases with distinct particle distibutions are different for different systems.

The particle density value in the bulk vary from one phase to the other

We propose a general method to understand all these features analytically

• We start with the continuum equation(s) that describe the particle dynamics in the steady state

• Phase-plane analysis is done for the equations: find the equilibrium points, do the the stability analysis, draw the phase-portrait.

• Bulk density values in different phases are given by the values of the equilibrium points (fixed points) of these equations

•The flow trajectories in the phase-portrait tell about the location/shapes of the boundary layers

•The number of phase transitions can be related to the number of equilibrium points.

References related to this work

Sutapa Mukherji, Phys. Rev. E 79, 041140 (2009)

Sutapa Mukherji, Phys. Rev. E 76, 011127 (2007)

This method gives a lot of insight about the phase transitions in all the models mentioned before

Rajendra Prasad Professor (Ph.D., Roorkee, 1976) rprasad@iitk.ac.in Ph: 7065/7092 (O - FB-373) Areas of Interest: Atomic clusters and nanostructures

Dep

artm

ent

of P

hysics

Hydrogenated Silicon Clusters

Rajendra PrasadWith

D. Balamurugan, M. K. Harbola, J . Thingna andS. Auluck

• Effect of Hydrogenation• Charge clusters – Symmetry Breaking• Photo-absorption cross section using TDDFT

Dep

artm

ent

of P

hysics

Bismuth Titanate

Rajendra PrasadWith

Amritendu Roy, Ashish Garg, Anurag Shrinagar and S. Auluck

• Shows ferroelectric behavior

• Important for FRAMs

• Explained ferroelectric behavior based on electronic structure calculations

• Found the correct ground state structure which gives rise to ferroelectric polarization

Ferroelectric BiT:B1a1 (7)

Dep

artm

ent

of P

hysics

Lithium Manganese Oxides

Rajendra PrasadWith

Roy Benedik, M. Thackray, S. L. Gupta, G. Singh and Rajeev Gupta

• Potential battery material

• Explained phase stability by doping

• Studied rhombohedral, monoclinic, orthorhombic and spinel phases Cubic Spinel (Fd3m)

Dep

artm

ent

of P

hysics

Fe-Nb Magnetic Multi-layers

Rajendra PrasadWith

N. N. Shukla and Arijit Sen

• Explained oscillatory exchange coupling based on electronic structure calculations

• Explained the mechanism of oscillatory exchange coupling

S. A. Ramakrishna

Associate Professor (Ph.D., RRI, 2001)

sar@iitk.ac.in Ph: 7449 (O – FB476)

Areas of Interest: Photonics & Waves in Random Media

31

Complex wave phenomena : Metamaterials, Plasmonics Negative Refractive Index

Summary of Research Activities:

Design of metamaterials with negative refractive index

Controlling near-field radiation with metamaterialsWave propagation aspects in dispersive metamaterials Plasmonics and structured metallic surfaces

Vitalstatistics of metamaterials activities:2 Ph.D. thesis (completed), 30 publications, and 1 book

32

Design of metamaterials

Metamaterials for optical frequenciesControllable dispersion via dielectric and

magnetic structural resonances

Nonlinear metamaterials via imbedded nonlinear materials in the structures

Acoustic metamaterials Design principle of hybridizing bands due to monopole and dipole resonances

Controllable metamaterials Imbedded resonant atoms/molecules in structures – coherent control by externally applied electromagnetic fields (EIT, Raman)

Switchable bandgaps, plasmas etc.

33

Manipulating the optical near-field

Perfect lens effect – Generalized perfect lens theorem: Complementary Optical Media

Curved perfect Lenses: Spherical perfect lenses and magnification of near-field imagesEffects of losses and geometry

Corners and checkerboards of negative refractive index: Total degeneracy of surface plasmon states

d d

34

Wave Propagation Aspects

New description in terms of time moments of Poynting vector

Comparison to arrival times measured by an absorbing detector.

New definitions for the arrival times for evanescent waves

Superluminal and ultra-slow pulse traversal times near resonances

Hartman effect for evanescent waves No reshaping delay for ε = µ A universal superluminal to

subluminal transition lengths in all causal media.

pulse propagation in dispersive materials pulse propagation in dispersive materials

Avinash Singh

Professor (Ph.D., Urbana-Champaign, 1987)

avinas@iitk.ac.in Ph: 7047 (O – FB376)

Areas of Interest: Strongly-correlated Systems

Zone-boundary magnon softening

orbital correlations corresponding to

(π/2,π/2,0) modesSpin-orbital interaction vertex

Featured in this month’s Physical Review website under “Kaleidoscope” http://www.aps.prb.org/kaleidoscope

Observed in ferromagnetic manganites such as Sm0.55Sr0.45MnO3

Pr0.55(Ca0.85Sr0.15)0.45MnO3

Metallic ferromagnetism: exchange of the “phi-meson”

J IJ= J 2 φ IJ

' ℏ '≈ U 2 N − 1 J 2

[U N − 1 J ]2

Inter-site spin couplings are mediated by exchange of the irreducible particle-hole propagator

This universal approach allows correlated motion of electrons (with orbital degeneracy N and Coulomb interactions U,V,J) to be incorporated systematically and non-perturbatively, keeping the Goldstone mode explicitly preserved.

S5/2 impurity spinsMn++ : [Ar]3d5

DMS: Ga1-xMnxAshost valence band

FM manganites eg band

Fe,Ni,Co 3d band

S=3/2 core spinslocalized t2g electronsMn+++

Itinerant electron spins

Effective quantum parameterfor multi-band systems

Metallic ferromagnets essentially involve only local couplings, such as –JSi.σI

as in j.A in QED. So how are the couplings mediated between spins Si and Sj ? Is there a universal mechanism?

Some experiments of interest …

Spin dynamics in GaMnAs SQUID (M Sperl 2007)

Neutron scattering

(Zhang 2007)

NQP states seen in tunneling conductance in Co2MnSi based magnetic tunnel junctions (Chioncel 2008)

Spin dynamics in YMnO3

T Chatterji (ILL Grenoble)

SPEELS study of ultra-thintransition-metal filmsTang 2007

Bi2201 X

ie 2007U

niversal high energy anomaly

in AR

PE

S spectra of high-

temperature superconductors

“Waterfalls” in cuprates

High-resolution ARPES studies of spectral properties of doped carriers in cuprates

key feature: high-energy kink in the hole dispersion

also relevant for carriers in orbitally ordered systems?

Mahendra K. Verma

Associate Professor (Ph.D., Maryland, 1994)

mkv@iitk.ac.in Ph: 7396 (O – FB472)

Areas of Interest: Nonlinear Physics, Magnetohydrodynamics

Turbulence Research @ IITK

Mahendra K. Verma, Supriyo Pal, Satwinder Jit Singh, Pankaj Mishra, Rakesh Yadav, Mani Chandra, Rohit Kumar, Ambrish Pande, Meghdoot, Pankaj Wahi, Krishna Kumar,...

Magnetic field in the Sun & Earth

http://www.damtp.cam.ac.uk/user/nr264/research-pics/spot.jpg

Reversal of Magnetic field

Glatzmaier

Our dynamo simulationsTaylor-Green structure (u field)

33-node cluster

Magnetic field

Period-doubling route to chaos

Entanglement in Spin/Electron Systems

V. Subrahmanyam

Current Research Interests:Quantum Spins, Magnetism, Superconductivity, Quantum Information and Communication, BEC

Entanglement Total System in aPure state

Subsystem Environment Entropy (T) = 0

No Entanglement: Pure Entropy (S) = 0

If Entanglement: Mixed Entropy (S) 0

Through Time Evolution Entanglement can be generated S can become mixed Decoherence

S and E cannot haveIndepend. Specification

Question: How Entangled is a given State? Multipartite Structure, Realistic Models, Quantum Gates Dynamics, Communication, MeasurementDecoherence & Feasibility, Algorithms and Circuits

Research Work carried out:

Quantum Entanglement Structure: Study Eigenstates of Spin Models Pair-wise Entanglement and Sharing, Metal-Insulator transitions, Time Reversal Symmertry

Entanglement Dynamics in Spin Models: Time Evolve Initial states

Transport of Quantum State through a spin chain, Generate Global Entanglement Localize Entanglement on a pair of spins, Distribution of Entanglement among pairs

(AL & VS)

Entanglement of Heisenberg Antiferromangetic :

) ( βα

State transport: Quantum Channel

m’thqubit

l’thqubit

βα , Coded at T=0 Recover Code At later T

Presence of Entangled pairs makes easier Recovery: Larger Fidelity

Maximal and Minimal spin states, Range of Entanglement, Cluster states

Qubit

.

2 nM

Spin Decoherence in Quantum Dots D. D. B. Rao, VR & VS (2006-8)

GaAs InAs About nuclei with spins(3/2,2.01) (9/2,5,53) Weakly int.

410)10( 12 eV

Inject qubits: one, two, …Dominant Interaction: Hyperfine

22

)0()( τtAA ePtP

* Nanomagnets: Fine NiO particles

Research in Progress:

Thesis work of S. K. Mishra

Super Paramagnet or Spin Glass? As size is brought down to < 10 nM

Finite-size effects: Magnetization Non-monotonic, Thermal fluctuations, Relaxation

* Global Entanglement: Spin-only States, Many-Electron states

Expts at IIT-K: K P Rajeev's Group

Metallic systems, Strongly-Correlated Systems, Superconductors

* Multi-Spcies Entanglement: Thermodynamic/Macroscopic Entanglement Entanglement Susceptibilities, Phase Transitions in Spin models

* Tripartite Entanglement: Measures and Resource

Condensed Matter Theory Group Research

1. Introduction: Flora and Fauna, Individual flavors and colors

2. Conclusions: Composition, Range & Expertise, Policy

Plan

Different ways of being associated with a Jungle