Recent research projects
Electronic structure and transport of disordered graphene
The recent experimental realization of single-layer graphene sheets
has spurred an enormous amount of activity in studying the electronic
properties of 2D chiral Dirac fermions in the context of solid state
materials physics. The low energy electronic states of graphene are
described by a massless Dirac equation. In clean isolated graphene
(the so-called intrinsic graphene) the Fermi energy lies exactly at
the Dirac point where the linear chiral electron and hole bands cross
each other. Several works calculated the graphene conductivity at the
Dirac point and found it to be either 0, infinity or, in the limit of
vanishing disorder, equal to the universal value 
.
In current experiments however the measured
conductivity at the Dirac point is finite and much bigger (by a factor
of 2-20) than the universal theoretical prediction 
and
varies strongly from sample to sample. The discrepancy can be
resolved if we consider that close to the Dirac point the average
carrier density vanishes and therefore the disorder induced density
fluctuations are expected to dominate the physics of graphene. As a
consequence close to the Dirac point the density landscape is
characterized by electron-hole puddles that have been observed
experimentally. Recently [1], in collaboration with
Sankar Das Sarma (University of Maryland), I developed a
Thomas-Fermi-Dirac (TFD) theory to calculate the carrier density of
graphene in presence of disorder. The approach is independent of the
disorder source, however recent transport results, away from the Dirac
point, provide convincing evidence that random charged impurities --
located in the graphene environment-- are the dominant source of
disorder in graphene, and therefore we applied the theory to the case
when the disorder is mainly due to charge impurities. The TFD theory
includes the effects of exchange and correlations in a way similar to
the Local Density approximation.
 |
| Density distribution at the Dirac point for a single
disorder realization.
The lower color plot shows the spatial distribution of the
disorder potential VD. The color plot above shows n(r), also
shown above in 3D.
The black lines define the boundaries of the electron-hole puddles. |
Our results show that the carrier
distribution, n(r), close to the Dirac point, is characterized by
two distinct types of inhomogeneities, namely, wide regions (i.e. big
puddles spanning the system size) of low density and few narrow
regions of high density with a typical correlation length of about 10
nm. This value agrees with recent STM results; the linear screening
approximation, at low impurity density, nimp, gives a typical
correlation length that is orders of magnitude bigger than what we
find. In addition we find that many-body effects become
quantitatively very important close to the Dirac point for low
impurity densities and that the density probability distribution,
P[n], at finite and small gate voltages, Vg, has a bimodal
character: a high and narrow peak at n=0 and a broad shoulder-peak
at finite n. The double peak structure for finite Vg provides
direct evidence for the existence of electron-hole puddles over a
finite voltage range.
Based on the success of the TFD theory to characterize the graphene
carrier density very recently [2]
in collaboration with Shaffique Adam (University of Maryland) and
Sankar Das Sarma (University of Maryland) I developed an effective
medium theory (EMT) for graphene that uses the density probability distribution
obtained with the TFD theory
to calculate the graphene conductivity.
 |
Graphene conductivity as a function of the gate voltage for different values of the impurity density.
|
 |
| Thermopower Q as a function of density close to the Dirac point for
T=300 K, nimp=1012 cm-2, rs=0.8 and d=1 nm,
obtained using a two-component (dashed line) model and the EMT with (red solid line) and without
exchange (blue solid line). |
The theory relies on the fact that
by virtue of the Klein paradox the p-n junction
resistivity across electron-hole puddles, in disordered graphene, is negligible
and therefore in current graphene samples the resistivity is determined
mostly by scattering processes inside the puddles
and not across their boundaries as assumed in previous works.
The theory is very powerful being able to:
-
Predict values of in very good agreement with experiments;
-
Describe quantitatively the dependence of 
on the
doping ~Vg including the
crossover or plateau region, i.e. the region where Vg
is finite but smaller than the range of values for
which 
exhibits a linear behavior;
-
Take into account the effect of exchange and correlation terms,
and show that many-body terms are essential to understand
the transport properties of graphene;
-
Explain the observed dependence of on the
sample quality (i.e. mobility);
-
Given the non-perturbative character the theory is valid
also for large values of the graphene fine-structure
constant rs>0.2; this allows the theory to explain
the dependence of on
rs recently observed experimentally and
predict its behavior over a wide interval of values of rs;
-
Predict the transport properties at very low but finite
long-range disorder; a regime not accessible in previous theories.
The approach is very general and allows the calcualtion of other transport
properties besides the conductivity [13].
The resonance peak in the electron-doped cuprate superconductors
Cuprate superconductors are among the most studied materials and yet, after 20 years, are still
largely not understood.
When doped, cuprate materials, below a critical temperature (Tc), become
superconducting. Most of the materials studied so far have
been hole-doped (h-doped). Recently however, advances in material fabrication,
have made possible to electron-dope these materials.
This experimental advance has opened a completely new way to explore
the nature of the correlations in the cuprates.
Inelastic neutron scattering experiments have shown
that
in the superconducting regime the electron-doped (e-doped) cuprates
exhibit a resonance peak reminiscent of the "resonance (41 meV) peak"
previously observed in hole-doped YBCO and Bi-2212.
Recently [4] I and my collaborators, Jan-Peter Ismer and Ilya Eremin
(Max Planck Institute) and Dirk Morr (UIC) have
shown that the recently observed resonance peak in the electron-doped superconductor
Pr0.88LaCe0.12CuO4-delta
is consistent with an overdamped spin exciton located near the particle-hole continuum.
This scenario is similar to the one that has been used successfully to explain
the peak in h-doped cuprates.
Our result suggests that e-doped and h-doped
are quite analogous and that the mechanism for superconductivity
might be the same in the two classes of materials.
We also
showed that a magnetic field in the ab-plane leads to an energy
splitting of the resonance which for typical fields is
sufficiently large to be experimentally observed in the
e-doped cuprates.
One of the most important questions regarding the nature of the
resonance mode in the h-doped cuprates is whether with decreasing
doping, the resonance mode transforms into the Goldstone mode of the
antiferromagnetic parent compounds. Important insight into this
question can be provided by those e-doped cuprates in which
superconductivity
coexists with antifferomagnetism.
With my collaborators I
predicted that in those parts of the
phase diagram in which superconductivity
coexists with antiferromagnetism
and the Neel temperature TN is
below Tc, the resonance peak
evolves into the Goldstone mode of the antiferromagnetic state as TN is
approached.
Spatially Dependent Kondo effect in quantum corrals
The Kondo effect exhibited by a magnetic impurity is one of the most
fundamental and important phenomena in condensed matter physics.
Over the last few years, the emergence of a Kondo effect in confined
host geometries with discrete energy levels, such as quantum
corrals, quantum dots, nanotubes and molecules has attracted
significant experimental and theoretical interest. In collaboration
with D. Morr I studied the Kondo effect produced by a magnetic
impurity placed inside a quantum corral on the surface of a metallic
host [5]. Previous theoretical studies had considered
this problem but none of these studies had addressed the question
whether the eigenmodes' spatial structure leads to a spatially
dependent Kondo effect. Combining a large-N expansion with a
generalized T-matrix approach we addressed this question
and found that the spatial structure of the corral's eigenmodes
leads to a spatially dependent Kondo effect whose signatures are
spatial variations of the Kondo temperature, TK, and of the
critical coupling, Jcr. Specifically we found that TK is the
largest and Jcr the smallest, at those locations where the
local density of states of the lowest energy eigenmode possesses a
maximum. Our results show that in presence of a corral TK,
depending on the position of the magnetic impurity, can
be up to three times higher or lower than for a system with no corral.
Moreover, we find that the screening of the magnetic
impurity leads to the formation of multiple Kondo resonances with
characteristic spatial patterns that provide clear experimental
signatures of the spatially dependent Kondo effect. Our results
demonstrate that quantum corrals provide new possibilities to
manipulate and explore the nature of the Kondo effect.
Bilayer Quantum Hall Systems
Quantum Hall bilayers (QHB) at total Landau level
filling factor nu=1 have ground states with
spontaneous interlayer phase coherence.
One of the most spectacular experimental manifestation of this order is
an enormous low-temperature enhancement
of the interlayer tunneling conductance
in samples with extremely
small inter-layer tunneling amplitudes.
The differential tunneling
conductance is large only at small bias voltages and reaches a finite
maximum value that can be as large as
~0.5 e^2/h at low temperatures.
In collaboration with Allan MacDonald and Alvaro Nunez I developed
a theory of the low-bias tunneling anomaly
[6]
[7]
[8]
Our theory sees interlayer tunneling phenomena as partially
analogous to both tunneling across a Josephson junction and spin-transfer
phenomena in ferromagnetic metals.
The key difference between these two examples of current driven order
parameter manipulation is that the bias is applied by a superconducting
condensate in the former case and by dissipative quasiparticles in the latter.
Our theory
predicts that the zero bias conductance is finite even in a perfect disorder free
bilayer at temperature T=0 and
in contrast to previous theoretical studies
is able to account for the main qualitative features of the experimental observations:
the voltage width of the anomaly, the finite value of the conductance
maximum, and the inverse relationship between these two quantities.
Spin Susceptibility from ARPES Spectra
The origin of the so called ``resonance peak'' observed in inelastic
neutron scattering (INS) experiments on the high-temperature
superconductors, and the nature of its coupling to charge
excitations has remained one of the major puzzles in this field. In
collaboration with D. Morr, M. Norman, M. Randeria and the
experimental group of J. C. Campuzano
[9] I have
recently developed a novel formalism to calculate the spin
susceptibility in the cuprate superconductors starting from the
single particle spectral function measured by ARPES. The results of
this approach show the emergence of a resonance peak below Tc
whose qualitative, and to a large extent quantitative features are
in good agreement with the experimental INS observations. In
particular, we find that the resonance exhibits a downward
dispersion in the vicinity of Q=(pi,pi), and a second
upward branch for momenta smaller than that connecting the nodal
points. Our results provide support for the interpretation of the
resonance peak as a spin exciton.
Identifying Collective Modes in Superconductors via Impurities
One of the most important issues in understanding the complex
behavior of the cuprate superconductors is the nature of the
collective modes in these materials, both above and below Tc.
A series of different experimental techniques have shown that these
modes can be pinned, either by the presence of vortices, or that of
impurities. In particular, NMR measurements have demonstrated that
magnetic Ni impurities in the high-temperature superconductor YBCO
induce a local spin-density wave (SDW), i.e., a magnetic droplet,
leading to a broadening of the NMR spectrum. With R. Nyberg and D.
Morr I recently considered the effect of an SDW induced by a
magnetic impurity on the local density of states (LDOS) in
d-wave superconductors [10].
Using both a Bogoliubov-de-Gennes approach and a generalized
T-matrix scattering formalism, we find that the presence of the
SDW significantly changes the local electronic structure of the
d-wave superconductor. In particular, it suppresses the
LDOS inside the droplet on the energy scale of the superconducting
gap without inducing an impurity state inside the gap. Moreover, the
spin-resolved LDOS exhibits characteristic differences on the two
sublattices of the antiferromagnetic droplet. The self-consistent
calculation of the superconducting order parameter showed
that it is suppressed only within a few lattice spacings of the
impurity, i.e., in the center of the droplet. This suppression,
however, has no qualitative effects on the spatial and frequency
form of the LDOS. This effect, together with the spatial dependence
of the LDOS should produce clear signatures in an STM experiment and
provide insight into the characteristic momentum dependence of the
mode as well as its correlation length.
Magnetization Damping in Ferromagnets
The problem of a detailed description of the magnetization M
dynamics in ferromagnets is still a not completely solved problem.
On the other hand the problem is extremely relevant for
several technological applications.
The magnetization thermal noise scales inversely with the volume
of the magnet and therefore places a constraint on the
reduction of the size of magnetic sensors.
The recent advances in nanofabrication
have then raised the problem of accurately describing the dynamics
of M and its fluctuations
in nanostructures for which old results based on the use
of the Fermi Golden rule are not applicable.
The standard approach to study the magnetization fluctuations
is to start from the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation.
In this equation
a random field h is present to reproduce the effect of thermal fluctuations
and the dissipation is assumed to be local in time.
Because of the fluctuation-dissipation theorem,
this implicitly requires the random field to have white noise properties.
On the other hand since the contribution of the random term
to the magnetization dynamics, Mxh, depends on M
the s-LLG equation exhibits white multiplicative noise.
As a consequence
in order to integrate
the s-LLG equation reliably we need to track the
evolution of M on very short time scales
for which the white noise approximation for h is unphysical.
To overcome these limitations with my collaborators O. Heinonen and A. MacDonald I
studied the dynamics of the magnetization coupled to a thermal bath of elastic modes
using a system plus reservoir approach starting from a realistic
magnetoelastic coupling [11]. After integrating out the elastic modes
we obtain a self-contained equation for the dynamics of the magnetization.
This equation is a generalization of the s-LLG equation.
The main differences between the s-LLG equation and the equation
that we derived is that both the memory friction kernel
and the random field are state dependent,
the memory friction kernel is nonlocal in time and space and
in general is a non-diagonal tensor.
Our derivation does not rely on the Fermi golden rule
and therefore the equation that we obtain can be used to describe
the dynamics of M also in nanostructures.
Applying our results to the case of thin films
we find that our theory describes the dynamics of the magnetization
in thin film ferromagnetic insulators in very good agreement
with the experimental results.
As experimental consequences we find that
the fluctuation correlation time is of the order of
the ratio between the film thickness, h, and the speed of sound
in the magnet and that the line-width of the
ferromagnetic resonance peak should scale as B12h
where B1 is the magnetoelastic coupling constant.
Decoherence processes of excitonic qubits in semiconductor quantum dots
In recent years semiconductor quantum dots (QD) have risen as
one of the most likely basic blocks for quantum computers.
Semiconductor quantum dots are attractive because they possess
energy structures and coherent optical properties similar to,
and dipole moments larger than, those of atoms.
Efforts in the past few years have led to successful observations of
Rabi oscillations (ROs) of excitonic states,
the hallmark for active manipulation of qubits in QDs.
However, all found that ROs damped out very quickly when the external field is increased.
Because QDs contain a macroscopic number of atoms, this strong decoherence process
must be due to unwanted coupling to other degrees of freedom.
Identification of the underlying mechanism is difficult
precisely because of this macroscopic nature.
Yet such understanding plays the most crucial role
in future development of quantum information technology in semiconductors.
In collaboration with A. MacDonald, C. Piermarocchi, T. Takagahara
and the experimental group of C. Shi we studied
the underlying mechanism for decoherence processes during active manipulation
of high quality factor excitonic qubits in InGaAs QDs [12].
Experiments showed a damping
of the Rabi oscillations that increased almost
linearly with the amplitude of the electric field of the exciting laser.
We were able to exclude dipole-dipole interactions
between excitons on different quantum dots and
bi-exciton excitations as possible source of damping, and to finally
identify the indirect excitation
of carriers in the wetting layer, that has compositional
fluctuations, as the process responsible
for the damping of the Rabi oscillations.
This result indicates that suppression of the
the compositional fluctuation of the wetting layer
is key to raise the quality factor of excitonic qubits
in semiconductor QD to a regime practical toward the realization of
quantum computation.
Works where the above research has been presented.
Ground-state of graphene in the presence of random charged impurities
E. Rossi, S. Das Sarma
Phys. Rev. Lett. 101, 166803 (2008).
Featured in the 'Virtual Journal of Nanoscale Science & Technology',
18, Issue 17, October 27, 2008.
[pdf]
[Abstract on arXiv]
Effective medium theory of disordered two-dimensional graphene
E. Rossi, S. Adam, S. Das Sarma
Phys. Rev. B 79, 245423 (2009).
[pdf]
[arXiv:0809.1425]
Theory of charged impurity scattering in two dimensional graphene
S. Adam, E. H. Hwang, E. Rossi, S. Das Sarma
Solid State Communications 149, 1072 (2009).
[pdf]
[arXiv:0812.1795]
Dynamical spin susceptibility and the resonance peak in the electron-doped cuprate superconductors
J.-P. Ismer, I. Eremin, E. Rossi, Dirk K. Morr
Phys. Rev. Lett. 99, 047005 (2007).
[pdf]
[Abstract on arXiv]
Spatially dependent Kondo-effect in quantum corrals
E. Rossi, D. K. Morr
Phys. Rev. Lett. 97, (2006).
Featured in the 'Virtual Journal of Nanoscale Science & Technology',
14, Issue 25, December 8, 2006.
[pdf]
[Abstract on arXiv]
Interlayer Transport in Bilayer Quantum Hall Systems
E. Rossi, A. S. Nunez, A. H. MacDonald
Phys. Rev. Lett. 95, 266804 (2005).
[pdf]
[Abstract on arXiv]
-
Collective transport in bilayer quantum Hall systems
A. A. Burkov, Y. N. Joglekar, E. Rossi, A. H. MacDonald
Physica E 22, 19 (2004).
[pdf]
[Abstract on arXiv]
Collective transport properties of bilayer-quantum-Hall excitonic condensates
A. H. MacDonald, A. A. Burkov, Y. N. Joglekar, E. Rossi
Physics of Semiconductors 171, 29 (2002).
[pdf]
[Abstract on arXiv]
Dynamic Response Functions from Angle Resolved Photoemission Spectra
U. Chatterjee, D. K. Morr, M. R. Norman, M. Randeria, A. Kanigel, M. Shi,
E. Rossi, A. Kaminski, H. M. Fretwell, S. Rosenkranz, K. Kadowaki, J. C. Campuzano
Phys. Rev. B 75, 172504 (2007).
[pdf]
[Abstract on arXiv]
Identifying Collective Modes in dx2-y2-wave superconductors via Impurities
R. H. Nyberg, E. Rossi, D. K. Morr
Phys. Rev. B 78, 054504 (2008).
[pdf]
[Abstract on arXiv]
Dynamics of magnetization coupled to a thermal bath of elastic modes
E. Rossi, O. G. Heinonen, A. H. MacDonald
72, 174412 (2005).
[pdf]
[Abstract on arXiv]
Decoherence processes during active manipulation of excitonic qubits in semiconductor quantum dots
Q. Q. Wang, A. Muller, P. Bianucci, E. Rossi,
Q. K. Xue, T. Takagahara, C. Piermarocchi, A. H. MacDonald, C. K. Shih
Phys. Rev. B 72, 035306 (2005).
[pdf]
[Abstract on arXiv]
Theory of thermopower in 2D graphene
E. H. Hwang, E. Rossi, S. Das Sarma
Preprint (2008).
[pdf][arXiv:0902.1749v1]