| dc.description.abstract | Transport of electrons through low-dimensional quantum conductors like nano-junctions has
been actively pursued research area for the last few decades. Experimental studies on nano-junctions
are nowadays routinely carried out around the globe thanks to the invention of nanoscale analysis
and manipulation techniques like the scanning tunneling microscope and the atomic force microscope. The
research on charge and heat transport in nano-junctions is not only motivated by the miniaturization of electronic devices relevant for applications, but also by the intriguing quantum mechanical
transport phenomena which differ from that in macroscopic conductors. Motivated by the feasibility of experimentally testing the theoretical predictions of various aspects of transport through
quantum junctions, the theoretical work on charge and heat transport through nano-junctions
presented in this thesis is carried out using quantum master equation and non-equilibrium Green functions approaches.
In chapter 1, experimental works that have motivated the theoretical work presented in this
thesis are briefly discussed, followed by a summary of key theoretical techniques which are used
to rationalize these experiments. A survey of important works on fluctuations of charge and
heat transport in quantum systems and fluctuation theorems satisfied by these fluctuations is also
presented in this chapter.
In chapter 2, the effect of system-reservoir coupling on charge currents flowing through nano-
junctions is studied using non-equilibrium Green functions method applied to two double-quantum
dot circuits. It is found that the charge currents do not always increase with the increasing system-
reservoir coupling strength. Further, this behavior depends on the way nanosystem is coupled to
the reservoirs. For the case when two quantum dots are serially coupled, that is, when the two
dots are coupled to two different reservoirs, the current exhibits a non-monotonic behavior and
diminishes for large coupling strengths. While for the case where two quantum dots are side-coupled
to the two reservoirs, that is, only one of the dots is coupled to the two reservoirs, the current
increases monotonically and saturates for asymptotically large system-reservoir coupling strength.
To rationalize this behavior, the charge currents flowing between system and reservoirs at steady
state are partitioned into the currents carried by populations in the single-particle energy eigenstates
of the nanosystem and the currents carried by the coherent superposition of these eigenstates. It is
shown that the currents carried by populations are always positive (in the direction of applied bias)
and increases monotonically with system-reservoir coupling strength. But the currents carried by
the coherent superposition of single-particle eigenstates becomes negative (opposite to the direction
of the applied bias) for large system-reservoir coupling. For the serially coupled case, this coherent
contribution becomes equal in magnitude to the sum of currents carried by the populations for
asymptotically large system-reservoir coupling strengths making the net current zero. While for
the side coupled case, this cancellation is not complete, making net current saturate to finite value
asymptotically. Further, this behavior is found to be robust to weak Coulomb interactions. These
theoretical predictions can be tested using either quantum dot junctions where system-reservoir
coupling strengths can be tuned using gate potentials, or using molecular junctions where system-
reservoir coupling strengths can be tuned by various means like chemical gating, by tuning Fermi
level of the metals or by tuning overlap of molecular orbitals with electronic states of the metals.
An important aspect of charge transport through nano-junctions is local currents flowing inside
the quantum systems. This is discussed in chapter 3. This work is motivated by the possibility of
inferring the pathways electrons can take through the molecule while flowing between the two reservoirs, either using inelastic electron tunneling spectroscopy or by measuring local magnetic fields
generated by these currents. To understand the local currents flowing inside quantum systems, two
simple models, a four quantum dot cyclic molecular junction symmetrically coupled to two reservoirs in the presence of applied magnetic field and a similar junction (in the absence of magnetic
field) but with an extra quantum dot substituted on one of the arms coupled to two reservoirs, are
studied using non-equilibrium Green functions method. For the symmetric junction, the currents
flowing through the two paths or branches inside the ring are found to have two contributions, one
due to the applied bias and the other due to the applied magnetic field. It is shown that these two
contributions can be tuned by adjusting the applied bias and the applied magnetic field such that
one of the branches is conducting selectively. For the asymmetric junction case, it is shown that
by tuning the applied bias and the system-reservoir coupling strength, a circulating current can be
induced inside the molecular junction.
Chapter 4 is a slight deviation from the general theme of the thesis in the sense that it is
not about the transport of electrons through quantum junctions but deals with a temporally driven
isolated quantum system. In this chapter, the statistics of work that is performed while preparing
displaced squeezed thermal state of a quantum optical oscillator from a thermal state by driving
with two classical electric fields (one-photon resonant and two-photon resonant drives) is explored.3
This work is motivated by recent theoretical and experimental works which showed the possibility
of using squeezed thermal reservoirs for designing heat engines whose efficiencies can surpass the
classical Carnot bound. Using standard quantum optics technique of Weyl generating function,
the moment generating function for the work done by two classical drives on the quantum optical
oscillator is obtained analytically. Using this, Jarzynski-Crooks fluctuation theorems for the work
distribution function are verified. It is found that the work statistics is qualitatively different for
the cases when only one of the drives is present. Further, it is found that the phase difference
between the two drives affects the work statistics in a non-trivial fashion where the most probable
work can shift to negative values (although on an average work is performed on the oscillator
conforming with the second law of thermodynamics) due to interference effects.
Chapter 5 investigates the possibility of pumping charge across a quantum junction which
is coupled to two unbiased reservoirs by temporally modulating system-reservoir coupling in an
adiabatic fashion. This work is motivated by the discrepancy between a recent theoretical work
which argued that the adiabatic modulation of system-reservoir coupling cannot break the detailed
balance and hence no net flux can flow between two unbiased reservoirs and a two-decade-old
experiment which found that net flux can flow between the reservoirs. By considering a simple
(system-reservoir coupling) driven resonant level model junction, the moment generating function
for the charge flowing between two unbiased reservoirs is computed analytically in the adiabatic
limit using non-equilibrium Green functions approach. It is found that the level broadening (lifetime broadening) which is absent in the simple second-order quantum master equation approaches
is crucial for the finite charge flux. Further, the direction of charge flux is found to be dependent on
the phase difference between the two system-reservoir drivings and the alignment of the resonant
level relative to the chemical potentials of the two reservoirs. The probability distribution function
for the charge flow is shown to satisfy a fluctuation theorem.
In chapter 6, the possibility of heat transport mediated by Coulomb interactions is explored.
This work is motivated by recent breakthroughs in experimental nano calorimetry. To understand
the role of Coulomb interactions on the heat transport in nano-junctions, a simple capacitively coupled double quantum dot junction is studied using quantum master equation and non-equilibrium
Green functions approaches. It is found that when the Coulomb interactions are treated within
the mean-field level, at steady-state no heat flows between the two reservoirs. This is because, at
this level of approximation, the system decouples into two independent resonant levels which are at
equilibrium. For going beyond the simple mean-field approximation, two approximate approaches
are employed; the Lindblad quantum master equation approach which treats system-reservoir coupling approximately and the non-equilibrium Green functions approach within the renormalized
random phase approximation which treats Coulomb interaction strength approximately. Using
these approaches, it is found that heat flux and its fluctuations are non-monotonic functions of
the Coulomb interaction strength and the system-reservoir coupling strength. Further, the thermodynamic consistency of these predictions is asserted by verifying the steady-state fluctuation
theorem for stochastic heat flux flowing between the two reservoirs using both the approximations
employed.
A summary of the work presented in this thesis is given in chapter 7. | en_US |
