Session P18: Focus Session: Electron, Ion, and Exciton Transport in Nanostructures - Quantum Transport I

Electrostatic tuning between 1-dimensional and 2-dimensional electron gases

Although low dimensional systems such as 1-D and 2-D electron gases have been separately studied in details, a system enabling co-existence of both dimensions is still challenging to achieve. Such a system where the dimensionality can be tuned between 1-D and 2-D electrons can be an extremely promising platform to explore new phenomena. Here we investigate a novel system based on vicinal GaN-based heterostructure where we exploit its polarization charges to demonstrate for the first time, direct electrostatic tuning of the dimensionality of electrons between 1-D and 2-D. This tuning is achieved by adjusting the Fermi level with applied gate bias. A capacitance-voltage profiling to probe the Fermi occupation function of electron gas was used to demonstrate distinct signatures of the density of states for both the dimensions at room temperature. We developed a 2-sub-band model consisting of 1-D and 2-D sub-bands to describe the behavior of the electron gas, which is in excellent agreement with our experimental data, confirming the co-existence of electrons of both dimensions. This demonstration of co-existence of 1-D and 2-D electrons and the ability to tune between their dimensions at room temperature could open new research paths for low-dimensional physics besides enabling devices with added functionalities.   

Quantum coherence phenomena in bismuth thin film nanostructures

We present low temperature quantum magnetotransport measurements on bismuth nanostructures. The large spin-orbit interaction and prominent surface states in Bi films are expected to produce non trivial mesoscopic quantum transport. Bi thin films are grown by thermal evaporation onto SiO$_2$ with a two-step process to optimize the film mobility and ensure oriented growth along the [111] direction. The optimization leads to a minimum thickness of 25 nm for continuous films. Structures as small as 100 nm are subsequently patterned into the film via lithographic techniques. Phase and spin coherence lengths are obtained by analyzing electron interference phenomena in mesoscopic wires and rings. We show that the phase coherence shows a decreasing trend with decreasing channel width. The decrease in phase coherence in Bi wires ranging in width from 1200 nm to 100 nm cannot readily be accounted for by increased boundary scattering. A width dependence of the spin coherence is also detected. The observed confinement dependence of the phase and spin coherence in Bi nanostructures will be discussed (DOE DE-FG02-08ER46532).   

Resistance oscillations and dephasing in ring patterns on InGaAs/InAlAs two-dimensional electron systems

In InGaAs/InAlAs heterostructures with spin-orbit interaction, patterned into mesoscopic rings, we experimentally investigate low-temperature Aharonov-Bohm resistance oscillations. The oscillation amplitude was studied as function of applied current and temperature, to obtain the dependence of these parameters on dephasing. Previous results on mesoscopic quantum interferometers have shown a lobe structure in the dependence of the oscillation amplitude on measurement bias, in some models ascribed to Coulomb interaction, and have surmised a universal behavior with an energy scale dependent on interferometer size. The ring interferometers studied here were of typical radius of 700 nm, and lithographic arm width of 300 nm, similar-sized but of higher carrier density than in the previous studies, and used for similar bias- and temperature-induced dephasing studies. The measurements so far show the expected temperature dependence, but have not revealed the lobe structure in the bias dependence. We discuss the results in the light of dephasing phenomena expected in mesoscopic quantum interferometers (DOE DE-FG02-08ER46532, NSF DMR-0520550).   

Transport through double quantum dot with electron-LO-phonon interaction

We theoretically study the transport through a serial double quantum dot (DQD) in the presence of electron-LO-phonon interaction. In contrast to the case of acoustic phonon,\footnote{P.\ Roulleau {\it et al}., Nat.\ Commun.\ {\bf 2}, 239 (2011).} the coherent coupling between an electron and an optical phonon, so-called polaron formation, has a small dissipation, which influences the transport properties markedly. We calculate the current through the DQD using the Keldysh Green function, as a function of the tuning of energy levels between the quantum dots, when the bias voltage is sufficiently large. The electron-phonon interaction is considered by the perturbation expansion. We find a subpeak structure of the current due to the polaron formation and evaluate elastic and inelastic components of the current.   

Imaging Spatial Current Eigenmodes in Nanoscopic Quantum Networks

Using the Keldysh Green's function formalism, we study the non-equilibrium charge transport in nanoscopic quantum networks [1]. Due to quantum confinement, charge transport takes place via current eigenmodes that possess characteristic spatial patterns of current paths. In the ballistic limit, these patterns exhibit unexpected features such as current backflow and closed loops of circulating currents. These current eigenmodes are the non-equilibrium analogue of eigenmodes in the local density of states of confined systems [2]. Moreover, we demonstrate that dephasing leads to a smooth evolution of the current patterns, and ultimately reproduces the charge transport in a classical resistor network. Finally, we propose a new method using scanning tunneling spectroscopy to image the spatial current patterns associated with individual current eigenmodes in nanoscopic quantum networks.\\[4pt] [1] T. Can, H. Dai, and D.K. Morr, in preparation\\[0pt] [2] M. Crommie, C. Lutz, and D. Eigler. Confinement of electrons to quantum corrals on a metal surface. Science, 262, 1993.   

Microscopic Theory for the 0.7 Anomaly in Quantum Point Contacts - the Role of Geometry- and Interaction-Enhanced Spin-Fluctuations

We present a detailed microscopic analysis of some local observables of a quantum point contact (QPC) to gain better understanding of the origin of the 0.7 conductance anomaly. We model the system by a one-dimensional tight binding model with local interactions, a smooth potential barrier and a homogeneous magnetic field. We calculate conductance $G$, local density $n$ and local magnetization $m$ as a function of magnetic field at zero temperature, using the functional Renormalization Group (fRG). Our potential can be tuned to describe the smooth crossover from a single barrier, representing a QPC, to a double barrier, modelling a quantum dot (QD) exhibiting the Kondo effect. We find that both geometries show interaction-enhanced spin-fluctuations, manifested via an enhanced local spin susceptibility, for gate voltages that lead to an anomalously large negative magnetoconductance, characterized by an anomalously small low-energy scale $B_*$. This finding explains why both the Kondo effect and the 0.7-anomaly exhibit a very similar conductance behavior at sufficiently low magnetic fields and temperatures ($T,B \ll T_*$), amenable to a similar Fermi-liquid description. We also show that at high fields ($B \gg B_*$) the analogy between Kondo effect and 0.7-anomaly breaks down.   

Towards a Fermi-Liquid description of the 0.7 Anomaly in Quantum Point Contacts

In addition to plateaus in integer values of $G_0 = \frac{2e^2}{h}$, the linear conductance of a quantum point contact (QPC) shows an anomalous shoulder at around $0.7 G_0$ that evolves in a characteristic fashion with rising magnetic field and temperature. We present a microscopic theory for the $0.7$ conductance anomaly, based on a one-dimensional tight binding model with a local interaction, a smooth potential barrier and a homogeneous magnetic Zeeman field. We calculate the conductance as a function of magnetic field and temperature using standard second order perturbation theory. Furthermore we use a more sophisticate method, the functional Renormalisation Group (fRG), to obtain a more reliable description at zero temperature and finite magnetic field. We analyze the leading temperature $T$ and magnetic field $B$ dependence of the conductance, which define, respectively, low-energy scales $T_\star$ and $B_\star$ and find that both $T_\star$ and $B_\star$ depend exponentially on gate voltage, whereas the ratio $\frac{B_\star}{T_\star}$ is almost independent of gate voltage. This result indicates that the low-energy behavior of the $0.7$ anomaly displays Fermi-liquid behavior. We present new experimental data that corroborate this conclusion.   

Quantum Wires with Electrons and Cold Atoms

Advances in atom trapping and atom chip techniques allow the controlled preparation and manipulation of clouds of cold, neutral atoms, in optical lattices as well as on lithographically patterned gate structures. This opens up many new possibilities to study quantum transport in systems other than semiconductor quantum dots or nanowires, with the exciting perspective of future ``atomtronic'' systems. Inspired by these developments, we study transport through two different interacting systems as a function of externally controllable parameters: Electrons in a nanowire, and cold atoms in a one-dimensional finite well. For a nanowire system we can demonstrate that Wigner crystallization occurs, when the length of the wire is changed in the experiment [1]. Distinct diamond patterns appear, when conductance is plotted against source-drain bias and the gate voltage, as common for quantum dot systems. The same holds for more general types of ``interaction blockade,'' and we demonstrate that such phenomena can also be studied by cold atom systems. \\[4pt] [1] Kristinsd\'ottir, L.H., J. Cremon, H. Nilsson, H. Xu, H. Linke, L. Samuelson, A. Wacker and S.M. Reimann, Phys. Rev. B \textbf{83}, 041101, (2011).   

Functional dependence of the exact time-dependent Kohn-Sham potential for quantum transport

We present methods for determining exact steady-state and time-dependent Kohn-Sham potentials from known charge and current densities. Applying these methods to cases of a single electron added to the conduction band of a model semiconductor, we calculate the exact Kohn-Sham potentials and discuss their meaning in the context of describing quantum transport. We show that the inclusion of a longitudinal Kohn-Sham vector potential is quite unavoidable in describing steady-state current-carrying systems, whereas the addition of an electron in a wavepacket state necessitates, inter alia, the appearance of an exchange-correlation electric field. We also present our findings on the functional dependence of the exact Kohn-Sham scalar and vector potentials on the charge and current density.   

Waiting time distributions of mesoscopic conductors

Electronic transport through mesoscopic structures is stochastic due to the quantum nature of the charge carriers. In full counting statistics the interest is in the number of particles that are detected in a given time interval. Another important and fundamental question concerns the waiting time between consecutive carriers. Recently, waiting time distributions (WTD) have been calculated for periodically driven systems described by master equations and shown to clearly distinguish random charge emissions from charge transfer processes which are frequency-locked to the period of the external drive [1]. In this work we investigate the WTD of a biased quantum point contact (QPC) with one channel [2]. The WTD clearly reflects the fermionic statistics of the elementary charges: with increasing transmission probability of the QPC, the WTD changes from that of a Poisson process for a nearly closed QPC to a Wigner-Dyson distribution, known from the analogous problem of free fermions described by random matrix theory. [1] M. Albert, C. Flindt and M. Buettiker, Phys. Rev. Lett. 107, 086805 (2011). [2] M. Albert, G. Haack, C. Flindt and M. Buettiker, \textit{in preparation}.   

Magnetic field induced mixed level Kondo effect in two-level quantum dots

Semiconductor quantum dots provide an easily tunable environment in which to investigate the Kondo effect. As it is known, Kondo correlations are suppressed by magnetic fields, showing e.g. a drop in the conductance of a quantum dot device. However, certain systems may exhibit an increasing conductance as a function of an applied magnetic field [1]. In this work we use the numerical renormalization group method to study a two-level quantum dot system with on-level and interlevel Coulomb repulsion, coupled to a single channel. When there is a finite detuning between levels, and a local singlet develops in one of them, the linear conductance of the device shows a maximum structure as a function of an in-plane magnetic field, which depends on the temperature of the system. This maximum occurs at a magnetic field strength such that the spin up state of one of the levels and spin down of the other are degenerate, allowing a ``mixed level'' Kondo effect. The respective spectral functions feature a resonance at the Fermi energy, commensurate with the Kondo physics. We discuss the properties of this mixed level Kondo state in terms of the detuning and the other parameters of the system. \\[4pt] [1] R. Sakano and N. Kawakami, PRB 73, 155332 (2006)   

Time dependent quantum transport in a vibrating quantum dot in Kondo regime

We employ the time dependent non-crossing approximation to investigate the effect of strong electron-phonon coupling on the instantaneous conductance and thermopower of a single electron transistor which is abruptly shifted into the Kondo regime via a gate voltage. We find that the instantaneous conductance exhibits decaying sinusoidal oscillations on the long timescale for infinitesimal bias [1]. The ambient temperature and electron-phonon coupling strength influence the amplitude of these oscillations and the frequency of oscillations is equal to the phonon frequency. We discuss the origin of these oscillations and the effect of finite bias on them. On the other hand, we argue that measurement of the decay time of thermopower to its steady state value in linear response might be an alternative tool in determination of the Kondo temperature and the actual value of the electron-phonon coupling strength in an experiment. \\[4pt] [1] A. Goker, J. Phys.: Condens. Matter, 23 (2011) 125302   

Dynamic response of a single-electron transistor in the ac Kondo regime

A single-electron transistor (SET) consisting of a small conducting island contacted by macroscopic conductors can be used to study strongly correlated electrons in artificial systems. SETs also provide possibilities of exploring non-equilibrium Kondo phenomena by applying source-drain voltage. In the context of recent measurements, we will discuss the non-trivial dynamics that emerges when externally imposed energy scales compete with the Kondo correlations. The response of the system to a simultaneous application of a magnetic field and a high-frequency modulation of the SET voltages will also be reported.   

Double Quantum Dot Kondo Effect in a Magnetic Field

Conventionally the Kondo effect is thought of as describing how conduction electrons screen a localized spin. More generally, it describes how itinerant electrons screen a degenerate degree of freedom of a localized site. A double quantum dot (with negligible inter-dot tunneling) can have both spin degeneracy, as well as a degeneracy associated with an electron being on dot 1 or dot 2. The latter degeneracy corresponds to a pseudo-spin degree of freedom that can also be screened by the Kondo effect [A. H\"{u}bel, et al. PRL 101, 186804 (2008)]. Applying a finite magnetic field can split the spin degeneracy of the dots, which should allow the realization of a purely pseudo-spin Kondo effect. We present conductance measurements of this double dot Kondo effect in a magnetic field. We compare our measurements to theoretical predictions for SU(2) Kondo to check whether we have realized a purely pseudo-spin Kondo effect in a double dot.   

Theory of anomalous magnetotransport in triple quantum dots

Magneto-transport measurements on a triple quantum dot ring have recently shown anomalous quantum oscillations with dominant frequencies separated by a factor of three in magnetic flux [1]. Such oscillations, suggestive of a one-third periodicity in the flux quantum, are usually not observed in larger mesoscopic rings in which only larger periods are observed. We develop a microscopic transport model for the triple dot and show that the anomalous oscillations can dominate the transport behavior under certain conditions. Furthermore, we discuss the range of validity of our model by studying dephasing due to broadening and electric dipole interactions. \\[4pt] [1] L. Gaudreau et al., Phys. Rev. B 80, 075415 (2009)