Person:

Venkatachalam, Vivek

When electrons are confined to a two dimensional layer with a perpendicular applied magnetic field, such that the ratio of electrons to flux quanta ((\nu)) is a small integer or simple rational value, these electrons condense into remarkable new phases of matter that are strikingly different from the metallic electron gas that exists in the absence of a magnetic field. These phases, called integer or fractional quantum Hall (IQH or FQH) states, appear to be conventional insulators in their bulk, but behave as a dissipationless metal along their edge. Furthermore, electrical measurements of such a system are largely insensitive to the detailed geometry of how the system is contacted or even how large the system is... only the order in which contacts are made appears to matter. This insensitivity to local geometry has since appeared in a number of other two and three dimensional systems, earning them the classification of "topological insulators" and prompting an enormous experimental and theoretical effort to understand their properties and perhaps manipulate these properties to create robust quantum information processors. The focus of this thesis will be two experiments designed to elucidate remarkable properties of the metallic edge and insulating bulk of certain FQH systems. To study such systems, we can use mesoscopic devices known as single electron transistors (SETs). These devices operate by watching single electrons hop into and out of a confining box and into a nearby wire (for measurement). If it is initially unfavorable for an electron to leave the box, it can be made favorable by bringing another charge nearby, modifying the energy of the confined electron and pushing it out of the box and into the nearby wire. In this way, the SET can measure nearby charges. Alternatively, we can heat up the nearby wire to make it easier for electrons to enter and leave the box. In this way, the SET is a sensitive thermometer. First, by operating the SET as an electrometer, we measure the local charge of the (\nu = 5/2) FQH state. An immediate consequence of measuring fractionally quantized conductance plateaus is that the charge of local excitations should be a fraction of (e), the charge of an electron. The simplest charge that would be expected at (\nu = 5/2) would (e/2). However, if the charged particles that condense into the (\nu = 5/2) FQH state are paired, the expected local charge becomes (e/4). By watching these local charges being added to compressible puddles at (\nu = 5/2) and (\nu = 5/7), we find that the local charge at (\nu = 5/2) is indeed (e/4), indicating that objects of charge (e) are pairing to form the ground state of the system. This has implications for the future possibility of detecting non-Abelian braiding statistics in this state, and is described in detail in Chapter 2. By further monitoring how eagerly these (e/4) particles enter puddles as we increase the temperature, we can attempt to identify the presence of some excess entropy related to an unconventional degeneracy of their ground state. Such an entropy would be expected if the (\nu = 5/2) state exhibited non-Abelian braiding statistics. Progress on these experiments and prospects for building a quantum computer are presented in Chapter 3. Next, by operating the SET as a thermometer, we monitor heat flow along the compressible edge and through the bulk of IQH and FQH states. As an edge is heated and charge on that edge is swept downstream by the external magnetic field, we expect that charge to carry the injected energy in the same downstream direction. However, for certain FQH states, this is not the case. By heating an edge with a quantum point contact (QPC) and monitoring the heat transported upstream and downstream, we find that heat can be transported upstream when the edge contains structure related to (\nu = 2/3) FQH physics. Surprisingly, this can be present even when the bulk is in a conventional insulating (IQH) state. Additionally, we unexpectedly find that the (\nu = 1) bulk is capable of transporting heat, while the (\nu = 2) and (\nu = 3) bulk are not. These experiments are presented in Chapter 4. Finally, in Chapter 5, we describe preliminary work on a very different type of topological material, the quantum spin Hall (QSH) insulator. Here, the spin of electrons takes the place of the external magnetic field, creating edge states that propagate in both directions. Each of these edges behaves as an ideal one-dimensional mode, with predicted resistance (h/e^2). By creating well-defined regions where these modes can exist, we identify and characterize the conductance associated with topological edges.

Electrons in two dimensions and strong magnetic fields can form an insulating two-dimensional system with conducting one-dimensional channels along the edge. Electron interactions in these edges can lead to independent transport of charge and heat, even in opposite directions. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream from the heater, we measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall (FQH) physics. Surprisingly, this can occur even when the bulk is in an integer quantum Hall state and the edge contains no signatures of FQH charge transport. We also find an unexpected bulk contribution to heat transport at ν = 1.

We present an imaging system for pan-neuronal recording in crawling Caenorhabditis elegans. A spinning disk confocal microscope, modified for automated tracking of the C. elegans head ganglia, simultaneously records the activity and position of ∼80 neurons that coexpress cytoplasmic calcium indicator GCaMP6s and nuclear localized red fluorescent protein at 10 volumes per second. We developed a behavioral analysis algorithm that maps the movements of the head ganglia to the animal’s posture and locomotion. Image registration and analysis software automatically assigns an index to each nucleus and calculates the corresponding calcium signal. Neurons with highly stereotyped positions can be associated with unique indexes and subsequently identified using an atlas of the worm nervous system. To test our system, we analyzed the brainwide activity patterns of moving worms subjected to thermosensory inputs. We demonstrate that our setup is able to uncover representations of sensory input and motor output of individual neurons from brainwide dynamics. Our imaging setup and analysis pipeline should facilitate mapping circuits for sensory to motor transformation in transparent behaving animals such as C. elegans and Drosophila larva.

The nematode Caenorhabditis elegans navigates toward a preferred temperature setpoint (Ts) determined by long-term temperature exposure. During thermotaxis, the worm migrates down temperature gradients at temperatures above Ts (negative thermotaxis) and performs isothermal tracking near Ts. Under some conditions, the worm migrates up temperature gradients below Ts (positive thermotaxis). Here, we analyze positive and negative thermotaxis toward Ts to study the role of specific neurons that have been proposed to be involved in thermotaxis using genetic ablation, behavioral tracking, and calcium imaging. We find differences in the strategies for positive and negative thermotaxis. Negative thermotaxis is achieved through biasing the frequency of reorientation maneuvers (turns and reversal turns) and biasing the direction of reorientation maneuvers toward colder temperatures. Positive thermotaxis, in contrast, biases only the direction of reorientation maneuvers toward warmer temperatures. We find that the AFD thermosensory neuron drives both positive and negative thermotaxis. The AIY interneuron, which is postsynaptic to AFD, may mediate the switch from negative to positive thermotaxis below Ts. We propose that multiple thermotactic behaviors, each defined by a distinct set of sensorimotor transformations, emanate from the AFD thermosensory neurons. AFD learns and stores the memory of preferred temperatures, detects temperature gradients, and drives the appropriate thermotactic behavior in each temperature regime by the flexible use of downstream circuits.

Animals find mates and food, and avoid predators, by navigating to regions within a favorable range of available sensory cues. How are these ranges set and recognized? Here we show that male Caenorhabditis elegans exhibit strong concentration preferences for sex-specific small molecule cues secreted by hermaphrodites, and that these preferences emerge from the collective dynamics of a single male-specific class of neurons, the cephalic sensory neurons (CEMs). Within a single worm, CEM responses are dissimilar, not determined by anatomical classification and can be excitatory or inhibitory. Response kinetics vary by concentration, suggesting a mechanism for establishing preferences. CEM responses are enhanced in the absence of synaptic transmission, and worms with only one intact CEM show nonpreferential attraction to all concentrations of ascaroside for which CEM is the primary sensor, suggesting that synaptic modulation of CEM responses is necessary for establishing preferences. A heterogeneous concentration-dependent sensory representation thus appears to allow a single neural class to set behavioral preferences and recognize ranges of sensory cues.