Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect [1], a paradigm of quantum mechanical phase coherence [2,3]. The phase coherence of transport through a quantum dot embedded in one arm of an open ring has been demonstrated [4]. The energy spectrum of closed rings [5] has only recently been analysed by optical experiments [6,7] and is the basis for the prediction of persistent currents [8] and related experiments [9-11]. Here we report magnetotransport experiments on a ring-shaped semiconductor quantum dot in the Coulomb blockade regime [12]. The measurements allow us to extract the discrete energy levels of a realistic ring, which are found to agree well with theoretical expectations. Such an agreement, so far only found for few-electron quantum dots, is here extended to a many-electron system [13]. In a semiclassical language our results indicate that electron motion is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots.
The phenomenon of spin resonance has had far-reaching influence since its discovery 70 years ago. Electron spin resonance driven by high-frequency magnetic fields has enhanced our understanding of quantum mechanics, and finds application in fields as diverse as medicine and quantum information. Spin resonance can also be induced by high-frequency electric fields in materials with a spin-orbit interaction; the oscillation of the electrons creates a momentum-dependent effective magnetic field acting on the electron spin. Here we report electron spin resonance due to a spin-orbit interaction that does not require external driving fields. The effect, which we term ballistic spin resonance, is driven by the free motion of electrons that bounce at frequencies of tens of gigahertz in micrometre-scale channels of a two-dimensional electron gas. This is a frequency range that is experimentally challenging to access in spin resonance, and especially difficult on a chip. The resonance is manifest in electrical measurements of pure spin currents-we see a strong suppression of spin relaxation length when the oscillating spin-orbit field is in resonance with spin precession in a static magnetic field. These findings illustrate how the spin-orbit interaction can be harnessed for spin manipulation in a spintronic circuit, and point the way to gate-tunable coherent spin rotations in ballistic nanostructures without external alternating current fields.
Coulomb blockade resonances are measured in a GaAs quantum dot in which both shape deformations and interactions are small. The parametric evolution of the Coulomb blockade peaks shows a pronounced pair correlation in both position and amplitude, which is interpreted as spin pairing. As a consequence, the nearest-neighbor distribution of peak spacings can be well approximated by a modified bimodal Wigner surmise, in which interactions are taken into account beyond the constant interaction model.
The entropy of an electronic system offers important insights into the nature of its quantum mechanical ground state. This is particularly valuable in cases where the state is difficult to identify by conventional experimental probes, such as conductance. Traditionally, entropy measurements are based on bulk properties, such as heat capacity, that are easily observed in macroscopic samples but are unmeasurably small in systems that consist of only a few particles [1, 2]. In this work, we develop a mesoscopic circuit to directly measure the entropy of just a few electrons, and demonstrate its efficacy using the well understood spin statistics of the first, second, and third electron ground states in a GaAs quantum dot [3][4][5][6][7][8]. The precision of this technique, quantifying the entropy of a single spin-1 2 to within 5% of the expected value of k B ln 2, shows its potential for probing more exotic systems. For example, entangled states or those with non-Abelian statistics could be clearly distinguished by their low-temperature entropy [9][10][11][12][13].Our approach is analogous to the milestone of spin-tocharge conversion achieved over a decade ago, in which the infinitesimal magnetic moments of a single spin were detected by transforming them into the presence or absence of an electron charge [14,15]. Following this example, we perform an entropy-to-charge conversion, making use of the Maxwell relationthat connects changes in entropy, particle number, and temperature (S, N , and T , respectively) to changes in the chemical potential, µ, a quantity that is simple to measure and control. The Maxwell relation in Eq. 1 forms the basis of two theoretical proposals to measure non-Abelian exchange of Moore-Read quasiparticles in the ν = 5 2 state via their entropy [9,10]. Reference 10 proposes a strategy by which quasiparticle entropy could be deduced from a V m id V p G sens N − 1 N ∂S/∂N = 0 b V m id V m id V p N − 1 N ∂S/∂N > 0 c Vp δGsens Vp δGsens I heat I sens V sens V p G sens δG sens AC DC 500nm FIG. 1.Measurement protocol (a) Scanning electron micrograph of a device similar to the one measured. Electrostatic gates (gold) define the circuit in a 2D electron gas (2DEG), with grey gates grounded. Squares indicate ohmic contacts to the 2DEG. The temperature of the electron reservoir in the middle (red) is oscillated using AC current, I heat , at frequency f heat through the quantum point contact (QPC) on the left. A portion of the 5 µm-wide reservoir has been removed here for clarity. The occupation of the quantum dot, tunnel coupled to the right side the reservoir, is tuned by Vp and monitored by Isens through the charge sensor QPC. Isens is split into DC and AC components, the latter being measured by a lock-in amplifier at 2f heat . (b) and (c) Simulated DC charge sensor signal, Gsens, for a transition from N − 1 → N electrons at two temperatures (T Red > T Blue ), showing two possible cases for ∂S ∂N . Insets show the corresponding difference, δGsens, between hot and cold curves.the temperature-depende...
Compressibility measurements are performed on a quantum point contact (QPC). Screening due to mobile charges in the QPC is measured quantitatively, using a second point contact. These measurements are performed from pinch-off through the opening of the first few modes in the QPC. While the measured signal closely matches a Thomas-Fermi-Poisson prediction, deviations from the classical behavior are apparent near the openings of the different modes. Density functional calculations attribute the deviations to a combination of a diverging density of states at the opening of each one-dimensional mode and exchange interaction, which is strongest for the first mode.
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