Capacitively Coupled QPC

• Capacitively Coupled QPC is a quantum point contact whose conductance is modulated by nearby electrostatic changes, functioning as a noninvasive charge sensor.
• It is applied in architectures like scanning-gate microscopy and quantum dot circuits to achieve precise charge, spin, and displacement detection.
• The coupling induces dynamic backaction and alters transport regimes, leading to advanced applications in thermal transistors and radio-frequency measurements.

Searching arXiv for recent and foundational papers on capacitively coupled quantum point contacts to support the article. A capacitively coupled quantum point contact (QPC) is a quantum point contact whose conductance, noise, or admittance is modulated by the electrostatic state of a nearby subsystem without requiring direct dc current flow between them. In this configuration, the QPC functions as an electrometer, transducer, or noise detector, while the same Coulomb coupling that enables readout can also shift conductance plateaus, induce backaction, and modify nonequilibrium transport. Across scanning-gate experiments, quantum-dot and double-quantum-dot circuits, coupled QPC pairs, and electromechanical devices, the central theme is the same: a nearby charge distribution changes the QPC potential landscape and therefore its transport response (Kozikov et al., 2015, Golubev et al., 2011).

1. Electrostatic mechanism and operating principle

In the experiments considered here, a QPC is typically defined electrostatically by split gates in a two-dimensional electron gas, with quantized conductance in units of $2e^2/h$. Capacitive coupling means that a nearby charge, gate, tip, or conductor shifts the effective potential at the constriction, thereby changing the QPC conductance or the gate voltage at which a given plateau occurs. In scanning-gate microscopy, this appears as a long-range “gating” effect: the tip-induced potential shifts the whole $G(V_\mathrm{g})$ curve, while a separate local effect depletes the two-dimensional electron gas and backscatters electrons (Kozikov et al., 2015).

A compact expression for the charge-sensing regime is given in the graphene electron-hole double-dot work: $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$ where $C_m$ is the mutual capacitance between the quantum dot and the QPC and $\Delta Q_\text{QD}$ is the change in dot charge occupancy. The response is maximized when the QPC is tuned to the steepest part of its pinch-off curve, so that small electrostatic shifts produce the largest transconductance (Hecker et al., 15 Sep 2025).

The same logic underlies semiconductor charge detectors more generally. In the tunable-detector study, the detector potential shift is described qualitatively through the mutual capacitance $C_{\rm QD-Det}$, with

$$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$

Reducing screening and increasing $C_{\rm QD-Det}$ therefore improves readout contrast (Rössler et al., 2012).

A recurrent misconception is that capacitive coupling is merely a parasitic perturbation. The literature shows a dual role. In some settings, especially scanning-gate experiments, the capacitive contribution is the dominant artifact that must be compensated. In charge sensing, thermometry, and noise detection, the same interaction is the signal channel itself.

2. Charge and spin sensing architectures

Capacitively coupled QPCs are widely used as detectors for nearby few-electron systems. The basic arrangement is a QPC placed close enough to a quantum dot or double quantum dot that a single charging event shifts the QPC conductance, but without appreciable direct current exchange between detector and object. Variants differ mainly in geometry, screening environment, and whether the coupling is purely electrostatic or “capacitively (and weakly tunnel-) coupled” (Kim et al., 2016, 0910.3631, Rössler et al., 2012).

Platform	Coupling geometry	Representative result
InGaAs quantum dot with vertically integrated QPC	QPC located slightly offset from the dot gate, within approximately 100 nm	DC sensitivity as high as 8.6%; signal-to-noise ratio of ~9:1 in 12.1 kHz bandwidth
Tunable GaAs detector-QPC	Gate gap, floating gate, or localized state in the constriction	$\Delta G_{\rm Det}$ up to $\sim 0.035 \times \frac{2e^2}{h}$; time-resolved detection at 1 kHz
In$G(V_\mathrm{g})$0Ga$G(V_\mathrm{g})$1As QD side-coupled to target QPC	Weakly tunnel-coupled, mainly capacitive, adjacent to the narrowest point	Spin polarization up to $G(V_\mathrm{g})$2 on the $G(V_\mathrm{g})$3 and $G(V_\mathrm{g})$4 plateaus
Bilayer graphene electron-hole double QD with QPC sensor	In-line arrangement with depletion gate suppressing screening	$G(V_\mathrm{g})$5 up to 160; bandwidth $G(V_\mathrm{g})$6 MHz

In the vertically integrated InGaAs device of E.T. Croke, M.G. Borselli, M.F. Gyure, et al., the QPC is formed in the lower well and is placed slightly offset from the accumulation-mode dot gate in the upper well. The charge state of the dot is measured by monitoring the differential transconductance of the QPC near pinch-off. Single-electron occupancy changes produced a QPC current change of 900 pA on a 10.5 nA background, corresponding to 8.6% sensitivity; random telegraph signal analysis yielded lifetimes of $G(V_\mathrm{g})$7 ms and $G(V_\mathrm{g})$8 ms for the filled and empty states of the one-electron dot (0910.3631).

Detector optimization has focused on the electrostatics of the detector-object pair. In the tunable charge-detector study, a nanometer-scale gap in the barrier gate increased the conductance step height from $G(V_\mathrm{g})$9 to $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$0; a floating gate increased it further to $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$1, although charge rearrangements and noise limited stability. The steepest response was obtained by tuning the QPC confinement into a localized state, yielding Coulomb blockade resonances and $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$2 in one sample (Rössler et al., 2012).

Capacitively coupled QPCs have also been used for local spin detection. In the spin-orbit-interaction experiment, a side-coupled quantum dot sampled single electrons from a target QPC with very slow rate, so that the disturbance to the object was very small. The spin polarization

$$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$3

was extracted by comparing the $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$4 and $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$5 tunneling processes of the detector dot. A high degree of spin polarization was detected when the QPC conductance stayed on a plateau at $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$6, and also on another plateau at $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$7; on the half-quantum plateau, $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$8 decreased with source-drain bias, whereas on the single-quantum plateau $$\Delta G_\text{QPC} \propto \frac{\partial G_\text{QPC}}{\partial V_g}\cdot C_m \cdot \Delta Q_\text{QD},$$9 increased with bias (Kim et al., 2016).

In bilayer graphene, the same electrostatic logic has been pushed to radio-frequency readout. The device used a capacitively coupled QPC arranged nearly in-line with neighboring electron and hole dots, while a depletion gate between them was used to deplete charge carrier density in the intermediate region and reduce screening. Time-resolved detection of charge states and magnetic-field-dependent tunneling rates was demonstrated, with $C_m$0 reported for the tunneling rate in the measured regime (Hecker et al., 15 Sep 2025).

3. Backaction, nonequilibrium transport, and fluctuation relations

In double-quantum-dot (DQD) circuits, a capacitively coupled QPC is not only a detector. It is also a nonequilibrium environment whose shot noise and voltage fluctuations modify DQD tunneling rates. This backaction is central to the full counting statistics and fluctuation-theorem analyses of DQD-QPC systems (Golubev et al., 2011, Cuetara et al., 2013).

For the coupled DQD-QPC electrometer, the total Hamiltonian in one formulation is

$C_m$1

with the QPC tunneling Hamiltonian

$C_m$2

so that the QPC transmission depends on the DQD charge state. The joint probability $C_m$3 of charges transferred through the DQD and the QPC is encoded by

$C_m$4

and the coupled process obeys the joint fluctuation theorem

$C_m$5

A central result is that the fluctuation theorem holds for the full DQD+QPC process; if QPC backaction is ignored, the DQD alone can appear to violate it (Golubev et al., 2011).

A complementary treatment derived effective fluctuation theorems for the DQD current alone, with an effective affinity $C_m$6 replacing the bare voltage bias: $C_m$7 This effective affinity reduces to the bare DQD affinity only when the QPC is at equilibrium, and it may even change sign if Coulomb drag of the QPC reverses the DQD current. The same analysis emphasized that QPC-induced transitions $C_m$8 act as a Bose-like nonequilibrium bath for the DQD (Cuetara et al., 2013).

Backaction can also generate directed transport. In the weak-tunneling QPC model coupled to a DQD, an electron on dot 1 increases the QPC barrier and reduces its conductivity,

$C_m$9

The biased QPC then provides a noise spectrum

$\Delta Q_\text{QD}$0

which can drive a ratchet current through the DQD even at zero DQD bias. At $\Delta Q_\text{QD}$1, the quoted expression is

$\Delta Q_\text{QD}$2

with current reversal as a function of DQD detuning $\Delta Q_\text{QD}$3 (Hussein et al., 2015).

The same Coulomb-coupled logic supports thermal functionality. In the three-terminal setup consisting of a single-level quantum dot capacitively coupled to a QPC, the QPC current is controlled by the temperature $\Delta Q_\text{QD}$4 of the base reservoir through the dot occupation probabilities

$\Delta Q_\text{QD}$5

The average QPC current is

$\Delta Q_\text{QD}$6

and the differential thermal sensitivity is

$\Delta Q_\text{QD}$7

The maximum occurs at $\Delta Q_\text{QD}$8, giving

$\Delta Q_\text{QD}$9

This device was analyzed both as a thermal transistor and as a minimally invasive thermometer (Yang et al., 2019).

These studies collectively show that “noninvasive” in the charge-sensing sense does not imply absence of dynamical influence. A capacitively coupled QPC can detect charge without particle exchange, yet its nonequilibrium fluctuations can still reshape transport, entropy production, and current statistics in the measured system.

4. Spatial gating, compensation, and mode-specific backscattering

A distinct usage of capacitively coupled QPC physics arises in scanning-gate microscopy, where the scanning tip is itself the capacitively coupled object. The key experimental difficulty is that the long-range gating effect of the tip often dominates over the local backscattering that one seeks to image. The grid-measurement method addressed this by measuring the full conductance trace $C_{\rm QD-Det}$0 at each tip position $C_{\rm QD-Det}$1, thereby constructing a three-dimensional dataset $C_{\rm QD-Det}$2 (Kozikov et al., 2015).

The compensation protocol identifies, at each tip position, the center of plateau $C_{\rm QD-Det}$3 as the minimum in $C_{\rm QD-Det}$4, determines the corresponding plateau voltage $C_{\rm QD-Det}$5, and extracts

$C_{\rm QD-Det}$6

To separate the influence on sequential plateaus, the work introduced

$C_{\rm QD-Det}$7

This procedure removed the spatially varying gating background and exposed localized quantum backscattering. After compensation, interference fringes and branching patterns reemerged, the mode structure of QPC plateaus was spatially resolved, and lobe patterns corresponding to up to five QPC modes became visible close to the QPC. The same dataset revealed regions of distorted plateaus, interpreted in the paper as non-adiabatic features or resonance-like structures, and these regions coincided with fringe spacings that deviated from the expected $C_{\rm QD-Det}$8 value (Kozikov et al., 2015).

The broader significance is methodological. In this context capacitive coupling is not a signal to be maximized but a background to be measured locally and removed. The paper therefore established that interference and plateau distortion can coexist, and that faithful mode-resolved imaging requires treating the capacitive shift as a position-dependent quantity rather than as a single global offset.

5. High-frequency, dispersive, and noise-transfer regimes

Capacitively coupled QPCs also operate in regimes where the relevant observable is not dc conductance but noise temperature, reflected RF phase, or the reactive part of the admittance. In coupled-QPC experiments, one QPC can generate high-frequency shot noise while another, electrically isolated at low frequency, detects it bolometrically through the coupling capacitance (0806.4805).

In the double-QPC shot-noise experiment, the two QPCs were capacitively coupled via center gate electrodes with a designed mutual capacitance $C_{\rm QD-Det}$9 fF and were each connected to resonant tank circuits at 3 MHz for noise thermometry. QPC1 was biased to generate shot noise; QPC2 was unbiased and fixed at the center of its first quantized conductance plateau. The measured excess noise temperature in QPC2 was found to be perfectly proportional to the excess noise temperature expected in QPC1 from shot-noise theory,

$$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$0

with an experimental efficiency factor $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$1. The same work reported an unexpected suppression of noise in the source QPC, interpreted as a possible cooling effect by the detector QPC (0806.4805).

A related but conceptually distinct development is dispersive gate sensing of the QPC’s own quantum capacitance. In that approach, a single gate electrode is wire-bonded to a superconducting inductor, so that the resonator phase shift tracks the local density of states via the quantum capacitance of the open QPC. The one-dimensional zero-temperature expression quoted for the quantum capacitance is

$$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$2

and the resonator shift obeys

$$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$3

This method resolved the Van Hove singularities of a one-dimensional ballistic system and detected localized states or charge traps even when transport was suppressed (Jarratt et al., 2019).

Radio-frequency charge sensing extends the same principles to fast time-domain readout. In bilayer graphene electron-hole double quantum dots, the capacitively coupled QPC was embedded in an $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$4 tank circuit with $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$5 and $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$6, resonant at $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$7. The reported $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$8 reached values up to 160 for optimal power and frequency, remained above unity for bandwidths up to at least 10 MHz, and stayed above 2.5 up to 250 kHz in time-resolved experiments (Hecker et al., 15 Sep 2025).

A related high-frequency circuit study, although based on galvanic rather than capacitive coupling to the microwave environment, clarified why such regimes matter for capacitively coupled operation as well. It emphasized that a QPC is characterized by a complex impedance consisting of quantized resistance, capacitance, and inductance elements, and reported operation at $$\Delta V_{\rm Det} = (C_{\rm QD-Det}/C_{\rm tot})\Delta Q.$$9 GHz with a conductance sensitivity of $C_{\rm QD-Det}$0 micro-e/$C_{\rm QD-Det}$1 and a bandwidth of $C_{\rm QD-Det}$2 MHz (Shanmugam et al., 2023). This supports a broader interpretation in which capacitively coupled QPC devices must be analyzed as full frequency-dependent admittance elements, not merely as static resistive detectors.

6. Electromechanical, thermal, and conceptual extensions

Capacitive coupling to a QPC is not limited to nearby electronic nanostructures. M. Poggio et al. used a QPC as a displacement transducer for a nearby micromechanical cantilever, where the conducting cantilever tip acted as a localized “third gate” above the QPC. The effective potential at the QPC was written as

$C_{\rm QD-Det}$3

leading to conductance modulation with displacement. In optimal configurations the conductance response reached $C_{\rm QD-Det}$4, the displacement sensitivity was below $C_{\rm QD-Det}$5, and active feedback cooling reduced the effective mode temperature to $C_{\rm QD-Det}$6 K (Montinaro et al., 2012).

These electromechanical results sharpen a general point: the performance ceiling is set jointly by the QPC’s intrinsic electronic noise and the strength of the capacitive coupling. The same statement recurs in charge sensing, RF reflectometry, and thermometry, even though the measured observable may be a conductance step, an RF phase shift, or a noise temperature rather than a displacement spectrum.

A more conceptual extension appears in the study of free-fermion subsystems connected through one or more QPCs. There, the entanglement entropy of a subsystem connected by a small number of QPCs was found to be sub-extensive. In the ground state, a single QPC gave $C_{\rm QD-Det}$7; at finite energy and for low $C_{\rm QD-Det}$8 and small $C_{\rm QD-Det}$9, the numerics showed

$\Delta G_{\rm Det}$0

and the increase per additional QPC was suggested to follow

$\Delta G_{\rm Det}$1

The same work contrasted this with classical ergodic and quantum chaotic systems, where equilibrium entropy and heat capacity are expected to be extensive, and noted that extensivity could in principle be recovered if the two systems were capacitively rather than via particle exchange coupled (Levine et al., 6 Jan 2025).

Taken together, these results place the capacitively coupled QPC at the intersection of mesoscopic transport, quantum measurement, and nonequilibrium thermodynamics. It can operate as a charge sensor, spin detector, shot-noise bolometer, displacement transducer, thermal transistor, thermometer, or local probe of quantum capacitance. The unifying constraint is equally clear: the same Coulomb interaction that provides sensitivity also determines screening, backaction, bandwidth, and the ultimate interpretation of the measured signal.