此篇論文在研究三粒子(trion (X^-))在二維具有能隙的石墨烯量子點的束縛能。此三粒子是由兩個電子和一個電洞所組成的。我們的研究選用含變分參數的試驗波函數(trial wave functions)做變分法(variational method)，並且討論改變一些變數對系統的影響，例如量子點的半徑、位障的高度。在能帶結構上，我們考慮兩種量子束縛的型態稱為第一型(type I)和第二型(type II)。計算結果得到，用高斯函數在第一型半徑為300 Å和位障高為0.375 Eg(Eg=能隙)的量子點的束縛能為-23.82 meV。在此條件下，由指數函數計算所得的束縛能為-21.38 meV。另外用高斯函數在第二型半徑為300 Å和位障高為0.5 Eg的量子點得到的束縛能為-7.02 meV，在此條件下，由指數函數所得的束縛能為-8.02 meV。當固定位障高度時，束縛能會隨著量子點半徑變大而變小，最後會趨近一個極限值。這個研究可應用在石墨烯和光子的量子網路中，在光子的量子位元(photon qubit)和有能隙石墨烯中兩個能谷量子位元(two-valley qubit)之間的量子態轉換。

The ground state binding energy of a trion (X^-) is studied here. The trion is composed of two electrons and a hole, and is confined in a two-dimensional quantum dot in gapped graphene. We perform the study within the variational method using special trial wave functions with variational parameters, and discuss the effect of various variables, such as the quantum dot radius and the potential barrier height. Two types of quantum confinement are considered, namely, type I and type II. The estimated binding energy is -23.82 meV(with a Gaussian trial wave function) and -21.38 meV (with an exponential trial wave function), respectively, for a type I quantum dot with radius = 300 Å and barrier height = 0.375 Eg (Eg = band gap). For a type II quantum dot with radius = 300 Å and barrier height = 0.5 Eg, the estimated binding energy is -7.02 meV (with Gaussian function) and -8.02 meV (with exponential function), respectively. For fixed barrier height, the binding energy decreases as the quantum dot radius increases, eventually down to a limiting value. The study is relevant to the quantum state transfer between a photon qubit and a two-valley qubit in gapped graphene for a “graphene + photon” quantum network.

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