Current-voltage characteristics of the N-I-PT-symmetric non-Hermitian superconductor junction as a probe of non-Hermitian formalisms

We study theoretically a junction consisting of a normal metal, PT-symmetric non-Hermitian superconductor, and an insulating thin layer between them (N-I-PTS junction). We calculate current-voltage characteristics for this junction using left-right and right-right bases and compare the results. We find that in the left-right basis, the Andreev-scattered particles move in the opposite direction compared to the right-right basis and conventional Andreev scattering. This leads to profound differences in current-voltage characteristics. Based on this and other signatures, we argue that left-right basis is not applicable in this case. Remarkably, we find that the growth and decay with time of the states with imaginary energies in right-right basis are equilibrated

Ordered spin states and quantum coherence in low-dimensional structures : quantum dots and nanowires

Since the development of microsized devices is moving forward at enormous speed, there is huge amount of new industrial opportunities. However such devices also require high precision and understanding of the operating of their constituent parts up to the quantum level. The device of the purely quantum nature being developed so far is quantum computer. However the physical realization of it is still not performed, as the requirements for it are very rigorous. In the pioneering work by Loss and DiVincenzo it was suggested to use a spin of electron placed in a quantum dot as an information qubit. Following this work the study of electron or hole spin qubits developed. Both experimental and theoretical tools for studying them greatly advanced. In the first part of the thesis we study the phonon-induced decoherence and relaxation of singlet-triplet qubits in the double quantum dots. First of all we consider AlGaAs/GaAs double quantum dots. The important result we present here is the strong dephasing that occurs at large detuning. This dephasing is due to two-phonon process that affects mainly singlet state of the qubit and consequently changes the splitting between singlet and triplet leading to dephasing. Remarkably at small detuning this dephasing process is suppressed and the decoherence time is by orders of magnitude longer than in case of large detuning and is mainly defined by one-phonon process. We also present the dependence of relaxation time and decoherence time on the strength of spin-orbit interaction and different directions of the system. Our results provide a deeper insight into the recently obtained experimental data. We also studied Si/SiGe quantum dots as a potential candidate for a qubit. Apart from the absence of hyperfine interaction and bulk spin-orbit interaction in the isotopically purified $^{28}$Si, its electron-phonon interaction is different from GaAs that also leads to longer qubit lifetimes. We study $S$-$T_-$ qubit near the anticrossing of the basis states. This particular region is interesting due to possibilities in operating the qubit. We show that the type of singlet plays a crucial role, i.e. whether it is a singlet with each dot singly occupied or a singlet with only one dot doubly occupied. Depending on the type of singlet the qubit lifetimes change by several orders of magnitude. We also study the influence of a micromagnet, usually used in experiments to operate the qubit, on the relaxation time and decoherence time and present the regime where its effect is negligible. We suggest how to test experimentally our theory of one-phonon and two-phonon processes separately. We also show how the relaxation and decoherence time depend on different system parameters for $S$-$T_0$ qubits. The second part of the thesis is devoted to the other important constituent part of microsized devices, namely nanowires. We are interested in the dynamic of polarization of localized spins in the nanowires, as it can affect such important device characteristics as e.g. conductance. We studied Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction-induced polarization in the nanowire in case when the voltage is applied to it. It was already proposed theoretically that in the ground state the localized spins in 1D systems align in a helix due to RKKY interaction. This polarization is still present until some critical temperature. The presence of such polarization acts as a spin filter for electrons, that most likely affects the conductance of the nanowire. Therefore we studied how this helical polarization changes when the voltage is applied. The key result is the appearance of the uniform polarization perpendicular to the helix plane, that occurs due to backscattering of electrons that is accompanied by flip-flop process with localized spins. When this uniform polarization is formed, the helix starts to rotate as a whole around the direction of the uniform polarization. We present the dependence of polarization of the localized spins on temperature and voltage. Remarkably the uniform polarization grows both with voltage and temperature in the given range of parameters. We also considered the electron-induced relaxation of the nuclear spins. As the electron spins and nuclear spins interact via hyperfine interaction, the nuclear relaxation time reflects some properties of electron bath. Namely, we see a strong dependence of nuclear relaxation time on spin-orbit interaction strength. We present here the dependence of the nuclear relaxation time on the external magnetic field and chemical potential of the wire, that can be experimentally varied via gate. The dependences for the strong spin-orbit interaction and for the weak one are substantially different. Moreover, they have distinct peaks, that allow to get the value of spin-orbit interaction amplitude with the high precision

Voltage induced conversion of helical to uniform nuclear spin polarization in a quantum wire

We study the effect of bias voltage on the nuclear spin polarization of a ballistic wire, which contains electrons and nuclei interacting via hyperfine interaction. In equilibrium, the localized nuclear spins are helically polarized due to the electron-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Focusing here on non-equilibrium, we find that an applied bias voltage induces a uniform polarization, from both helically polarized and unpolarized spins available for spin flips. Once a macroscopic uniform polarization in the nuclei is established, the nuclear spin helix rotates with frequency proportional to the uniform polarization. The uniform nuclear spin polarization monotonically increases as a function of both voltage and temperature, reflecting a thermal activation behavior. Our predictions offer specific ways to test experimentally the presence of a nuclear spin helix polarization in semiconducting quantum wires.Comment: 8 pages, 4 figure

Equal contribution of even and odd frequency pairing to transport across normal metal-superconductor junctions

Odd-frequency pairing is an unconventional type of Cooper pairing in superconductors related to the frequency dependence of the corresponding anomalous Green function. We show by a combination of analytical and numerical methods that odd-frequency pairing is ubiquitously present in the current of Andreev-scattered particles across a junction formed by a normal metal (N) and a superconductor (S), even if the superconducting pairing is of conventional $s$-wave, spin singlet type. We carefully analyze the conductance of NS junctions with different pairing symmetries ($s$-wave, $p$-wave, $d$-wave). In all cases, we identify a generic equal balance of even and odd frequency pairing to the contributions related to Andreev reflection. This analysis shows in retrospect that the presence of odd-frequency pairing in electric currents across NS junctions is rather the rule, not the exception. This insight stems from an alternative approach of analyzing the transport problem of hybrid structures. It is based on the Kubo-Greenwood formula with direct access to symmetries of the anomalous Green functions characterizing the superconducting pairing. We expect that our predictions substantially enrich the interpretation of transport data across NS junctions in many material combinations.Comment: 31 pages, 22 figure

Peningkatan Keterampilan Menulis Aksara Jawa melalui Penggunaan Model Pembelajaran Kooperatif Tipe Teams Games Tournament dan Media Ular Tangga

Dini Noviana Saputri. K4214008. Peningkatan Keterampilan Menulis Aksara Jawa Melalui Penggunaan Model Pembelajaran Kooperatif Tipe Teams Games Tournament Dengan Media Ular Tangga Pada Siswa Kelas VII F SMP Negeri 8 Surakarta. Skripsi. Surakarta: Fakultas Keguruan dan Ilmu Pendidikan, Universitas Sebelas Maret Surakarta, Oktober 2018. Bagi siswa yang mempelajari bahasa Jawa sebagai bahasa kedua atau ketiga, membaca dan menulis huruf Jawa merupakan materi yang dianggap sulit. Oleh karena itu, siswa tidak suka dan tidak tertarik mempelajarinya. Tujuan penelitian ini adalah untuk meningkatkan motivasi dan kemampuan menulis huruf Jawa dengan metode kooperatif Teams Games Tournament dan meda permainan Ular Tangga pada siswa kelas VII F SMP Negeri 8 Surakarta tahun ajaran 2017/2018, penelitian ini merupakan penelitian tindakan kelas dengan dua siklus. Setiap siklus terdiri atas kegiatan perencanaan, pelaksanaan, pengamatan dan refleksi. Subjek dari penelitian ini adalah siswa kelas VII F yang berjumlah 32 orang siswa dengan 14 siswa laki-laki dan 18 siswa perempuan. Teknik pengumpulan data yang digunakan adalah observasi, wawancara, analisis dokumen dan tes. Pengujian validitas data menggunakan teknik triangulasi sumber dan triangulasi metode. Kemudian, teknik analisis data yang digunakan adalah analisis deskriptif komparatif dan analisis kritis. Analisis data menunjukkan adanya peningkatan baik dalam segi motivasi belajar maupun segi kualitas hasil belajar. Motivasi belajar siswa saat pratindakan hanya sebesar 49,80%, kemudian meningkat pada siklus I menjadi 60,9%, dan meningkat lagi menjadi 80,66% pada siklus II. Sedangkan, pada segi kualitas hasil belajar siswa juga diketahui hanya sebesar 37,5%, kemudian mengalami peningkatan pada siklus I sebesar 59,4%, dan meningkat lagi pada siklus II menjadi 78,1%. Hasil penelitian ini menunjukkan bahwa melalui permainan Ular Tangga yang dilaksanakan bersama teman memungkinkan siswa lebih termotivasi untuk menguasai penulisan Aksara Jawa. Selain itu, dengan diberlakukannya kompetisi antar kelompok dapat menciptakan suasana belajar yang lebih menyenangkan dan menantang. Simpulan dari penelitian ini adalah penerapan metode TGT dan media Ular Tangga dapat meningkatkan motivasi belajar dan kualitas hasil belajar menulis aksara Jawa pada siswa kelas VII F SMP Negeri 8 Surakarta

Spin-orbit coupling in quasi-one-dimensional Wigner crystals

We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit

Majorana bound states in nanowire-superconductor hybrid systems in periodic magnetic fields

We study how the shape of a periodic magnetic field affects the presence of Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by the field configurations that can be produced by an array of nanomagnets, we consider spiral fields with an elliptic cross-section and fields with two sinusoidal components. We show that MBS are robust to imperfect helical magnetic fields. In particular, if the amplitude of one component is tuned to the value determined by the superconducting order parameter in the wire, the MBS can exist even if the second component has a much smaller amplitude. We also explore the effect of the chemical potential on the phase diagram. Our analysis is both numerical and analytical, with good agreement between the two methods