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Register a new userConductance distributions of 1D-disordered wires at finite temperature and bias voltage
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We calculate the distribution of the conductance G in a one-dimensional disordered wire at finite temperature T and bias voltage V in a independent-electron picture and assuming full coherent transport. At high enough temperature and bias voltage, where several resonances of the system contribute to the conductance, the distribution P(G(T,V)) can be represented with good accuracy by autoconvolutions of the distribution of the conductance at zero temperature and zero bias voltage. The number of convolutions depends on T and V. In the regime of very low T and V, where only one resonance is relevant to G(T,V), the conductance distribution is analyzed by a resonant tunneling conductance model. Strong effects of finite T and V on the conductance distribution are observed and well described by our theoretical analysis, as we verify by performing a number of numerical simulations of a one-dimensional disordered wire at different temperatures, voltages, and lengths of the wire. Analytical estimates for the first moments of P(G(T,V)) at high temperature and bias voltage are also provided.
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Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length $L$ of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of $L$ from the Ohmic limit of short wires to the regime of a broad conductance distribution when $L$ exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary $L$. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.
We study numerically the charge conductance distributions of disordered quantum spin-Hall (QSH) systems using a quantum network model. We have found that the conductance distribution at the metal-QSH insulator transition is clearly different from that at the metal-ordinary insulator transition. Thus the critical conductance distribution is sensitive not only to the boundary condition but also to the presence of edge states in the adjacent insulating phase. We have also calculated the point-contact conductance. Even when the two-terminal conductance is approximately quantized, we find large fluctuations in the point-contact conductance. Furthermore, we have found a semi-circular relation between the average of the point-contact conductance and its fluctuation.
The zero-bias peak (ZBP) is understood as the definite signature of a Majorana bound state (MBS) when attached to a semi-infinite Kitaev nanowire (KNW) nearby zero temperature. However, such characteristics concerning the realization of the KNW constitute a profound experimental challenge. We explore theoretically a QD connected to a topological KNW of finite size at non-zero temperatures and show that overlapped MBSs of the wire edges can become effectively decoupled from each other and the characteristic ZBP can be fully recovered if one tunes the system into the leaked Majorana fermion fixed point. At very low temperatures, the MBSs become strongly coupled similarly to what happens in the Kondo effect. We derive universal features of the conductance as a function of the temperature and the relevant crossover temperatures. Our findings offer additional guides to identify signatures of MBSs in solid state setups.
We study the non-linear conductance $mathcal{G}simpartial^2I/partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductances functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $mathcal{G}sim0.006,E_mathrm{Th}^{-1}$ (and $langlemathcal{G}rangle=0$), where $E_mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $mathcal{G}_asim0.001,(gE_mathrm{Th})^{-1}$, where $ggg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_varphill L$, where $L_varphi$ is the phase coherence length, we get $mathcal{G}sim(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$, and $mathcal{G}_asim(L_varphi/L)^{11/2}(gE_mathrm{Th})^{-1}llmathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_Tll L_varphill L$ where $L_T=sqrt{D/T}$, we obtain $mathcal{G}sim(L_T/L)(L_varphi/L)^{7/2}E_mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $mathcal{G}_asim(L_T/L)^2(L_varphi/L)^{7/2}(gE_mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.
Motivated by a recent experimental report[1] claiming the likely observation of the Majorana mode in a semiconductor-superconductor hybrid structure[2,3,4,5], we study theoretically the dependence of the zero bias conductance peak associated with the zero-energy Majorana mode in the topological superconducting phase as a function of temperature, tunnel barrier potential, and a magnetic field tilted from the direction of the wire for realistic wires of finite lengths. We find that higher temperatures and tunnel barriers as well as a large magnetic field in the direction transverse to the wire length could very strongly suppress the zero-bias conductance peak as observed in Ref.[1]. We also show that a strong magnetic field along the wire could eventually lead to the splitting of the zero bias peak into a doublet with the doublet energy splitting oscillating as a function of increasing magnetic field. Our results based on the standard theory of topological superconductivity in a semiconductor hybrid structure in the presence of proximity-induced superconductivity, spin-orbit coupling, and Zeeman splitting show that the recently reported experimental data are generally consistent with the existing theory that led to the predictions for the existence of the Majorana modes in the semiconductor hybrid structures in spite of some apparent anomalies in the experimental observations at first sight. We also make several concrete new predictions for future observations regarding Majorana splitting in finite wires used in the experiments.
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