We study theoretically the Meissner effect in non-Hermitian systems of BCS type, i.e., with an electronelectron interaction leading to the mean-field description in a Cooper channel, via superfluid stiffness. We show that depending on the values of the mean fields, chemical potential, and temperature, we obtain a paramagnetic or diamagnetic Meissner effect. Notably, the positive real part of the product of the mean fields guarantees a diamagnetic Meissner effect in an s-wave three-dimensional (3D) non-Hermitian superconductor. Once the mean fields are close to being anti-Hermitian, 2D s-, px-, and d-wave superconductors exhibit interesting behavior, including negative superfluid stiffness giving the paramagnetic Meissner effect for certain parameters. Negative superfluid stiffness indicates instability of this collective state.

We study theoretically a setup consisting of excitons formed in two valleys, with proximity-induced Cooper pairing, different in the conduction and valence bands. Due to the combination of a Coulomb interaction with superconducting proximity effects, Cooper pairing between electrons from conduction and valence bands from different valleys is formed. This finite-energy intervalley Cooper pairing has both even- and odd-frequency contributions. We show that there is a phase transition into the formation of a robust macroscopic condensate of such Cooper pairs and present characteristics of the corresponding Higgs modes.

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.

We study theoretically a junction consisting of a normal metal, PT-symmetric non-Hermitian superconductor, and an insulating thin layer between them. 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 with 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 the 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 the right-right basis are equilibrated.

We show theoretically that the measurement of a PT-symmetric non-Hermitian superconductor by angleresolved photoelectron fluctuation spectroscopy (ARPFS) provides a particular signature. In fact, the signal is negative in a single-band case in contrast to the ARPFS signal of Hermitian superconductors. We suggest that the negative fluctuations can be explained by a remarkable pairing phenomenon: If the interaction between electrons in this PT-symmetric non-Hermitian superconductor is attractive, then the interaction between holes (i.e., missing electrons) is repulsive and vice versa. This difference in the sign of the interactions gives rise to negative cross correlations. Here, we propose how such an electron-electron interaction can occur due to the spatiotemporal modulation of the material. We also discuss the observability of this signature in multiband systems.

Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.

We study theoretically a junction of a PT -symmetric non-Hermitian superconductor (PTS) placed between two conventional superconductors. We show that due to non-Hermitian electron-electron interaction in the PTS region and the combination of symmetries, only discrete values of phases of the conventional superconductors yield solutions for Andreev bound states. Remarkably, in the case of 0 and π , we obtain growing and decaying in time Andreev bound states. For π/ 2 and 3 π/ 2 , there is a Majorana zero mode penetrating through the junction in only one direction forming a quasiparticle supercurrent.

Unconventional superconductivity is usually associated with symmetry breaking in the system.Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries.We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur.We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.

We propose a scheme to perform braiding and all other unitary operations with Majorana modes in one dimension that, in contrast to previous proposals, is solely based on resonant manipulation involving the first excited state extended over the modes. The detection of the population of the excited state also enables initialization and read-out. We provide an elaborated illustration of the scheme with a concrete device.

We propose a measurement scheme to directly detect odd-frequency superconductivity via time- and angle-resolved photoelectron fluctuation spectroscopy. The scheme includes two consecutive, non-overlapping probe pulses applied to a superconducting sample. The photoemitted electrons are collected in a momentum-resolved fashion. Correlations between signals with opposite momenta are analyzed. Remarkably, these correlations are directly proportional to the absolute square of the time-ordered anomalous Green's function of the superconductor. This setup allows for the direct detection of the "hidden order parameter" of odd-frequency pairing. We illustrate this general scheme by analyzing the signal for the prototypical case of a two-band superconductor.

The recent proposals of devices with overlapping Andreev bound states (ABS) open up the opportunities to control and fine-tune their spectrum, that can be used in various applications. In this Article, we study the ABS in a device consisting of a semiconducting nanowire covered with three superconducting leads. The ABS are formed at two junctions where the wire is not covered. They overlap in the wire where the electron propagation is 1D, and in one of the leads where the propagation is 3D. We identify a number of regimes where these two overlaps either dominate or compete, depending on the junction separation $L$ as compared to the correlation lengths $\xi_{\rm w}$, $\xi_{\rm s}$ in the wire and in the lead, respectively. We utilize a simple model of 1D electron spectrum in the nanowire and take into account the quality of the contact between the nanowire and the superconducting lead. We present the spectra for different $L$, detailing the transition from a single-ABS in the regime of strong 1D hybridization to two almost independent ABS hybridized at the degeneracy points, in the regime of weak 1D hybridization. We present the details of merging the upper ABS with the continuous spectrum upon decreasing $L$. We study in detail the effect of quantum interference due to the phase accumulated during the electron passage between the junctions. We develop a perturbation theory for analytical treatment of hybridization. We address an interesting separate case of fully transparent junctions. We derive and exemplify a perturbation theory suitable for the competition regime demonstrating the interference of 1D and two 3D transmission amplitudes.

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.

The recent proposals of devices with overlapping Andreev bound states (ABS) open up the opportunities to control and fine-tune their spectrum, that can be used in various applications. In this Article, we study the ABS in a device consisting of a semiconducting nanowire covered with three superconducting leads. The ABS are formed at two junctions where the wire is not covered. They overlap in the wire where the electron propagation is 1D, and in one of the leads where the propagation is 3D. We identify a number of regimes where these two overlaps either dominate or compete, depending on the junction separation $L$ as compared to the correlation lengths $\xi_{\rm w}$, $\xi_{\rm s}$ in the wire and in the lead, respectively. We utilize a simple model of 1D electron spectrum in the nanowire and take into account the quality of the contact between the nanowire and the superconducting lead. We present the spectra for different $L$, detailing the transition from a single-ABS in the regime of strong 1D hybridization to two almost independent ABS hybridized at the degeneracy points, in the regime of weak 1D hybridization. We present the details of merging the upper ABS with the continuous spectrum upon decreasing $L$. We study in detail the effect of quantum interference due to the phase accumulated during the electron passage between the junctions. We develop a perturbation theory for analytical treatment of hybridization. We address an interesting separate case of fully transparent junctions. We derive and exemplify a perturbation theory suitable for the competition regime demonstrating the interference of 1D and two 3D transmission amplitudes.

The recent proposals of experiments with single Andreev bound states make relevant a detailed analysis of these states in multiterminal superconducting nanostructures. We evaluate the energy splitting of degenerate Andreev bound states that overlap in a superconducting lead, and find that the splitting is reduced in comparison with their energy by a small factor root RG(Q), with RG(Q) being the dimensionless resistance of the overlap region in the normal state. This permits quantum manipulation of the quasiparticles in these states. We provide a simple scheme of such manipulation.

We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.

Many quantum dot qubits operate in regimes where the energy splittings between qubit states are large and phonons can be the dominant source of decoherence. The recently proposed charge quadrupole qubit, based on one electron in a triple quantum dot, employs a highly symmetric charge distribution to suppress the influence of long-wavelength charge noise. To study the effects of phonons on the charge quadrupole qubit, we consider Larmor and Ramsey pulse sequences to identify favorable operating parameters. We show that phonon-induced decoherence increases with the qubit frequency, in contrast to the effects of charge noise. We also show that there is an optimum value of the tunnel coupling of the qubit at which the decohering effects of phonons and charge noise are small enough to be consistent with single qubit gate fidelities > 99.99%.

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 the 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 the spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian anymore 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 a Wigner crystal in this limit.

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 nonequilibrium, 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.