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The electron number-parity of the ground state of a semiconductor narowireproximity-coupled to a bulk superconductor can alternate between the quantisedvalues $\pm 1$ if parameters such as the wire length $L$, the chemicalpotential $\mu$ or the magnetic field $B$ are varied inside the topologicalsuperconductor phase. % The parity jumps, which may be interpreted as changesin the occupancy of the fermion state formed from the pair of Majorana modes atopposite ends of the wire, are accompanied by jumps $\delta N$ in the charge ofthe nanowire, whose values decrease exponentially with the wire length. % Westudy theoretically the dependence of $\delta N$ on system parameters, andcompare the locations in the $\mu$-$B$ plane of parity jumps when the nanowireis or is not proximity-coupled to a bulk superconductor. % We show that,despite the fact that the wave functions of the Majorana modes are localisednear the two ends of the wire, the charge-density jumps have spatialdistributions that are essentially uniform along the wire length, beingproportional to the product of the two Majorana wave functions. % We explainhow charge measurements, say by an external single-electron transistor, couldreveal these effects. % Whereas existing experimental methods require directcontact to the wire for tunneling measurements, charge sensing avoids thisissue and provides an orthogonal measurement to confirm recent experimentaldevelopments. % Furthermore, by comparing density of states measurements whichshow Majorana features at the wire ends with the uniformly-distributed chargemeasurements, one can rule out alternative explanations for earlier results. %We shed light on a new parameter regime for these wire-superconductor hybridsystems, and propose a related experiment to measure spin density.

Detecting Majoranas in 1D wires by charge sensing