On-Chip Microwave Quantum Hall Circulator

6 MB·

by  A. C. Mahoney

On-Chip Microwave Quantum Hall Circulator
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1 A. C. Mahoney,1,2∗ J. I. Colless,1,2∗ S. J. Pauka,1,2 J. M. Hornibrook1,2,
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2 J. D. Watson3,4, G. C. Gardner4,5, M. J. Manfra3,4,5, A. C. Doherty1, and D. J. Reilly1,2†

n
a
J
1ARCCentreofExcellenceforEngineeredQuantumSystems,
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SchoolofPhysics,TheUniversityofSydney,Sydney,NewSouthWales2006,Australia.

]
ll 2 MicrosoftStationQSydney,TheUniversityofSydney,Sydney,NewSouthWales2006,Australia.
a
h 3DepartmentofPhysicsandAstronomy,PurdueUniversity,WestLafayette,Indiana47907,USA.
-
s 4BirckNanotechnologyCenter,SchoolofMaterialsEngineeringandSchoolofElectrical
e
m
andComputerEngineering,PurdueUniversity,WestLafayette,Indiana47907,USA.
.
t 5MicrosoftStationQPurdue,PurdueUniversity,WestLafayette,Indiana47907,USA.
a
m
-
d ∗Theseauthorscontributedequallytothiswork.
n
o †Towhomcorrespondenceshouldbeaddressed;E-mail: [email protected]
c
[

1
Circulatorsarenon-reciprocalcircuitelementsintegraltotechnologiesinclud-
v
4
ing radar systems, microwave communication transceivers, and the readout
3
6
of quantum information devices. Their non-reciprocity arises from the in-
0
0
terference of microwaves over the centimetre-scale of the signal wavelength
.
1
0 in the presence of bulky magnetic media that break time-reversal symmetry.
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1 Here we realize a completely passive on-chip microwave circulator with size
:
v
1/1000th the wavelength by exploiting the chiral, ‘slow-light’ response of a
i
X
2-dimensional electron gas (2DEG) in the quantum Hall regime. For an in-
r
a
tegrated GaAs device with 330 µm diameter and ∼ 1 GHz centre frequency,
a non-reciprocity of 25 dB is observed over a 50 MHz bandwidth. Further-
more, the direction of circulation can be selected dynamically by varying the
magnetic field, an aspect that may enable reconfigurable passive routing of
microwavesignalson-chip.
1
Miniaturized, non-reciprocal devices are currently of broad interest for enabling new appli-
cations in acoustics [1], photonics [2, 3], transceiver technology [4], and in the regime of near
quantum-limitedmeasurement[5,6,7,8,9],wheretheyareneededtoisolatequbitsfromtheir
noisy readout circuits. Since the 1950s, passive circuit elements exhibiting non-reciprocity at
microwave frequencies have been implemented using bulky magnetic devices that are compa-
rable in scale to the centimetre wavelength of signals in their operating band. The footprint of
thesecomponentsposesamajorlimitationtointegratingentiresystemsonachip,suchaswhat
isrequired,forinstance,toscale-upquantumcomputingtechnology.
A seemingly obvious means of realizing non-reciprocity on a semiconductor chip is to use
theHalleffect,whereanexternalmagneticfieldbreaksthetimereversalsymmetryofelectrical
transport [10]. Hall-based devices were ruled out in 1954 however [11], since near the elec-
trical contacts, where the current and voltage are collinear, dissipation is so significant that the
usefulness of this approach is greatly limited. This dissipative mechanism has an analog in the
quantumHallregimewherethetwo-terminalresistanceofadeviceisalwaysfiniteoverascale
of the inelastic scattering length as carriers transition from their contacts to the dissipationless,
one-dimensional (1D) edge-states that support transport [12]. Recently, Viola and DiVincenzo
[9]haveproposedameansofaddressingthelimitationimposedby2-terminaldissipation,sug-
gesting the possibility of coupling microwave signals to the edge of a quantum Hall device
reactively, without using traditional ohmic contacts. In a geometry where the signal ports of
thedevicearepositionedorthogonaltoanincompressiblequantumHalledge-state,microwave
power is coupled capacitively and non-dissipative transport in one-direction appears possible
[9].
Here we engineer, on-chip, a chiral microwave interferometer that yields a high degree of
non-reciprocity and dynamic range, with the low-dissipation inherent to edge transport in the
quantum Hall regime. Configured as a completely passive 3-port circulator, our device demon-
stratesnon-reciprocaloperationatfrequenciesandmagneticfieldscommonlyusedfortheread
outofspinqubits[13,14,15],facilitatingintegrationwithsuchsemiconductortechnologies. In
comparison to traditional ferrite-based microwave components, this quantum Hall circulator is
reduced insize by afactor ∼1/1000th thewavelength and exhibitsa new modeof operation in
which the direction of circulation can be dynamically reconfigured by altering the strength of
2
the magnetic field. A simple model based on a Fano-resonance mechanism [16] qualitatively
accountsfortheobservedphenomena.
Central to the operation of our device are edge magnetoplasmons (EMPs) [17] that prop-
agate along a quantum Hall edge in response to a capacitively coupled microwave excitation
(cid:126) (cid:126)
[18, 19, 20, 21]. These chiral excitations travel with a velocity v ∼ |E|/|B|, set by the
EMP
(cid:126) (cid:126)
ratio of the electric field E at the sample boundary and the applied magnetic field B [18]. For
a high mobility 2DEG formed at the interface of the semiconductors GaAs and AlGaAs (see
supplementary materials for details), the velocity of the EMP modes is typically v ∼105
EMP
ms−1 [22, 23], some 1000 times slower than the speed of light in the semiconductor dielectric.
InordertoexploittheseEMPstorealizenon-reciprocalmicrowavedevices,wefirstdetecttheir
presence in a contactless etched disk of quantum Hall fluid by coupling to a proximal metallic
coplanartransmissionline(CTL)[24],asshowninFig. 1Aand1B.Bymeasuringthetransmit-
ted microwave power through the transmission line as a function of frequency f, a spectrum of
discrete features is observed with applied magnetic field B (Fig. 1C). We identify EMP modes
in the data with frequencies set by the edge velocity and circumference of the disk, following
the dependence f ∼ B−1(log(B2) + const.) [17], consistent with the dielectric constant of
GaAs [19, 25] (see supplementary materials). Comparing the microwave spectrum to transport
measurementsfromaHall-baronthesamechip(Fig. 1D),wenotethatathighfield(withonly
the last few Landau levels occupied) features resolve into discrete, crescent-shaped resonances
thatcoincidewithminimainthelongitudinalresistanceR ,wheredissipationissuppressed.
xx
3
A C
f S21 Absorption ΔS21 (dB)
T = 293 K
B (T)
0 0.1 1 2
T = 4 K
Atten.
G = + 40 dB
T = 20 mK ε* ≈ 8.7 6 (Gf
6 H
2 z)
50 Ω
CTL z)
H
G
f (
500 μm ν = 4
ν = 3
2 ν = 2
B + + + + B D
+
+ ω
- 0 10
ω - +- - -- - + R (KΩ)XY 1XX (KΩ)R
- - 2ω0
+ + - 0 0
1 2
E t B (T)
Disk of 2DEG
Figure 1: Detecting microwave edge magnetoplasmons (EMPs). (A) Experimental setup
including photograph of a coplanar transmission line device similar to that used to perform
measurements coupled to a 350 µm etched disc of 2DEG (black dashed circle) at fridge tem-
perature T = 20 mK. A vector network analyser is used to excite EMP modes across a wide
frequency range and microwave absorption is measured as the ratio of the amplified output to
input signal (S ) from the CTL. (B) Illustration of the fundamental (top row) and first har-
21
monic (bottom row) EMP modes as they evolve with time, where ω is the fundamental mode
0
(cid:126)
and 2ω the first harmonic (adapted from [17]). Charge distributions and electric fields E are
0
indicated schematically. An external magnetic field B applied to the device points out of the
page. (C) EMP spectrum of the quantum Hall disk showing absorbed microwave power as a
function of frequency and magnetic field. Data has had a background, obtained at high field,
subtracted. Inset shows the position of absorption dips at integer quantum Hall filling factors.
Black line is a fit that allows an average dielectric constant of (cid:15)∗ ≈ 8.7 to be extracted, con-
sistent with excitations of an edge-state in GaAs (see supplementary material). (D) Transverse
4
(R ) and longitudinal (R ) Hall resistance measurements taken at T = 20 mK on a Hall bar
xy xx
proximaltothemicrowavedisk. The2DEGis270nmbelowthesurfacewithcarrierdensityn
s
=1.1x1011 cm−2,andmobilityµ=5.2x106 cm2/Vs.
Totestiftheseedgemagnetoplasmonssupportthenon-reciprocaltransmissionofmicrowaves,
weimplementastandardcirculatorconfiguration,with3portsarrangedat120-degreeintervals
around a disk of 2DEG (330 µm diameter), as shown in Fig. 2A and 2B. For a single edge
at high magnetic field, a voltage applied to a port capacitance induces an orthogonal current
in the edge-state, with an impedance of the order of the inverse conductance quantum (∼ 26
kΩ). Givenourmeasurementsetupuseselectroniccomponentswithacharacteristicimpedance
of Z ∼ 50 Ω, we have added an impedance matching circuit to enhance the response of each
0
port (our matching network is a series chip-inductor L = 47 nH in resonance with the stray
capacitance C , see supplementary materials). The circulator is further embedded in a re-
stray
flectometryconfiguration(seeFig2C)thatenablesameasurementoftheportreflectionaswell
as port transmission coefficient, from which dissipation can be estimated. As a control we first
measure all microwave S-parameters at zero magnetic field, observing that all directions and
ports are equivalent, as shown in Fig. 2D. An overall frequency-dependent, but reciprocal re-
sponsecanbeassociatedwiththeimpedancematchingnetwork,withmatchingfrequencysetto
(cid:113)
1/ LC ∼ 1 GHz. All subsequent measurements are normalized relative to this zero-field
stray
transmissionresponse.
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A C
1 mm 3
T = 4 K T = 20 mK
c
2 stray L = 47 nH
cpl = -16 dB c
edge c
p
2΄ 1
G = +40 dB
B 3 D
S
-20 B = 0 T S13
31
S
B) 2΄1
d S
S ( S12
32
2 1 -60 S2΄3
0.6 1.0 1.4
330 μm
f (GHz)
Disk of 2DEG
Figure 2: Experimental setup for determining the response of the on-chip circulator. (A)
Photographofcirculatordeviceshowingthethreecoplanartransmissionlinesconnectedtocop-
per chip-inductors (47 nH) for impedance matching. (B) Close-up of false-coloured photo of
the circulator showing 330 µm diameter 2DEG disc with a 20 µm gap to the metal defining
the three signal ports. (C) Circuit schematic of the experimental setup indicating port-to-edge
capacitive coupling C and direct parasitic coupling between ports C . Resonant (LC )
edge p stray
matching circuits are indicated with blue boxes. The input of port 2 passes through a direc-
tional coupler, with the reflected signal coupled to the output line (denoted 2(cid:48)) and amplified.
(D) Shows the full 6-way transmission response of the circulator at zero magnetic field, with
S-parametermeasurementsindicatingcompletereciprocityandafrequencyresponsethatarises
from the matching networks. For each port the measured response of the amplifiers, couplers
andcoldattenuatorsinthecircuithavebeensubtracted.
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Turning to our key result, Figure 3 shows the full transmission response of the 3-port cir-
culator in the presence of a magnetic field that breaks time-reversal symmetry. Similar to the
EMP spectrum of Fig. 1C, we first observe the presence of EMPs that enhance the transmitted
power at certain frequencies, broadly following an approximate f ∼ B−1 dispersion relation,
as is seen in Fig. 3A (S ) and 3B (S ). Strikingly, there are regions of the spectrum where
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the transmitted power appears to flow in either a forward or reverse direction with respect to
thechiralityoftheedge. Particularlyapparentarethecrescent-shapedfeaturesthatswitchfrom
forward to reverse transmission at distinct frequencies. This phenomenon, with a peak near the
fundamental frequency ofthe EMP mode and a dip near the first EMP harmonic, isseen for all
S-parametersinthechiral(clockwise)directionofthe3-portdevice(seesolidlinesinFig. 3D).
To measure the extent of non-reciprocity in our circulator, Figure 3C shows the difference be-
tween forward and reverse power by subtracting S from S . Unlike the B = 0 data shown in
31 13
Fig. 2D, we now observe a strong directional dependence in the isolation between ports, that
approach 40 dB at particular frequencies and magnetic fields (Fig. 3F). Alternatively, we can
also test for non-reciprocity by comparing the response of signals from two different inputs of
the circulator to a common output. Since the device is geometrically symmetric, the response
from the separate paths S and S are the same at B = 0, (see Fig. 2D). In the presence of
2(cid:48)1 2(cid:48)3
a magnetic field however, Fig. 3G shows that these paths are no longer equivalent, but depend
ratheronthedirectionofthefield. Thisisclearinthedata(Fig. 3G),sinceblueandredfeatures
arenotmirroredaboutB =0.
7
A D 40
S B = 3.7 T S
13 40 13
2 S
31
S S
1 0 13 (dB) S (dB) 0 SS213΄221
S
-40 2΄3
-40
B E 40
S B = 2.1 T
31 40
2
GHz) 0 31 (dS (dB) 0
f (1 B) S
-40
-40
C F 40
S - S
13 31
40
2
)
Δ B
0 S (d S (d 0
1 B Δ
)
-40
-40
0 1 2 3 4 0.6 1.0 1.4
B (T) f (GHz) B = 3.7 T
B = 2.1 T
G
S - S
2’1 2’3
40
2
) Δ
Hz ν = 2 S
G 0 (d
f ( B)
1
ν = 1
-40
-4 -2 0 2 4
B (T)
Figure 3: The non-reciprocal response of the quantum Hall circulator. (A and B) Port
transmission S and S with frequency and magnetic field. All measurements have been nor-
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malized to the gain-corrected background at B = 0 (shown in Fig. 2D), which defines the 0 dB
colourscale. (C)DifferentialmicrowaveresponseS −S showingstrong,frequencyandB-
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dependentnon-reciprocity. (DandE)ShowthefullcombinationoftransmissionS-parameters,
taken at B-fields indicated by the symbols in C. (F) shows slices through the colour scale data
in C demonstrating forward and reverse circulation. (G) Isolation, S -S measured at posi-
2(cid:48)1 2(cid:48)3
tive and negative magnetic fields. Note the anti-symmetry of the features with respect to the B
=0axis.
ComparingthemicrowaveresponseofthecirculatortoindependentquantumHalltransport
data suggests two distinct regimes. Between integer filling factors, where R is maximised in
xx
transport,thereisalargenon-reciprocityinthemicrowaveresponse,butalsolikelystrongdissi-
pation. Contrasting these broadregions are narrowcrescent-shaped features that occurat fields
corresponding to integer filling. These narrow features are particularly strong at frequencies
near twice the fundamental EMP resonance. Again, overlaying these features with transport
measurements on the Hall bar indicates they align with minima in R , where dissipation is
xx
suppressed. Microwave loss measurements, taken by summing the transmitted and reflected
signalincomparisontotheincidentpower,areconsistentwithalevelofdissipationsetbyR
xx
asmeasuredintransport.
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A B
S31 3 B EMP 1
φ = π
C
edge Out φ C In
In Out edge
C
p C
p
C D 2
20 B = 3.7 T B = 3.3 T
20
0
0
S13 - S31
-20
-20 S13
B) Data B) Data S31
d d
( 20 (
S S 20
0
0
S13 - S31
-20
-20 S13
Model Model
S31
0.4 0.8 1.2 0.4 0.8 1.2
f (GHz) f (GHz)
f (GHz)
E G 0.9 1.1
B T = 20 mK T = 4 K 6 B = 1.78 T 1 FF
T
(
a
2 0 .u
0 .)
1
-6
3 0.9 1.1
F H 6 B = 3.7 T 1
2 0
)
V 0
m
1 V (
-6 Port 2
3
Port 3
0 20 40
T (ns)
10